Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Exact expanded first-order arithmetic statement
forall ab ac db dc w r pb pc nb nc qb qc mb mc rb rc sb sc. (exists ics_coefficient_positive_span_add_first ics_coefficient_positive_scale_span_add_first ics_coefficient_negative_span_add_first ics_coefficient_negative_scale_span_add_first. (exists ics_raw_positive_span_add_first_image ics_raw_positive_scale_span_add_first_image ics_raw_negative_span_add_first_image ics_raw_negative_scale_span_add_first_image. (((exists ff_pp_mcp_smatrix_ics_span_add_first_image_raw ff_pps_mcp_smatrix_ics_span_add_first_image_raw ff_nn_mcp_smatrix_ics_span_add_first_image_raw ff_nns_mcp_smatrix_ics_span_add_first_image_raw ff_pn_mcp_smatrix_ics_span_add_first_image_raw ff_pns_mcp_smatrix_ics_span_add_first_image_raw ff_np_mcp_smatrix_ics_span_add_first_image_raw ff_nps_mcp_smatrix_ics_span_add_first_image_raw. ((forall ff_index_mcp_prefix_ics_span_add_first_image_raw_pp. (exists mcp_gap_ics_span_add_first_image_raw_pp_index. mcp_gap_ics_span_add_first_image_raw_pp_index + S (ff_index_mcp_prefix_ics_span_add_first_image_raw_pp) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_first_image_raw_pp ff_column_mcp_prefix_ics_span_add_first_image_raw_pp ff_value_mcp_prefix_ics_span_add_first_image_raw_pp. ((ff_index_mcp_prefix_ics_span_add_first_image_raw_pp) = (1) * ff_row_mcp_prefix_ics_span_add_first_image_raw_pp + ff_column_mcp_prefix_ics_span_add_first_image_raw_pp /\ ((exists mcp_gap_ics_span_add_first_image_raw_pp_column. mcp_gap_ics_span_add_first_image_raw_pp_column + S (ff_column_mcp_prefix_ics_span_add_first_image_raw_pp) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_first_image_raw_pp_cell ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell ff_right_mcp_cell_ics_span_add_first_image_raw_pp_cell ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell. ((forall ff_index_mcp_ics_span_add_first_image_raw_pp_cell_row ff_source_mcp_ics_span_add_first_image_raw_pp_cell_row ff_target_mcp_ics_span_add_first_image_raw_pp_cell_row. (exists mcp_gap_ics_span_add_first_image_raw_pp_cell_row_bound. mcp_gap_ics_span_add_first_image_raw_pp_cell_row_bound + S (ff_index_mcp_ics_span_add_first_image_raw_pp_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pp_cell_row_source. fs_h_mcp_ics_span_add_first_image_raw_pp_cell_row_source + S (ff_source_mcp_ics_span_add_first_image_raw_pp_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pp_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pp_cell_row_source. ab = fs_q_mcp_ics_span_add_first_image_raw_pp_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pp_cell_row)) * ac) + (ff_source_mcp_ics_span_add_first_image_raw_pp_cell_row))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pp_cell_row_target. fs_h_mcp_ics_span_add_first_image_raw_pp_cell_row_target + S (ff_target_mcp_ics_span_add_first_image_raw_pp_cell_row) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pp_cell_row_target. ff_left_mcp_cell_ics_span_add_first_image_raw_pp_cell = fs_q_mcp_ics_span_add_first_image_raw_pp_cell_row_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell) + (ff_target_mcp_ics_span_add_first_image_raw_pp_cell_row))) -> ff_target_mcp_ics_span_add_first_image_raw_pp_cell_row = ff_source_mcp_ics_span_add_first_image_raw_pp_cell_row) /\ ((forall ff_index_mcp_ics_span_add_first_image_raw_pp_cell_column ff_source_mcp_ics_span_add_first_image_raw_pp_cell_column ff_target_mcp_ics_span_add_first_image_raw_pp_cell_column. (exists mcp_gap_ics_span_add_first_image_raw_pp_cell_column_bound. mcp_gap_ics_span_add_first_image_raw_pp_cell_column_bound + S (ff_index_mcp_ics_span_add_first_image_raw_pp_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pp_cell_column_source. fs_h_mcp_ics_span_add_first_image_raw_pp_cell_column_source + S (ff_source_mcp_ics_span_add_first_image_raw_pp_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_pp) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pp_cell_column)) * ics_coefficient_positive_scale_span_add_first)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pp_cell_column_source. ics_coefficient_positive_span_add_first = fs_q_mcp_ics_span_add_first_image_raw_pp_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_pp) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pp_cell_column)) * ics_coefficient_positive_scale_span_add_first) + (ff_source_mcp_ics_span_add_first_image_raw_pp_cell_column))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pp_cell_column_target. fs_h_mcp_ics_span_add_first_image_raw_pp_cell_column_target + S (ff_target_mcp_ics_span_add_first_image_raw_pp_cell_column) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pp_cell_column_target. ff_right_mcp_cell_ics_span_add_first_image_raw_pp_cell = fs_q_mcp_ics_span_add_first_image_raw_pp_cell_column_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell) + (ff_target_mcp_ics_span_add_first_image_raw_pp_cell_column))) -> ff_target_mcp_ics_span_add_first_image_raw_pp_cell_column = ff_source_mcp_ics_span_add_first_image_raw_pp_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot ff_scale_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_first_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell) + (fpmp_left_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_first_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pp_cell) + (fpmp_right_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_pp) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_pp))) /\ forall ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum ff_r_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum ff_s_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot = ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot) + (ff_a_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum = ff_r_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum + ff_a_dot_mcp_ics_span_add_first_image_raw_pp_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_first_image_raw_pp_entry. fs_h_mcp_ics_span_add_first_image_raw_pp_entry + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_pp) = S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pp_entry. ff_pp_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_pp_entry * S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_add_first_image_raw) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_pp))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_first_image_raw_nn. (exists mcp_gap_ics_span_add_first_image_raw_nn_index. mcp_gap_ics_span_add_first_image_raw_nn_index + S (ff_index_mcp_prefix_ics_span_add_first_image_raw_nn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_first_image_raw_nn ff_column_mcp_prefix_ics_span_add_first_image_raw_nn ff_value_mcp_prefix_ics_span_add_first_image_raw_nn. ((ff_index_mcp_prefix_ics_span_add_first_image_raw_nn) = (1) * ff_row_mcp_prefix_ics_span_add_first_image_raw_nn + ff_column_mcp_prefix_ics_span_add_first_image_raw_nn /\ ((exists mcp_gap_ics_span_add_first_image_raw_nn_column. mcp_gap_ics_span_add_first_image_raw_nn_column + S (ff_column_mcp_prefix_ics_span_add_first_image_raw_nn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_first_image_raw_nn_cell ff_left_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell ff_right_mcp_cell_ics_span_add_first_image_raw_nn_cell ff_right_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell. ((forall ff_index_mcp_ics_span_add_first_image_raw_nn_cell_row ff_source_mcp_ics_span_add_first_image_raw_nn_cell_row ff_target_mcp_ics_span_add_first_image_raw_nn_cell_row. (exists mcp_gap_ics_span_add_first_image_raw_nn_cell_row_bound. mcp_gap_ics_span_add_first_image_raw_nn_cell_row_bound + S (ff_index_mcp_ics_span_add_first_image_raw_nn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_nn_cell_row_source. fs_h_mcp_ics_span_add_first_image_raw_nn_cell_row_source + S (ff_source_mcp_ics_span_add_first_image_raw_nn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_nn_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_nn_cell_row_source. db = fs_q_mcp_ics_span_add_first_image_raw_nn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_nn_cell_row)) * dc) + (ff_source_mcp_ics_span_add_first_image_raw_nn_cell_row))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_nn_cell_row_target. fs_h_mcp_ics_span_add_first_image_raw_nn_cell_row_target + S (ff_target_mcp_ics_span_add_first_image_raw_nn_cell_row) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_nn_cell_row_target. ff_left_mcp_cell_ics_span_add_first_image_raw_nn_cell = fs_q_mcp_ics_span_add_first_image_raw_nn_cell_row_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell) + (ff_target_mcp_ics_span_add_first_image_raw_nn_cell_row))) -> ff_target_mcp_ics_span_add_first_image_raw_nn_cell_row = ff_source_mcp_ics_span_add_first_image_raw_nn_cell_row) /\ ((forall ff_index_mcp_ics_span_add_first_image_raw_nn_cell_column ff_source_mcp_ics_span_add_first_image_raw_nn_cell_column ff_target_mcp_ics_span_add_first_image_raw_nn_cell_column. (exists mcp_gap_ics_span_add_first_image_raw_nn_cell_column_bound. mcp_gap_ics_span_add_first_image_raw_nn_cell_column_bound + S (ff_index_mcp_ics_span_add_first_image_raw_nn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_nn_cell_column_source. fs_h_mcp_ics_span_add_first_image_raw_nn_cell_column_source + S (ff_source_mcp_ics_span_add_first_image_raw_nn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_nn) + (1) * ff_index_mcp_ics_span_add_first_image_raw_nn_cell_column)) * ics_coefficient_negative_scale_span_add_first)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_nn_cell_column_source. ics_coefficient_negative_span_add_first = fs_q_mcp_ics_span_add_first_image_raw_nn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_nn) + (1) * ff_index_mcp_ics_span_add_first_image_raw_nn_cell_column)) * ics_coefficient_negative_scale_span_add_first) + (ff_source_mcp_ics_span_add_first_image_raw_nn_cell_column))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_nn_cell_column_target. fs_h_mcp_ics_span_add_first_image_raw_nn_cell_column_target + S (ff_target_mcp_ics_span_add_first_image_raw_nn_cell_column) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_nn_cell_column_target. ff_right_mcp_cell_ics_span_add_first_image_raw_nn_cell = fs_q_mcp_ics_span_add_first_image_raw_nn_cell_column_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell) + (ff_target_mcp_ics_span_add_first_image_raw_nn_cell_column))) -> ff_target_mcp_ics_span_add_first_image_raw_nn_cell_column = ff_source_mcp_ics_span_add_first_image_raw_nn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot ff_scale_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_first_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell) + (fpmp_left_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_first_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_nn_cell) + (fpmp_right_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_nn) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_nn))) /\ forall ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum ff_r_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum ff_s_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot = ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot) + (ff_a_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum = ff_r_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum + ff_a_dot_mcp_ics_span_add_first_image_raw_nn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_first_image_raw_nn_entry. fs_h_mcp_ics_span_add_first_image_raw_nn_entry + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_nn) = S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_nn_entry. ff_nn_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_nn_entry * S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_add_first_image_raw) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_nn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_first_image_raw_pn. (exists mcp_gap_ics_span_add_first_image_raw_pn_index. mcp_gap_ics_span_add_first_image_raw_pn_index + S (ff_index_mcp_prefix_ics_span_add_first_image_raw_pn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_first_image_raw_pn ff_column_mcp_prefix_ics_span_add_first_image_raw_pn ff_value_mcp_prefix_ics_span_add_first_image_raw_pn. ((ff_index_mcp_prefix_ics_span_add_first_image_raw_pn) = (1) * ff_row_mcp_prefix_ics_span_add_first_image_raw_pn + ff_column_mcp_prefix_ics_span_add_first_image_raw_pn /\ ((exists mcp_gap_ics_span_add_first_image_raw_pn_column. mcp_gap_ics_span_add_first_image_raw_pn_column + S (ff_column_mcp_prefix_ics_span_add_first_image_raw_pn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_first_image_raw_pn_cell ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell ff_right_mcp_cell_ics_span_add_first_image_raw_pn_cell ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell. ((forall ff_index_mcp_ics_span_add_first_image_raw_pn_cell_row ff_source_mcp_ics_span_add_first_image_raw_pn_cell_row ff_target_mcp_ics_span_add_first_image_raw_pn_cell_row. (exists mcp_gap_ics_span_add_first_image_raw_pn_cell_row_bound. mcp_gap_ics_span_add_first_image_raw_pn_cell_row_bound + S (ff_index_mcp_ics_span_add_first_image_raw_pn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pn_cell_row_source. fs_h_mcp_ics_span_add_first_image_raw_pn_cell_row_source + S (ff_source_mcp_ics_span_add_first_image_raw_pn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pn_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pn_cell_row_source. ab = fs_q_mcp_ics_span_add_first_image_raw_pn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pn_cell_row)) * ac) + (ff_source_mcp_ics_span_add_first_image_raw_pn_cell_row))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pn_cell_row_target. fs_h_mcp_ics_span_add_first_image_raw_pn_cell_row_target + S (ff_target_mcp_ics_span_add_first_image_raw_pn_cell_row) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pn_cell_row_target. ff_left_mcp_cell_ics_span_add_first_image_raw_pn_cell = fs_q_mcp_ics_span_add_first_image_raw_pn_cell_row_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell) + (ff_target_mcp_ics_span_add_first_image_raw_pn_cell_row))) -> ff_target_mcp_ics_span_add_first_image_raw_pn_cell_row = ff_source_mcp_ics_span_add_first_image_raw_pn_cell_row) /\ ((forall ff_index_mcp_ics_span_add_first_image_raw_pn_cell_column ff_source_mcp_ics_span_add_first_image_raw_pn_cell_column ff_target_mcp_ics_span_add_first_image_raw_pn_cell_column. (exists mcp_gap_ics_span_add_first_image_raw_pn_cell_column_bound. mcp_gap_ics_span_add_first_image_raw_pn_cell_column_bound + S (ff_index_mcp_ics_span_add_first_image_raw_pn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pn_cell_column_source. fs_h_mcp_ics_span_add_first_image_raw_pn_cell_column_source + S (ff_source_mcp_ics_span_add_first_image_raw_pn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_pn) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pn_cell_column)) * ics_coefficient_negative_scale_span_add_first)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pn_cell_column_source. ics_coefficient_negative_span_add_first = fs_q_mcp_ics_span_add_first_image_raw_pn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_pn) + (1) * ff_index_mcp_ics_span_add_first_image_raw_pn_cell_column)) * ics_coefficient_negative_scale_span_add_first) + (ff_source_mcp_ics_span_add_first_image_raw_pn_cell_column))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_pn_cell_column_target. fs_h_mcp_ics_span_add_first_image_raw_pn_cell_column_target + S (ff_target_mcp_ics_span_add_first_image_raw_pn_cell_column) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pn_cell_column_target. ff_right_mcp_cell_ics_span_add_first_image_raw_pn_cell = fs_q_mcp_ics_span_add_first_image_raw_pn_cell_column_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell) + (ff_target_mcp_ics_span_add_first_image_raw_pn_cell_column))) -> ff_target_mcp_ics_span_add_first_image_raw_pn_cell_column = ff_source_mcp_ics_span_add_first_image_raw_pn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot ff_scale_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_first_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell) + (fpmp_left_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_first_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_pn_cell) + (fpmp_right_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_pn) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_pn))) /\ forall ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum ff_r_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum ff_s_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot = ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot) + (ff_a_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum = ff_r_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum + ff_a_dot_mcp_ics_span_add_first_image_raw_pn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_first_image_raw_pn_entry. fs_h_mcp_ics_span_add_first_image_raw_pn_entry + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_pn) = S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_pn_entry. ff_pn_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_pn_entry * S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_add_first_image_raw) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_pn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_first_image_raw_np. (exists mcp_gap_ics_span_add_first_image_raw_np_index. mcp_gap_ics_span_add_first_image_raw_np_index + S (ff_index_mcp_prefix_ics_span_add_first_image_raw_np) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_first_image_raw_np ff_column_mcp_prefix_ics_span_add_first_image_raw_np ff_value_mcp_prefix_ics_span_add_first_image_raw_np. ((ff_index_mcp_prefix_ics_span_add_first_image_raw_np) = (1) * ff_row_mcp_prefix_ics_span_add_first_image_raw_np + ff_column_mcp_prefix_ics_span_add_first_image_raw_np /\ ((exists mcp_gap_ics_span_add_first_image_raw_np_column. mcp_gap_ics_span_add_first_image_raw_np_column + S (ff_column_mcp_prefix_ics_span_add_first_image_raw_np) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_first_image_raw_np_cell ff_left_scale_mcp_cell_ics_span_add_first_image_raw_np_cell ff_right_mcp_cell_ics_span_add_first_image_raw_np_cell ff_right_scale_mcp_cell_ics_span_add_first_image_raw_np_cell. ((forall ff_index_mcp_ics_span_add_first_image_raw_np_cell_row ff_source_mcp_ics_span_add_first_image_raw_np_cell_row ff_target_mcp_ics_span_add_first_image_raw_np_cell_row. (exists mcp_gap_ics_span_add_first_image_raw_np_cell_row_bound. mcp_gap_ics_span_add_first_image_raw_np_cell_row_bound + S (ff_index_mcp_ics_span_add_first_image_raw_np_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_np_cell_row_source. fs_h_mcp_ics_span_add_first_image_raw_np_cell_row_source + S (ff_source_mcp_ics_span_add_first_image_raw_np_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_np_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_np_cell_row_source. db = fs_q_mcp_ics_span_add_first_image_raw_np_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_first_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_add_first_image_raw_np_cell_row)) * dc) + (ff_source_mcp_ics_span_add_first_image_raw_np_cell_row))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_np_cell_row_target. fs_h_mcp_ics_span_add_first_image_raw_np_cell_row_target + S (ff_target_mcp_ics_span_add_first_image_raw_np_cell_row) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_np_cell_row_target. ff_left_mcp_cell_ics_span_add_first_image_raw_np_cell = fs_q_mcp_ics_span_add_first_image_raw_np_cell_row_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_np_cell) + (ff_target_mcp_ics_span_add_first_image_raw_np_cell_row))) -> ff_target_mcp_ics_span_add_first_image_raw_np_cell_row = ff_source_mcp_ics_span_add_first_image_raw_np_cell_row) /\ ((forall ff_index_mcp_ics_span_add_first_image_raw_np_cell_column ff_source_mcp_ics_span_add_first_image_raw_np_cell_column ff_target_mcp_ics_span_add_first_image_raw_np_cell_column. (exists mcp_gap_ics_span_add_first_image_raw_np_cell_column_bound. mcp_gap_ics_span_add_first_image_raw_np_cell_column_bound + S (ff_index_mcp_ics_span_add_first_image_raw_np_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_np_cell_column_source. fs_h_mcp_ics_span_add_first_image_raw_np_cell_column_source + S (ff_source_mcp_ics_span_add_first_image_raw_np_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_np) + (1) * ff_index_mcp_ics_span_add_first_image_raw_np_cell_column)) * ics_coefficient_positive_scale_span_add_first)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_np_cell_column_source. ics_coefficient_positive_span_add_first = fs_q_mcp_ics_span_add_first_image_raw_np_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_first_image_raw_np) + (1) * ff_index_mcp_ics_span_add_first_image_raw_np_cell_column)) * ics_coefficient_positive_scale_span_add_first) + (ff_source_mcp_ics_span_add_first_image_raw_np_cell_column))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_np_cell_column_target. fs_h_mcp_ics_span_add_first_image_raw_np_cell_column_target + S (ff_target_mcp_ics_span_add_first_image_raw_np_cell_column) = S ((S (ff_index_mcp_ics_span_add_first_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_np_cell_column_target. ff_right_mcp_cell_ics_span_add_first_image_raw_np_cell = fs_q_mcp_ics_span_add_first_image_raw_np_cell_column_target * S ((S (ff_index_mcp_ics_span_add_first_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_np_cell) + (ff_target_mcp_ics_span_add_first_image_raw_np_cell_column))) -> ff_target_mcp_ics_span_add_first_image_raw_np_cell_column = ff_source_mcp_ics_span_add_first_image_raw_np_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_first_image_raw_np_cell_dot ff_scale_dot_mcp_ics_span_add_first_image_raw_np_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_first_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_first_image_raw_np_cell) + (fpmp_left_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_first_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_first_image_raw_np_cell) + (fpmp_right_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_np_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_first_image_raw_np_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_np_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_np) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_np))) /\ forall ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum ff_r_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum ff_s_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_np_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_first_image_raw_np_cell_dot = ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_first_image_raw_np_cell_dot) + (ff_a_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum = ff_r_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum + ff_a_dot_mcp_ics_span_add_first_image_raw_np_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_first_image_raw_np_entry. fs_h_mcp_ics_span_add_first_image_raw_np_entry + S (ff_value_mcp_prefix_ics_span_add_first_image_raw_np) = S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_np_entry. ff_np_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_np_entry * S ((S (ff_index_mcp_prefix_ics_span_add_first_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_add_first_image_raw) + (ff_value_mcp_prefix_ics_span_add_first_image_raw_np))))))) /\ ((forall ff_index_mcp_add_ics_span_add_first_image_raw_positive ff_left_mcp_add_ics_span_add_first_image_raw_positive ff_right_mcp_add_ics_span_add_first_image_raw_positive ff_target_mcp_add_ics_span_add_first_image_raw_positive. (exists mcp_gap_ics_span_add_first_image_raw_positive_bound. mcp_gap_ics_span_add_first_image_raw_positive_bound + S (ff_index_mcp_add_ics_span_add_first_image_raw_positive) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_positive_left. fs_h_mcp_ics_span_add_first_image_raw_positive_left + S (ff_left_mcp_add_ics_span_add_first_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_positive_left. ff_pp_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_positive_left * S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_add_first_image_raw) + (ff_left_mcp_add_ics_span_add_first_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_positive_right. fs_h_mcp_ics_span_add_first_image_raw_positive_right + S (ff_right_mcp_add_ics_span_add_first_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_positive_right. ff_nn_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_positive_right * S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_add_first_image_raw) + (ff_right_mcp_add_ics_span_add_first_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_positive_target. fs_h_mcp_ics_span_add_first_image_raw_positive_target + S (ff_target_mcp_add_ics_span_add_first_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_positive)) * ics_raw_positive_scale_span_add_first_image)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_positive_target. ics_raw_positive_span_add_first_image = fs_q_mcp_ics_span_add_first_image_raw_positive_target * S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_positive)) * ics_raw_positive_scale_span_add_first_image) + (ff_target_mcp_add_ics_span_add_first_image_raw_positive))) -> ff_target_mcp_add_ics_span_add_first_image_raw_positive = ff_left_mcp_add_ics_span_add_first_image_raw_positive + ff_right_mcp_add_ics_span_add_first_image_raw_positive) /\ (forall ff_index_mcp_add_ics_span_add_first_image_raw_negative ff_left_mcp_add_ics_span_add_first_image_raw_negative ff_right_mcp_add_ics_span_add_first_image_raw_negative ff_target_mcp_add_ics_span_add_first_image_raw_negative. (exists mcp_gap_ics_span_add_first_image_raw_negative_bound. mcp_gap_ics_span_add_first_image_raw_negative_bound + S (ff_index_mcp_add_ics_span_add_first_image_raw_negative) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_negative_left. fs_h_mcp_ics_span_add_first_image_raw_negative_left + S (ff_left_mcp_add_ics_span_add_first_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_negative_left. ff_pn_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_negative_left * S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_add_first_image_raw) + (ff_left_mcp_add_ics_span_add_first_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_negative_right. fs_h_mcp_ics_span_add_first_image_raw_negative_right + S (ff_right_mcp_add_ics_span_add_first_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_add_first_image_raw)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_negative_right. ff_np_mcp_smatrix_ics_span_add_first_image_raw = fs_q_mcp_ics_span_add_first_image_raw_negative_right * S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_add_first_image_raw) + (ff_right_mcp_add_ics_span_add_first_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_add_first_image_raw_negative_target. fs_h_mcp_ics_span_add_first_image_raw_negative_target + S (ff_target_mcp_add_ics_span_add_first_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_negative)) * ics_raw_negative_scale_span_add_first_image)) /\ exists fs_q_mcp_ics_span_add_first_image_raw_negative_target. ics_raw_negative_span_add_first_image = fs_q_mcp_ics_span_add_first_image_raw_negative_target * S ((S (ff_index_mcp_add_ics_span_add_first_image_raw_negative)) * ics_raw_negative_scale_span_add_first_image) + (ff_target_mcp_add_ics_span_add_first_image_raw_negative))) -> ff_target_mcp_add_ics_span_add_first_image_raw_negative = ff_left_mcp_add_ics_span_add_first_image_raw_negative + ff_right_mcp_add_ics_span_add_first_image_raw_negative))))))) /\ (forall ics_index_span_add_first_image_equal ics_value0_span_add_first_image_equal ics_value1_span_add_first_image_equal ics_value2_span_add_first_image_equal ics_value3_span_add_first_image_equal. (exists ics_gap_span_add_first_image_equal_bound. ics_gap_span_add_first_image_equal_bound + S (ics_index_span_add_first_image_equal) = (r)) -> (((exists fs_h_ics_span_add_first_image_equal_at0. fs_h_ics_span_add_first_image_equal_at0 + S (ics_value0_span_add_first_image_equal) = S ((S (ics_index_span_add_first_image_equal)) * ics_raw_positive_scale_span_add_first_image)) /\ exists fs_q_ics_span_add_first_image_equal_at0. ics_raw_positive_span_add_first_image = fs_q_ics_span_add_first_image_equal_at0 * S ((S (ics_index_span_add_first_image_equal)) * ics_raw_positive_scale_span_add_first_image) + (ics_value0_span_add_first_image_equal))) -> (((exists fs_h_ics_span_add_first_image_equal_at1. fs_h_ics_span_add_first_image_equal_at1 + S (ics_value1_span_add_first_image_equal) = S ((S (ics_index_span_add_first_image_equal)) * ics_raw_negative_scale_span_add_first_image)) /\ exists fs_q_ics_span_add_first_image_equal_at1. ics_raw_negative_span_add_first_image = fs_q_ics_span_add_first_image_equal_at1 * S ((S (ics_index_span_add_first_image_equal)) * ics_raw_negative_scale_span_add_first_image) + (ics_value1_span_add_first_image_equal))) -> (((exists fs_h_ics_span_add_first_image_equal_at2. fs_h_ics_span_add_first_image_equal_at2 + S (ics_value2_span_add_first_image_equal) = S ((S (ics_index_span_add_first_image_equal)) * pc)) /\ exists fs_q_ics_span_add_first_image_equal_at2. pb = fs_q_ics_span_add_first_image_equal_at2 * S ((S (ics_index_span_add_first_image_equal)) * pc) + (ics_value2_span_add_first_image_equal))) -> (((exists fs_h_ics_span_add_first_image_equal_at3. fs_h_ics_span_add_first_image_equal_at3 + S (ics_value3_span_add_first_image_equal) = S ((S (ics_index_span_add_first_image_equal)) * nc)) /\ exists fs_q_ics_span_add_first_image_equal_at3. nb = fs_q_ics_span_add_first_image_equal_at3 * S ((S (ics_index_span_add_first_image_equal)) * nc) + (ics_value3_span_add_first_image_equal))) -> ics_value0_span_add_first_image_equal + ics_value3_span_add_first_image_equal = ics_value2_span_add_first_image_equal + ics_value1_span_add_first_image_equal))))) -> (exists ics_coefficient_positive_span_add_second ics_coefficient_positive_scale_span_add_second ics_coefficient_negative_span_add_second ics_coefficient_negative_scale_span_add_second. (exists ics_raw_positive_span_add_second_image ics_raw_positive_scale_span_add_second_image ics_raw_negative_span_add_second_image ics_raw_negative_scale_span_add_second_image. (((exists ff_pp_mcp_smatrix_ics_span_add_second_image_raw ff_pps_mcp_smatrix_ics_span_add_second_image_raw ff_nn_mcp_smatrix_ics_span_add_second_image_raw ff_nns_mcp_smatrix_ics_span_add_second_image_raw ff_pn_mcp_smatrix_ics_span_add_second_image_raw ff_pns_mcp_smatrix_ics_span_add_second_image_raw ff_np_mcp_smatrix_ics_span_add_second_image_raw ff_nps_mcp_smatrix_ics_span_add_second_image_raw. ((forall ff_index_mcp_prefix_ics_span_add_second_image_raw_pp. (exists mcp_gap_ics_span_add_second_image_raw_pp_index. mcp_gap_ics_span_add_second_image_raw_pp_index + S (ff_index_mcp_prefix_ics_span_add_second_image_raw_pp) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_second_image_raw_pp ff_column_mcp_prefix_ics_span_add_second_image_raw_pp ff_value_mcp_prefix_ics_span_add_second_image_raw_pp. ((ff_index_mcp_prefix_ics_span_add_second_image_raw_pp) = (1) * ff_row_mcp_prefix_ics_span_add_second_image_raw_pp + ff_column_mcp_prefix_ics_span_add_second_image_raw_pp /\ ((exists mcp_gap_ics_span_add_second_image_raw_pp_column. mcp_gap_ics_span_add_second_image_raw_pp_column + S (ff_column_mcp_prefix_ics_span_add_second_image_raw_pp) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_second_image_raw_pp_cell ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell ff_right_mcp_cell_ics_span_add_second_image_raw_pp_cell ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell. ((forall ff_index_mcp_ics_span_add_second_image_raw_pp_cell_row ff_source_mcp_ics_span_add_second_image_raw_pp_cell_row ff_target_mcp_ics_span_add_second_image_raw_pp_cell_row. (exists mcp_gap_ics_span_add_second_image_raw_pp_cell_row_bound. mcp_gap_ics_span_add_second_image_raw_pp_cell_row_bound + S (ff_index_mcp_ics_span_add_second_image_raw_pp_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pp_cell_row_source. fs_h_mcp_ics_span_add_second_image_raw_pp_cell_row_source + S (ff_source_mcp_ics_span_add_second_image_raw_pp_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pp_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pp_cell_row_source. ab = fs_q_mcp_ics_span_add_second_image_raw_pp_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pp_cell_row)) * ac) + (ff_source_mcp_ics_span_add_second_image_raw_pp_cell_row))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pp_cell_row_target. fs_h_mcp_ics_span_add_second_image_raw_pp_cell_row_target + S (ff_target_mcp_ics_span_add_second_image_raw_pp_cell_row) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pp_cell_row_target. ff_left_mcp_cell_ics_span_add_second_image_raw_pp_cell = fs_q_mcp_ics_span_add_second_image_raw_pp_cell_row_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell) + (ff_target_mcp_ics_span_add_second_image_raw_pp_cell_row))) -> ff_target_mcp_ics_span_add_second_image_raw_pp_cell_row = ff_source_mcp_ics_span_add_second_image_raw_pp_cell_row) /\ ((forall ff_index_mcp_ics_span_add_second_image_raw_pp_cell_column ff_source_mcp_ics_span_add_second_image_raw_pp_cell_column ff_target_mcp_ics_span_add_second_image_raw_pp_cell_column. (exists mcp_gap_ics_span_add_second_image_raw_pp_cell_column_bound. mcp_gap_ics_span_add_second_image_raw_pp_cell_column_bound + S (ff_index_mcp_ics_span_add_second_image_raw_pp_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pp_cell_column_source. fs_h_mcp_ics_span_add_second_image_raw_pp_cell_column_source + S (ff_source_mcp_ics_span_add_second_image_raw_pp_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_pp) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pp_cell_column)) * ics_coefficient_positive_scale_span_add_second)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pp_cell_column_source. ics_coefficient_positive_span_add_second = fs_q_mcp_ics_span_add_second_image_raw_pp_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_pp) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pp_cell_column)) * ics_coefficient_positive_scale_span_add_second) + (ff_source_mcp_ics_span_add_second_image_raw_pp_cell_column))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pp_cell_column_target. fs_h_mcp_ics_span_add_second_image_raw_pp_cell_column_target + S (ff_target_mcp_ics_span_add_second_image_raw_pp_cell_column) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pp_cell_column_target. ff_right_mcp_cell_ics_span_add_second_image_raw_pp_cell = fs_q_mcp_ics_span_add_second_image_raw_pp_cell_column_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell) + (ff_target_mcp_ics_span_add_second_image_raw_pp_cell_column))) -> ff_target_mcp_ics_span_add_second_image_raw_pp_cell_column = ff_source_mcp_ics_span_add_second_image_raw_pp_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot ff_scale_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_second_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell) + (fpmp_left_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_second_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pp_cell) + (fpmp_right_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_pp) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_pp))) /\ forall ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum ff_r_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum ff_s_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot = ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot) + (ff_a_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum = ff_r_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum + ff_a_dot_mcp_ics_span_add_second_image_raw_pp_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_second_image_raw_pp_entry. fs_h_mcp_ics_span_add_second_image_raw_pp_entry + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_pp) = S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pp_entry. ff_pp_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_pp_entry * S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_add_second_image_raw) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_pp))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_second_image_raw_nn. (exists mcp_gap_ics_span_add_second_image_raw_nn_index. mcp_gap_ics_span_add_second_image_raw_nn_index + S (ff_index_mcp_prefix_ics_span_add_second_image_raw_nn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_second_image_raw_nn ff_column_mcp_prefix_ics_span_add_second_image_raw_nn ff_value_mcp_prefix_ics_span_add_second_image_raw_nn. ((ff_index_mcp_prefix_ics_span_add_second_image_raw_nn) = (1) * ff_row_mcp_prefix_ics_span_add_second_image_raw_nn + ff_column_mcp_prefix_ics_span_add_second_image_raw_nn /\ ((exists mcp_gap_ics_span_add_second_image_raw_nn_column. mcp_gap_ics_span_add_second_image_raw_nn_column + S (ff_column_mcp_prefix_ics_span_add_second_image_raw_nn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_second_image_raw_nn_cell ff_left_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell ff_right_mcp_cell_ics_span_add_second_image_raw_nn_cell ff_right_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell. ((forall ff_index_mcp_ics_span_add_second_image_raw_nn_cell_row ff_source_mcp_ics_span_add_second_image_raw_nn_cell_row ff_target_mcp_ics_span_add_second_image_raw_nn_cell_row. (exists mcp_gap_ics_span_add_second_image_raw_nn_cell_row_bound. mcp_gap_ics_span_add_second_image_raw_nn_cell_row_bound + S (ff_index_mcp_ics_span_add_second_image_raw_nn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_nn_cell_row_source. fs_h_mcp_ics_span_add_second_image_raw_nn_cell_row_source + S (ff_source_mcp_ics_span_add_second_image_raw_nn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_nn_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_nn_cell_row_source. db = fs_q_mcp_ics_span_add_second_image_raw_nn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_nn_cell_row)) * dc) + (ff_source_mcp_ics_span_add_second_image_raw_nn_cell_row))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_nn_cell_row_target. fs_h_mcp_ics_span_add_second_image_raw_nn_cell_row_target + S (ff_target_mcp_ics_span_add_second_image_raw_nn_cell_row) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_nn_cell_row_target. ff_left_mcp_cell_ics_span_add_second_image_raw_nn_cell = fs_q_mcp_ics_span_add_second_image_raw_nn_cell_row_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell) + (ff_target_mcp_ics_span_add_second_image_raw_nn_cell_row))) -> ff_target_mcp_ics_span_add_second_image_raw_nn_cell_row = ff_source_mcp_ics_span_add_second_image_raw_nn_cell_row) /\ ((forall ff_index_mcp_ics_span_add_second_image_raw_nn_cell_column ff_source_mcp_ics_span_add_second_image_raw_nn_cell_column ff_target_mcp_ics_span_add_second_image_raw_nn_cell_column. (exists mcp_gap_ics_span_add_second_image_raw_nn_cell_column_bound. mcp_gap_ics_span_add_second_image_raw_nn_cell_column_bound + S (ff_index_mcp_ics_span_add_second_image_raw_nn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_nn_cell_column_source. fs_h_mcp_ics_span_add_second_image_raw_nn_cell_column_source + S (ff_source_mcp_ics_span_add_second_image_raw_nn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_nn) + (1) * ff_index_mcp_ics_span_add_second_image_raw_nn_cell_column)) * ics_coefficient_negative_scale_span_add_second)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_nn_cell_column_source. ics_coefficient_negative_span_add_second = fs_q_mcp_ics_span_add_second_image_raw_nn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_nn) + (1) * ff_index_mcp_ics_span_add_second_image_raw_nn_cell_column)) * ics_coefficient_negative_scale_span_add_second) + (ff_source_mcp_ics_span_add_second_image_raw_nn_cell_column))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_nn_cell_column_target. fs_h_mcp_ics_span_add_second_image_raw_nn_cell_column_target + S (ff_target_mcp_ics_span_add_second_image_raw_nn_cell_column) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_nn_cell_column_target. ff_right_mcp_cell_ics_span_add_second_image_raw_nn_cell = fs_q_mcp_ics_span_add_second_image_raw_nn_cell_column_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell) + (ff_target_mcp_ics_span_add_second_image_raw_nn_cell_column))) -> ff_target_mcp_ics_span_add_second_image_raw_nn_cell_column = ff_source_mcp_ics_span_add_second_image_raw_nn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot ff_scale_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_second_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell) + (fpmp_left_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_second_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_nn_cell) + (fpmp_right_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_nn) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_nn))) /\ forall ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum ff_r_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum ff_s_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot = ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot) + (ff_a_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum = ff_r_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum + ff_a_dot_mcp_ics_span_add_second_image_raw_nn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_second_image_raw_nn_entry. fs_h_mcp_ics_span_add_second_image_raw_nn_entry + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_nn) = S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_nn_entry. ff_nn_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_nn_entry * S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_add_second_image_raw) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_nn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_second_image_raw_pn. (exists mcp_gap_ics_span_add_second_image_raw_pn_index. mcp_gap_ics_span_add_second_image_raw_pn_index + S (ff_index_mcp_prefix_ics_span_add_second_image_raw_pn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_second_image_raw_pn ff_column_mcp_prefix_ics_span_add_second_image_raw_pn ff_value_mcp_prefix_ics_span_add_second_image_raw_pn. ((ff_index_mcp_prefix_ics_span_add_second_image_raw_pn) = (1) * ff_row_mcp_prefix_ics_span_add_second_image_raw_pn + ff_column_mcp_prefix_ics_span_add_second_image_raw_pn /\ ((exists mcp_gap_ics_span_add_second_image_raw_pn_column. mcp_gap_ics_span_add_second_image_raw_pn_column + S (ff_column_mcp_prefix_ics_span_add_second_image_raw_pn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_second_image_raw_pn_cell ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell ff_right_mcp_cell_ics_span_add_second_image_raw_pn_cell ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell. ((forall ff_index_mcp_ics_span_add_second_image_raw_pn_cell_row ff_source_mcp_ics_span_add_second_image_raw_pn_cell_row ff_target_mcp_ics_span_add_second_image_raw_pn_cell_row. (exists mcp_gap_ics_span_add_second_image_raw_pn_cell_row_bound. mcp_gap_ics_span_add_second_image_raw_pn_cell_row_bound + S (ff_index_mcp_ics_span_add_second_image_raw_pn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pn_cell_row_source. fs_h_mcp_ics_span_add_second_image_raw_pn_cell_row_source + S (ff_source_mcp_ics_span_add_second_image_raw_pn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pn_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pn_cell_row_source. ab = fs_q_mcp_ics_span_add_second_image_raw_pn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pn_cell_row)) * ac) + (ff_source_mcp_ics_span_add_second_image_raw_pn_cell_row))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pn_cell_row_target. fs_h_mcp_ics_span_add_second_image_raw_pn_cell_row_target + S (ff_target_mcp_ics_span_add_second_image_raw_pn_cell_row) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pn_cell_row_target. ff_left_mcp_cell_ics_span_add_second_image_raw_pn_cell = fs_q_mcp_ics_span_add_second_image_raw_pn_cell_row_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell) + (ff_target_mcp_ics_span_add_second_image_raw_pn_cell_row))) -> ff_target_mcp_ics_span_add_second_image_raw_pn_cell_row = ff_source_mcp_ics_span_add_second_image_raw_pn_cell_row) /\ ((forall ff_index_mcp_ics_span_add_second_image_raw_pn_cell_column ff_source_mcp_ics_span_add_second_image_raw_pn_cell_column ff_target_mcp_ics_span_add_second_image_raw_pn_cell_column. (exists mcp_gap_ics_span_add_second_image_raw_pn_cell_column_bound. mcp_gap_ics_span_add_second_image_raw_pn_cell_column_bound + S (ff_index_mcp_ics_span_add_second_image_raw_pn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pn_cell_column_source. fs_h_mcp_ics_span_add_second_image_raw_pn_cell_column_source + S (ff_source_mcp_ics_span_add_second_image_raw_pn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_pn) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pn_cell_column)) * ics_coefficient_negative_scale_span_add_second)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pn_cell_column_source. ics_coefficient_negative_span_add_second = fs_q_mcp_ics_span_add_second_image_raw_pn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_pn) + (1) * ff_index_mcp_ics_span_add_second_image_raw_pn_cell_column)) * ics_coefficient_negative_scale_span_add_second) + (ff_source_mcp_ics_span_add_second_image_raw_pn_cell_column))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_pn_cell_column_target. fs_h_mcp_ics_span_add_second_image_raw_pn_cell_column_target + S (ff_target_mcp_ics_span_add_second_image_raw_pn_cell_column) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pn_cell_column_target. ff_right_mcp_cell_ics_span_add_second_image_raw_pn_cell = fs_q_mcp_ics_span_add_second_image_raw_pn_cell_column_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell) + (ff_target_mcp_ics_span_add_second_image_raw_pn_cell_column))) -> ff_target_mcp_ics_span_add_second_image_raw_pn_cell_column = ff_source_mcp_ics_span_add_second_image_raw_pn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot ff_scale_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_second_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell) + (fpmp_left_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_second_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_pn_cell) + (fpmp_right_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_pn) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_pn))) /\ forall ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum ff_r_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum ff_s_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot = ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot) + (ff_a_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum = ff_r_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum + ff_a_dot_mcp_ics_span_add_second_image_raw_pn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_second_image_raw_pn_entry. fs_h_mcp_ics_span_add_second_image_raw_pn_entry + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_pn) = S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_pn_entry. ff_pn_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_pn_entry * S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_add_second_image_raw) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_pn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_second_image_raw_np. (exists mcp_gap_ics_span_add_second_image_raw_np_index. mcp_gap_ics_span_add_second_image_raw_np_index + S (ff_index_mcp_prefix_ics_span_add_second_image_raw_np) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_second_image_raw_np ff_column_mcp_prefix_ics_span_add_second_image_raw_np ff_value_mcp_prefix_ics_span_add_second_image_raw_np. ((ff_index_mcp_prefix_ics_span_add_second_image_raw_np) = (1) * ff_row_mcp_prefix_ics_span_add_second_image_raw_np + ff_column_mcp_prefix_ics_span_add_second_image_raw_np /\ ((exists mcp_gap_ics_span_add_second_image_raw_np_column. mcp_gap_ics_span_add_second_image_raw_np_column + S (ff_column_mcp_prefix_ics_span_add_second_image_raw_np) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_second_image_raw_np_cell ff_left_scale_mcp_cell_ics_span_add_second_image_raw_np_cell ff_right_mcp_cell_ics_span_add_second_image_raw_np_cell ff_right_scale_mcp_cell_ics_span_add_second_image_raw_np_cell. ((forall ff_index_mcp_ics_span_add_second_image_raw_np_cell_row ff_source_mcp_ics_span_add_second_image_raw_np_cell_row ff_target_mcp_ics_span_add_second_image_raw_np_cell_row. (exists mcp_gap_ics_span_add_second_image_raw_np_cell_row_bound. mcp_gap_ics_span_add_second_image_raw_np_cell_row_bound + S (ff_index_mcp_ics_span_add_second_image_raw_np_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_np_cell_row_source. fs_h_mcp_ics_span_add_second_image_raw_np_cell_row_source + S (ff_source_mcp_ics_span_add_second_image_raw_np_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_np_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_np_cell_row_source. db = fs_q_mcp_ics_span_add_second_image_raw_np_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_second_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_add_second_image_raw_np_cell_row)) * dc) + (ff_source_mcp_ics_span_add_second_image_raw_np_cell_row))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_np_cell_row_target. fs_h_mcp_ics_span_add_second_image_raw_np_cell_row_target + S (ff_target_mcp_ics_span_add_second_image_raw_np_cell_row) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_np_cell_row_target. ff_left_mcp_cell_ics_span_add_second_image_raw_np_cell = fs_q_mcp_ics_span_add_second_image_raw_np_cell_row_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_np_cell) + (ff_target_mcp_ics_span_add_second_image_raw_np_cell_row))) -> ff_target_mcp_ics_span_add_second_image_raw_np_cell_row = ff_source_mcp_ics_span_add_second_image_raw_np_cell_row) /\ ((forall ff_index_mcp_ics_span_add_second_image_raw_np_cell_column ff_source_mcp_ics_span_add_second_image_raw_np_cell_column ff_target_mcp_ics_span_add_second_image_raw_np_cell_column. (exists mcp_gap_ics_span_add_second_image_raw_np_cell_column_bound. mcp_gap_ics_span_add_second_image_raw_np_cell_column_bound + S (ff_index_mcp_ics_span_add_second_image_raw_np_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_np_cell_column_source. fs_h_mcp_ics_span_add_second_image_raw_np_cell_column_source + S (ff_source_mcp_ics_span_add_second_image_raw_np_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_np) + (1) * ff_index_mcp_ics_span_add_second_image_raw_np_cell_column)) * ics_coefficient_positive_scale_span_add_second)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_np_cell_column_source. ics_coefficient_positive_span_add_second = fs_q_mcp_ics_span_add_second_image_raw_np_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_second_image_raw_np) + (1) * ff_index_mcp_ics_span_add_second_image_raw_np_cell_column)) * ics_coefficient_positive_scale_span_add_second) + (ff_source_mcp_ics_span_add_second_image_raw_np_cell_column))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_np_cell_column_target. fs_h_mcp_ics_span_add_second_image_raw_np_cell_column_target + S (ff_target_mcp_ics_span_add_second_image_raw_np_cell_column) = S ((S (ff_index_mcp_ics_span_add_second_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_np_cell_column_target. ff_right_mcp_cell_ics_span_add_second_image_raw_np_cell = fs_q_mcp_ics_span_add_second_image_raw_np_cell_column_target * S ((S (ff_index_mcp_ics_span_add_second_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_np_cell) + (ff_target_mcp_ics_span_add_second_image_raw_np_cell_column))) -> ff_target_mcp_ics_span_add_second_image_raw_np_cell_column = ff_source_mcp_ics_span_add_second_image_raw_np_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_second_image_raw_np_cell_dot ff_scale_dot_mcp_ics_span_add_second_image_raw_np_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_second_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_second_image_raw_np_cell) + (fpmp_left_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_second_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_second_image_raw_np_cell) + (fpmp_right_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_np_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_second_image_raw_np_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_np_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_np) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_np))) /\ forall ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum ff_r_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum ff_s_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_np_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_second_image_raw_np_cell_dot = ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_second_image_raw_np_cell_dot) + (ff_a_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum = ff_r_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum + ff_a_dot_mcp_ics_span_add_second_image_raw_np_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_second_image_raw_np_entry. fs_h_mcp_ics_span_add_second_image_raw_np_entry + S (ff_value_mcp_prefix_ics_span_add_second_image_raw_np) = S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_np_entry. ff_np_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_np_entry * S ((S (ff_index_mcp_prefix_ics_span_add_second_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_add_second_image_raw) + (ff_value_mcp_prefix_ics_span_add_second_image_raw_np))))))) /\ ((forall ff_index_mcp_add_ics_span_add_second_image_raw_positive ff_left_mcp_add_ics_span_add_second_image_raw_positive ff_right_mcp_add_ics_span_add_second_image_raw_positive ff_target_mcp_add_ics_span_add_second_image_raw_positive. (exists mcp_gap_ics_span_add_second_image_raw_positive_bound. mcp_gap_ics_span_add_second_image_raw_positive_bound + S (ff_index_mcp_add_ics_span_add_second_image_raw_positive) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_positive_left. fs_h_mcp_ics_span_add_second_image_raw_positive_left + S (ff_left_mcp_add_ics_span_add_second_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_positive_left. ff_pp_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_positive_left * S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_add_second_image_raw) + (ff_left_mcp_add_ics_span_add_second_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_positive_right. fs_h_mcp_ics_span_add_second_image_raw_positive_right + S (ff_right_mcp_add_ics_span_add_second_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_positive_right. ff_nn_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_positive_right * S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_add_second_image_raw) + (ff_right_mcp_add_ics_span_add_second_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_positive_target. fs_h_mcp_ics_span_add_second_image_raw_positive_target + S (ff_target_mcp_add_ics_span_add_second_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_positive)) * ics_raw_positive_scale_span_add_second_image)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_positive_target. ics_raw_positive_span_add_second_image = fs_q_mcp_ics_span_add_second_image_raw_positive_target * S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_positive)) * ics_raw_positive_scale_span_add_second_image) + (ff_target_mcp_add_ics_span_add_second_image_raw_positive))) -> ff_target_mcp_add_ics_span_add_second_image_raw_positive = ff_left_mcp_add_ics_span_add_second_image_raw_positive + ff_right_mcp_add_ics_span_add_second_image_raw_positive) /\ (forall ff_index_mcp_add_ics_span_add_second_image_raw_negative ff_left_mcp_add_ics_span_add_second_image_raw_negative ff_right_mcp_add_ics_span_add_second_image_raw_negative ff_target_mcp_add_ics_span_add_second_image_raw_negative. (exists mcp_gap_ics_span_add_second_image_raw_negative_bound. mcp_gap_ics_span_add_second_image_raw_negative_bound + S (ff_index_mcp_add_ics_span_add_second_image_raw_negative) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_negative_left. fs_h_mcp_ics_span_add_second_image_raw_negative_left + S (ff_left_mcp_add_ics_span_add_second_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_negative_left. ff_pn_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_negative_left * S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_add_second_image_raw) + (ff_left_mcp_add_ics_span_add_second_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_negative_right. fs_h_mcp_ics_span_add_second_image_raw_negative_right + S (ff_right_mcp_add_ics_span_add_second_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_add_second_image_raw)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_negative_right. ff_np_mcp_smatrix_ics_span_add_second_image_raw = fs_q_mcp_ics_span_add_second_image_raw_negative_right * S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_add_second_image_raw) + (ff_right_mcp_add_ics_span_add_second_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_add_second_image_raw_negative_target. fs_h_mcp_ics_span_add_second_image_raw_negative_target + S (ff_target_mcp_add_ics_span_add_second_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_negative)) * ics_raw_negative_scale_span_add_second_image)) /\ exists fs_q_mcp_ics_span_add_second_image_raw_negative_target. ics_raw_negative_span_add_second_image = fs_q_mcp_ics_span_add_second_image_raw_negative_target * S ((S (ff_index_mcp_add_ics_span_add_second_image_raw_negative)) * ics_raw_negative_scale_span_add_second_image) + (ff_target_mcp_add_ics_span_add_second_image_raw_negative))) -> ff_target_mcp_add_ics_span_add_second_image_raw_negative = ff_left_mcp_add_ics_span_add_second_image_raw_negative + ff_right_mcp_add_ics_span_add_second_image_raw_negative))))))) /\ (forall ics_index_span_add_second_image_equal ics_value0_span_add_second_image_equal ics_value1_span_add_second_image_equal ics_value2_span_add_second_image_equal ics_value3_span_add_second_image_equal. (exists ics_gap_span_add_second_image_equal_bound. ics_gap_span_add_second_image_equal_bound + S (ics_index_span_add_second_image_equal) = (r)) -> (((exists fs_h_ics_span_add_second_image_equal_at0. fs_h_ics_span_add_second_image_equal_at0 + S (ics_value0_span_add_second_image_equal) = S ((S (ics_index_span_add_second_image_equal)) * ics_raw_positive_scale_span_add_second_image)) /\ exists fs_q_ics_span_add_second_image_equal_at0. ics_raw_positive_span_add_second_image = fs_q_ics_span_add_second_image_equal_at0 * S ((S (ics_index_span_add_second_image_equal)) * ics_raw_positive_scale_span_add_second_image) + (ics_value0_span_add_second_image_equal))) -> (((exists fs_h_ics_span_add_second_image_equal_at1. fs_h_ics_span_add_second_image_equal_at1 + S (ics_value1_span_add_second_image_equal) = S ((S (ics_index_span_add_second_image_equal)) * ics_raw_negative_scale_span_add_second_image)) /\ exists fs_q_ics_span_add_second_image_equal_at1. ics_raw_negative_span_add_second_image = fs_q_ics_span_add_second_image_equal_at1 * S ((S (ics_index_span_add_second_image_equal)) * ics_raw_negative_scale_span_add_second_image) + (ics_value1_span_add_second_image_equal))) -> (((exists fs_h_ics_span_add_second_image_equal_at2. fs_h_ics_span_add_second_image_equal_at2 + S (ics_value2_span_add_second_image_equal) = S ((S (ics_index_span_add_second_image_equal)) * qc)) /\ exists fs_q_ics_span_add_second_image_equal_at2. qb = fs_q_ics_span_add_second_image_equal_at2 * S ((S (ics_index_span_add_second_image_equal)) * qc) + (ics_value2_span_add_second_image_equal))) -> (((exists fs_h_ics_span_add_second_image_equal_at3. fs_h_ics_span_add_second_image_equal_at3 + S (ics_value3_span_add_second_image_equal) = S ((S (ics_index_span_add_second_image_equal)) * mc)) /\ exists fs_q_ics_span_add_second_image_equal_at3. mb = fs_q_ics_span_add_second_image_equal_at3 * S ((S (ics_index_span_add_second_image_equal)) * mc) + (ics_value3_span_add_second_image_equal))) -> ics_value0_span_add_second_image_equal + ics_value3_span_add_second_image_equal = ics_value2_span_add_second_image_equal + ics_value1_span_add_second_image_equal))))) -> (forall ics_index_span_add_sum ics_value0_span_add_sum ics_value1_span_add_sum ics_value2_span_add_sum ics_value3_span_add_sum ics_value4_span_add_sum ics_value5_span_add_sum. (exists ics_gap_span_add_sum_bound. ics_gap_span_add_sum_bound + S (ics_index_span_add_sum) = (r)) -> (((exists fs_h_ics_span_add_sum_at0. fs_h_ics_span_add_sum_at0 + S (ics_value0_span_add_sum) = S ((S (ics_index_span_add_sum)) * pc)) /\ exists fs_q_ics_span_add_sum_at0. pb = fs_q_ics_span_add_sum_at0 * S ((S (ics_index_span_add_sum)) * pc) + (ics_value0_span_add_sum))) -> (((exists fs_h_ics_span_add_sum_at1. fs_h_ics_span_add_sum_at1 + S (ics_value1_span_add_sum) = S ((S (ics_index_span_add_sum)) * nc)) /\ exists fs_q_ics_span_add_sum_at1. nb = fs_q_ics_span_add_sum_at1 * S ((S (ics_index_span_add_sum)) * nc) + (ics_value1_span_add_sum))) -> (((exists fs_h_ics_span_add_sum_at2. fs_h_ics_span_add_sum_at2 + S (ics_value2_span_add_sum) = S ((S (ics_index_span_add_sum)) * qc)) /\ exists fs_q_ics_span_add_sum_at2. qb = fs_q_ics_span_add_sum_at2 * S ((S (ics_index_span_add_sum)) * qc) + (ics_value2_span_add_sum))) -> (((exists fs_h_ics_span_add_sum_at3. fs_h_ics_span_add_sum_at3 + S (ics_value3_span_add_sum) = S ((S (ics_index_span_add_sum)) * mc)) /\ exists fs_q_ics_span_add_sum_at3. mb = fs_q_ics_span_add_sum_at3 * S ((S (ics_index_span_add_sum)) * mc) + (ics_value3_span_add_sum))) -> (((exists fs_h_ics_span_add_sum_at4. fs_h_ics_span_add_sum_at4 + S (ics_value4_span_add_sum) = S ((S (ics_index_span_add_sum)) * rc)) /\ exists fs_q_ics_span_add_sum_at4. rb = fs_q_ics_span_add_sum_at4 * S ((S (ics_index_span_add_sum)) * rc) + (ics_value4_span_add_sum))) -> (((exists fs_h_ics_span_add_sum_at5. fs_h_ics_span_add_sum_at5 + S (ics_value5_span_add_sum) = S ((S (ics_index_span_add_sum)) * sc)) /\ exists fs_q_ics_span_add_sum_at5. sb = fs_q_ics_span_add_sum_at5 * S ((S (ics_index_span_add_sum)) * sc) + (ics_value5_span_add_sum))) -> ics_value4_span_add_sum + (ics_value1_span_add_sum + ics_value3_span_add_sum) = (ics_value0_span_add_sum + ics_value2_span_add_sum) + ics_value5_span_add_sum) -> (exists ics_coefficient_positive_span_add_result ics_coefficient_positive_scale_span_add_result ics_coefficient_negative_span_add_result ics_coefficient_negative_scale_span_add_result. (exists ics_raw_positive_span_add_result_image ics_raw_positive_scale_span_add_result_image ics_raw_negative_span_add_result_image ics_raw_negative_scale_span_add_result_image. (((exists ff_pp_mcp_smatrix_ics_span_add_result_image_raw ff_pps_mcp_smatrix_ics_span_add_result_image_raw ff_nn_mcp_smatrix_ics_span_add_result_image_raw ff_nns_mcp_smatrix_ics_span_add_result_image_raw ff_pn_mcp_smatrix_ics_span_add_result_image_raw ff_pns_mcp_smatrix_ics_span_add_result_image_raw ff_np_mcp_smatrix_ics_span_add_result_image_raw ff_nps_mcp_smatrix_ics_span_add_result_image_raw. ((forall ff_index_mcp_prefix_ics_span_add_result_image_raw_pp. (exists mcp_gap_ics_span_add_result_image_raw_pp_index. mcp_gap_ics_span_add_result_image_raw_pp_index + S (ff_index_mcp_prefix_ics_span_add_result_image_raw_pp) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_result_image_raw_pp ff_column_mcp_prefix_ics_span_add_result_image_raw_pp ff_value_mcp_prefix_ics_span_add_result_image_raw_pp. ((ff_index_mcp_prefix_ics_span_add_result_image_raw_pp) = (1) * ff_row_mcp_prefix_ics_span_add_result_image_raw_pp + ff_column_mcp_prefix_ics_span_add_result_image_raw_pp /\ ((exists mcp_gap_ics_span_add_result_image_raw_pp_column. mcp_gap_ics_span_add_result_image_raw_pp_column + S (ff_column_mcp_prefix_ics_span_add_result_image_raw_pp) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_result_image_raw_pp_cell ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell ff_right_mcp_cell_ics_span_add_result_image_raw_pp_cell ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell. ((forall ff_index_mcp_ics_span_add_result_image_raw_pp_cell_row ff_source_mcp_ics_span_add_result_image_raw_pp_cell_row ff_target_mcp_ics_span_add_result_image_raw_pp_cell_row. (exists mcp_gap_ics_span_add_result_image_raw_pp_cell_row_bound. mcp_gap_ics_span_add_result_image_raw_pp_cell_row_bound + S (ff_index_mcp_ics_span_add_result_image_raw_pp_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pp_cell_row_source. fs_h_mcp_ics_span_add_result_image_raw_pp_cell_row_source + S (ff_source_mcp_ics_span_add_result_image_raw_pp_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pp_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pp_cell_row_source. ab = fs_q_mcp_ics_span_add_result_image_raw_pp_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pp_cell_row)) * ac) + (ff_source_mcp_ics_span_add_result_image_raw_pp_cell_row))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pp_cell_row_target. fs_h_mcp_ics_span_add_result_image_raw_pp_cell_row_target + S (ff_target_mcp_ics_span_add_result_image_raw_pp_cell_row) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pp_cell_row_target. ff_left_mcp_cell_ics_span_add_result_image_raw_pp_cell = fs_q_mcp_ics_span_add_result_image_raw_pp_cell_row_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell) + (ff_target_mcp_ics_span_add_result_image_raw_pp_cell_row))) -> ff_target_mcp_ics_span_add_result_image_raw_pp_cell_row = ff_source_mcp_ics_span_add_result_image_raw_pp_cell_row) /\ ((forall ff_index_mcp_ics_span_add_result_image_raw_pp_cell_column ff_source_mcp_ics_span_add_result_image_raw_pp_cell_column ff_target_mcp_ics_span_add_result_image_raw_pp_cell_column. (exists mcp_gap_ics_span_add_result_image_raw_pp_cell_column_bound. mcp_gap_ics_span_add_result_image_raw_pp_cell_column_bound + S (ff_index_mcp_ics_span_add_result_image_raw_pp_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pp_cell_column_source. fs_h_mcp_ics_span_add_result_image_raw_pp_cell_column_source + S (ff_source_mcp_ics_span_add_result_image_raw_pp_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_pp) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pp_cell_column)) * ics_coefficient_positive_scale_span_add_result)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pp_cell_column_source. ics_coefficient_positive_span_add_result = fs_q_mcp_ics_span_add_result_image_raw_pp_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_pp) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pp_cell_column)) * ics_coefficient_positive_scale_span_add_result) + (ff_source_mcp_ics_span_add_result_image_raw_pp_cell_column))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pp_cell_column_target. fs_h_mcp_ics_span_add_result_image_raw_pp_cell_column_target + S (ff_target_mcp_ics_span_add_result_image_raw_pp_cell_column) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pp_cell_column_target. ff_right_mcp_cell_ics_span_add_result_image_raw_pp_cell = fs_q_mcp_ics_span_add_result_image_raw_pp_cell_column_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell) + (ff_target_mcp_ics_span_add_result_image_raw_pp_cell_column))) -> ff_target_mcp_ics_span_add_result_image_raw_pp_cell_column = ff_source_mcp_ics_span_add_result_image_raw_pp_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot ff_scale_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_result_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell) + (fpmp_left_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_result_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pp_cell) + (fpmp_right_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_pp) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_pp))) /\ forall ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum ff_r_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum ff_s_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot = ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot) + (ff_a_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum = ff_r_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum + ff_a_dot_mcp_ics_span_add_result_image_raw_pp_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_result_image_raw_pp_entry. fs_h_mcp_ics_span_add_result_image_raw_pp_entry + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_pp) = S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pp_entry. ff_pp_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_pp_entry * S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_add_result_image_raw) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_pp))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_result_image_raw_nn. (exists mcp_gap_ics_span_add_result_image_raw_nn_index. mcp_gap_ics_span_add_result_image_raw_nn_index + S (ff_index_mcp_prefix_ics_span_add_result_image_raw_nn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_result_image_raw_nn ff_column_mcp_prefix_ics_span_add_result_image_raw_nn ff_value_mcp_prefix_ics_span_add_result_image_raw_nn. ((ff_index_mcp_prefix_ics_span_add_result_image_raw_nn) = (1) * ff_row_mcp_prefix_ics_span_add_result_image_raw_nn + ff_column_mcp_prefix_ics_span_add_result_image_raw_nn /\ ((exists mcp_gap_ics_span_add_result_image_raw_nn_column. mcp_gap_ics_span_add_result_image_raw_nn_column + S (ff_column_mcp_prefix_ics_span_add_result_image_raw_nn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_result_image_raw_nn_cell ff_left_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell ff_right_mcp_cell_ics_span_add_result_image_raw_nn_cell ff_right_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell. ((forall ff_index_mcp_ics_span_add_result_image_raw_nn_cell_row ff_source_mcp_ics_span_add_result_image_raw_nn_cell_row ff_target_mcp_ics_span_add_result_image_raw_nn_cell_row. (exists mcp_gap_ics_span_add_result_image_raw_nn_cell_row_bound. mcp_gap_ics_span_add_result_image_raw_nn_cell_row_bound + S (ff_index_mcp_ics_span_add_result_image_raw_nn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_nn_cell_row_source. fs_h_mcp_ics_span_add_result_image_raw_nn_cell_row_source + S (ff_source_mcp_ics_span_add_result_image_raw_nn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_nn_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_nn_cell_row_source. db = fs_q_mcp_ics_span_add_result_image_raw_nn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_nn_cell_row)) * dc) + (ff_source_mcp_ics_span_add_result_image_raw_nn_cell_row))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_nn_cell_row_target. fs_h_mcp_ics_span_add_result_image_raw_nn_cell_row_target + S (ff_target_mcp_ics_span_add_result_image_raw_nn_cell_row) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_nn_cell_row_target. ff_left_mcp_cell_ics_span_add_result_image_raw_nn_cell = fs_q_mcp_ics_span_add_result_image_raw_nn_cell_row_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell) + (ff_target_mcp_ics_span_add_result_image_raw_nn_cell_row))) -> ff_target_mcp_ics_span_add_result_image_raw_nn_cell_row = ff_source_mcp_ics_span_add_result_image_raw_nn_cell_row) /\ ((forall ff_index_mcp_ics_span_add_result_image_raw_nn_cell_column ff_source_mcp_ics_span_add_result_image_raw_nn_cell_column ff_target_mcp_ics_span_add_result_image_raw_nn_cell_column. (exists mcp_gap_ics_span_add_result_image_raw_nn_cell_column_bound. mcp_gap_ics_span_add_result_image_raw_nn_cell_column_bound + S (ff_index_mcp_ics_span_add_result_image_raw_nn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_nn_cell_column_source. fs_h_mcp_ics_span_add_result_image_raw_nn_cell_column_source + S (ff_source_mcp_ics_span_add_result_image_raw_nn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_nn) + (1) * ff_index_mcp_ics_span_add_result_image_raw_nn_cell_column)) * ics_coefficient_negative_scale_span_add_result)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_nn_cell_column_source. ics_coefficient_negative_span_add_result = fs_q_mcp_ics_span_add_result_image_raw_nn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_nn) + (1) * ff_index_mcp_ics_span_add_result_image_raw_nn_cell_column)) * ics_coefficient_negative_scale_span_add_result) + (ff_source_mcp_ics_span_add_result_image_raw_nn_cell_column))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_nn_cell_column_target. fs_h_mcp_ics_span_add_result_image_raw_nn_cell_column_target + S (ff_target_mcp_ics_span_add_result_image_raw_nn_cell_column) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_nn_cell_column_target. ff_right_mcp_cell_ics_span_add_result_image_raw_nn_cell = fs_q_mcp_ics_span_add_result_image_raw_nn_cell_column_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell) + (ff_target_mcp_ics_span_add_result_image_raw_nn_cell_column))) -> ff_target_mcp_ics_span_add_result_image_raw_nn_cell_column = ff_source_mcp_ics_span_add_result_image_raw_nn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot ff_scale_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_result_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell) + (fpmp_left_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_result_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_nn_cell) + (fpmp_right_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_nn) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_nn))) /\ forall ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum ff_r_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum ff_s_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot = ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot) + (ff_a_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum = ff_r_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum + ff_a_dot_mcp_ics_span_add_result_image_raw_nn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_result_image_raw_nn_entry. fs_h_mcp_ics_span_add_result_image_raw_nn_entry + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_nn) = S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_nn_entry. ff_nn_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_nn_entry * S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_add_result_image_raw) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_nn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_result_image_raw_pn. (exists mcp_gap_ics_span_add_result_image_raw_pn_index. mcp_gap_ics_span_add_result_image_raw_pn_index + S (ff_index_mcp_prefix_ics_span_add_result_image_raw_pn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_result_image_raw_pn ff_column_mcp_prefix_ics_span_add_result_image_raw_pn ff_value_mcp_prefix_ics_span_add_result_image_raw_pn. ((ff_index_mcp_prefix_ics_span_add_result_image_raw_pn) = (1) * ff_row_mcp_prefix_ics_span_add_result_image_raw_pn + ff_column_mcp_prefix_ics_span_add_result_image_raw_pn /\ ((exists mcp_gap_ics_span_add_result_image_raw_pn_column. mcp_gap_ics_span_add_result_image_raw_pn_column + S (ff_column_mcp_prefix_ics_span_add_result_image_raw_pn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_result_image_raw_pn_cell ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell ff_right_mcp_cell_ics_span_add_result_image_raw_pn_cell ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell. ((forall ff_index_mcp_ics_span_add_result_image_raw_pn_cell_row ff_source_mcp_ics_span_add_result_image_raw_pn_cell_row ff_target_mcp_ics_span_add_result_image_raw_pn_cell_row. (exists mcp_gap_ics_span_add_result_image_raw_pn_cell_row_bound. mcp_gap_ics_span_add_result_image_raw_pn_cell_row_bound + S (ff_index_mcp_ics_span_add_result_image_raw_pn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pn_cell_row_source. fs_h_mcp_ics_span_add_result_image_raw_pn_cell_row_source + S (ff_source_mcp_ics_span_add_result_image_raw_pn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pn_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pn_cell_row_source. ab = fs_q_mcp_ics_span_add_result_image_raw_pn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pn_cell_row)) * ac) + (ff_source_mcp_ics_span_add_result_image_raw_pn_cell_row))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pn_cell_row_target. fs_h_mcp_ics_span_add_result_image_raw_pn_cell_row_target + S (ff_target_mcp_ics_span_add_result_image_raw_pn_cell_row) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pn_cell_row_target. ff_left_mcp_cell_ics_span_add_result_image_raw_pn_cell = fs_q_mcp_ics_span_add_result_image_raw_pn_cell_row_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell) + (ff_target_mcp_ics_span_add_result_image_raw_pn_cell_row))) -> ff_target_mcp_ics_span_add_result_image_raw_pn_cell_row = ff_source_mcp_ics_span_add_result_image_raw_pn_cell_row) /\ ((forall ff_index_mcp_ics_span_add_result_image_raw_pn_cell_column ff_source_mcp_ics_span_add_result_image_raw_pn_cell_column ff_target_mcp_ics_span_add_result_image_raw_pn_cell_column. (exists mcp_gap_ics_span_add_result_image_raw_pn_cell_column_bound. mcp_gap_ics_span_add_result_image_raw_pn_cell_column_bound + S (ff_index_mcp_ics_span_add_result_image_raw_pn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pn_cell_column_source. fs_h_mcp_ics_span_add_result_image_raw_pn_cell_column_source + S (ff_source_mcp_ics_span_add_result_image_raw_pn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_pn) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pn_cell_column)) * ics_coefficient_negative_scale_span_add_result)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pn_cell_column_source. ics_coefficient_negative_span_add_result = fs_q_mcp_ics_span_add_result_image_raw_pn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_pn) + (1) * ff_index_mcp_ics_span_add_result_image_raw_pn_cell_column)) * ics_coefficient_negative_scale_span_add_result) + (ff_source_mcp_ics_span_add_result_image_raw_pn_cell_column))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_pn_cell_column_target. fs_h_mcp_ics_span_add_result_image_raw_pn_cell_column_target + S (ff_target_mcp_ics_span_add_result_image_raw_pn_cell_column) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pn_cell_column_target. ff_right_mcp_cell_ics_span_add_result_image_raw_pn_cell = fs_q_mcp_ics_span_add_result_image_raw_pn_cell_column_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell) + (ff_target_mcp_ics_span_add_result_image_raw_pn_cell_column))) -> ff_target_mcp_ics_span_add_result_image_raw_pn_cell_column = ff_source_mcp_ics_span_add_result_image_raw_pn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot ff_scale_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_result_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell) + (fpmp_left_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_result_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_pn_cell) + (fpmp_right_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_pn) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_pn))) /\ forall ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum ff_r_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum ff_s_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot = ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot) + (ff_a_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum = ff_r_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum + ff_a_dot_mcp_ics_span_add_result_image_raw_pn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_result_image_raw_pn_entry. fs_h_mcp_ics_span_add_result_image_raw_pn_entry + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_pn) = S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_pn_entry. ff_pn_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_pn_entry * S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_add_result_image_raw) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_pn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_add_result_image_raw_np. (exists mcp_gap_ics_span_add_result_image_raw_np_index. mcp_gap_ics_span_add_result_image_raw_np_index + S (ff_index_mcp_prefix_ics_span_add_result_image_raw_np) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_add_result_image_raw_np ff_column_mcp_prefix_ics_span_add_result_image_raw_np ff_value_mcp_prefix_ics_span_add_result_image_raw_np. ((ff_index_mcp_prefix_ics_span_add_result_image_raw_np) = (1) * ff_row_mcp_prefix_ics_span_add_result_image_raw_np + ff_column_mcp_prefix_ics_span_add_result_image_raw_np /\ ((exists mcp_gap_ics_span_add_result_image_raw_np_column. mcp_gap_ics_span_add_result_image_raw_np_column + S (ff_column_mcp_prefix_ics_span_add_result_image_raw_np) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_add_result_image_raw_np_cell ff_left_scale_mcp_cell_ics_span_add_result_image_raw_np_cell ff_right_mcp_cell_ics_span_add_result_image_raw_np_cell ff_right_scale_mcp_cell_ics_span_add_result_image_raw_np_cell. ((forall ff_index_mcp_ics_span_add_result_image_raw_np_cell_row ff_source_mcp_ics_span_add_result_image_raw_np_cell_row ff_target_mcp_ics_span_add_result_image_raw_np_cell_row. (exists mcp_gap_ics_span_add_result_image_raw_np_cell_row_bound. mcp_gap_ics_span_add_result_image_raw_np_cell_row_bound + S (ff_index_mcp_ics_span_add_result_image_raw_np_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_np_cell_row_source. fs_h_mcp_ics_span_add_result_image_raw_np_cell_row_source + S (ff_source_mcp_ics_span_add_result_image_raw_np_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_np_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_np_cell_row_source. db = fs_q_mcp_ics_span_add_result_image_raw_np_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_add_result_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_add_result_image_raw_np_cell_row)) * dc) + (ff_source_mcp_ics_span_add_result_image_raw_np_cell_row))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_np_cell_row_target. fs_h_mcp_ics_span_add_result_image_raw_np_cell_row_target + S (ff_target_mcp_ics_span_add_result_image_raw_np_cell_row) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_np_cell_row_target. ff_left_mcp_cell_ics_span_add_result_image_raw_np_cell = fs_q_mcp_ics_span_add_result_image_raw_np_cell_row_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_np_cell) + (ff_target_mcp_ics_span_add_result_image_raw_np_cell_row))) -> ff_target_mcp_ics_span_add_result_image_raw_np_cell_row = ff_source_mcp_ics_span_add_result_image_raw_np_cell_row) /\ ((forall ff_index_mcp_ics_span_add_result_image_raw_np_cell_column ff_source_mcp_ics_span_add_result_image_raw_np_cell_column ff_target_mcp_ics_span_add_result_image_raw_np_cell_column. (exists mcp_gap_ics_span_add_result_image_raw_np_cell_column_bound. mcp_gap_ics_span_add_result_image_raw_np_cell_column_bound + S (ff_index_mcp_ics_span_add_result_image_raw_np_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_np_cell_column_source. fs_h_mcp_ics_span_add_result_image_raw_np_cell_column_source + S (ff_source_mcp_ics_span_add_result_image_raw_np_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_np) + (1) * ff_index_mcp_ics_span_add_result_image_raw_np_cell_column)) * ics_coefficient_positive_scale_span_add_result)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_np_cell_column_source. ics_coefficient_positive_span_add_result = fs_q_mcp_ics_span_add_result_image_raw_np_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_add_result_image_raw_np) + (1) * ff_index_mcp_ics_span_add_result_image_raw_np_cell_column)) * ics_coefficient_positive_scale_span_add_result) + (ff_source_mcp_ics_span_add_result_image_raw_np_cell_column))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_np_cell_column_target. fs_h_mcp_ics_span_add_result_image_raw_np_cell_column_target + S (ff_target_mcp_ics_span_add_result_image_raw_np_cell_column) = S ((S (ff_index_mcp_ics_span_add_result_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_np_cell_column_target. ff_right_mcp_cell_ics_span_add_result_image_raw_np_cell = fs_q_mcp_ics_span_add_result_image_raw_np_cell_column_target * S ((S (ff_index_mcp_ics_span_add_result_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_np_cell) + (ff_target_mcp_ics_span_add_result_image_raw_np_cell_column))) -> ff_target_mcp_ics_span_add_result_image_raw_np_cell_column = ff_source_mcp_ics_span_add_result_image_raw_np_cell_column) /\ (exists ff_code_dot_mcp_ics_span_add_result_image_raw_np_cell_dot ff_scale_dot_mcp_ics_span_add_result_image_raw_np_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_add_result_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_add_result_image_raw_np_cell) + (fpmp_left_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_add_result_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_add_result_image_raw_np_cell) + (fpmp_right_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_np_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_add_result_image_raw_np_cell_dot = ff_q_fpmp_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_np_cell_dot) + (fpmp_target_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_start. ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_start. ff_u_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_np) = S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_np))) /\ forall ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum ff_r_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum ff_s_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_np_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_add_result_image_raw_np_cell_dot = ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_add_result_image_raw_np_cell_dot) + (ff_a_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) + (ff_r_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum) + (ff_s_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum = ff_r_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum + ff_a_dot_mcp_ics_span_add_result_image_raw_np_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_add_result_image_raw_np_entry. fs_h_mcp_ics_span_add_result_image_raw_np_entry + S (ff_value_mcp_prefix_ics_span_add_result_image_raw_np) = S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_np_entry. ff_np_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_np_entry * S ((S (ff_index_mcp_prefix_ics_span_add_result_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_add_result_image_raw) + (ff_value_mcp_prefix_ics_span_add_result_image_raw_np))))))) /\ ((forall ff_index_mcp_add_ics_span_add_result_image_raw_positive ff_left_mcp_add_ics_span_add_result_image_raw_positive ff_right_mcp_add_ics_span_add_result_image_raw_positive ff_target_mcp_add_ics_span_add_result_image_raw_positive. (exists mcp_gap_ics_span_add_result_image_raw_positive_bound. mcp_gap_ics_span_add_result_image_raw_positive_bound + S (ff_index_mcp_add_ics_span_add_result_image_raw_positive) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_positive_left. fs_h_mcp_ics_span_add_result_image_raw_positive_left + S (ff_left_mcp_add_ics_span_add_result_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_positive_left. ff_pp_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_positive_left * S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_add_result_image_raw) + (ff_left_mcp_add_ics_span_add_result_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_positive_right. fs_h_mcp_ics_span_add_result_image_raw_positive_right + S (ff_right_mcp_add_ics_span_add_result_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_positive_right. ff_nn_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_positive_right * S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_add_result_image_raw) + (ff_right_mcp_add_ics_span_add_result_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_positive_target. fs_h_mcp_ics_span_add_result_image_raw_positive_target + S (ff_target_mcp_add_ics_span_add_result_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_positive)) * ics_raw_positive_scale_span_add_result_image)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_positive_target. ics_raw_positive_span_add_result_image = fs_q_mcp_ics_span_add_result_image_raw_positive_target * S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_positive)) * ics_raw_positive_scale_span_add_result_image) + (ff_target_mcp_add_ics_span_add_result_image_raw_positive))) -> ff_target_mcp_add_ics_span_add_result_image_raw_positive = ff_left_mcp_add_ics_span_add_result_image_raw_positive + ff_right_mcp_add_ics_span_add_result_image_raw_positive) /\ (forall ff_index_mcp_add_ics_span_add_result_image_raw_negative ff_left_mcp_add_ics_span_add_result_image_raw_negative ff_right_mcp_add_ics_span_add_result_image_raw_negative ff_target_mcp_add_ics_span_add_result_image_raw_negative. (exists mcp_gap_ics_span_add_result_image_raw_negative_bound. mcp_gap_ics_span_add_result_image_raw_negative_bound + S (ff_index_mcp_add_ics_span_add_result_image_raw_negative) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_negative_left. fs_h_mcp_ics_span_add_result_image_raw_negative_left + S (ff_left_mcp_add_ics_span_add_result_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_negative_left. ff_pn_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_negative_left * S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_add_result_image_raw) + (ff_left_mcp_add_ics_span_add_result_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_negative_right. fs_h_mcp_ics_span_add_result_image_raw_negative_right + S (ff_right_mcp_add_ics_span_add_result_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_add_result_image_raw)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_negative_right. ff_np_mcp_smatrix_ics_span_add_result_image_raw = fs_q_mcp_ics_span_add_result_image_raw_negative_right * S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_add_result_image_raw) + (ff_right_mcp_add_ics_span_add_result_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_add_result_image_raw_negative_target. fs_h_mcp_ics_span_add_result_image_raw_negative_target + S (ff_target_mcp_add_ics_span_add_result_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_negative)) * ics_raw_negative_scale_span_add_result_image)) /\ exists fs_q_mcp_ics_span_add_result_image_raw_negative_target. ics_raw_negative_span_add_result_image = fs_q_mcp_ics_span_add_result_image_raw_negative_target * S ((S (ff_index_mcp_add_ics_span_add_result_image_raw_negative)) * ics_raw_negative_scale_span_add_result_image) + (ff_target_mcp_add_ics_span_add_result_image_raw_negative))) -> ff_target_mcp_add_ics_span_add_result_image_raw_negative = ff_left_mcp_add_ics_span_add_result_image_raw_negative + ff_right_mcp_add_ics_span_add_result_image_raw_negative))))))) /\ (forall ics_index_span_add_result_image_equal ics_value0_span_add_result_image_equal ics_value1_span_add_result_image_equal ics_value2_span_add_result_image_equal ics_value3_span_add_result_image_equal. (exists ics_gap_span_add_result_image_equal_bound. ics_gap_span_add_result_image_equal_bound + S (ics_index_span_add_result_image_equal) = (r)) -> (((exists fs_h_ics_span_add_result_image_equal_at0. fs_h_ics_span_add_result_image_equal_at0 + S (ics_value0_span_add_result_image_equal) = S ((S (ics_index_span_add_result_image_equal)) * ics_raw_positive_scale_span_add_result_image)) /\ exists fs_q_ics_span_add_result_image_equal_at0. ics_raw_positive_span_add_result_image = fs_q_ics_span_add_result_image_equal_at0 * S ((S (ics_index_span_add_result_image_equal)) * ics_raw_positive_scale_span_add_result_image) + (ics_value0_span_add_result_image_equal))) -> (((exists fs_h_ics_span_add_result_image_equal_at1. fs_h_ics_span_add_result_image_equal_at1 + S (ics_value1_span_add_result_image_equal) = S ((S (ics_index_span_add_result_image_equal)) * ics_raw_negative_scale_span_add_result_image)) /\ exists fs_q_ics_span_add_result_image_equal_at1. ics_raw_negative_span_add_result_image = fs_q_ics_span_add_result_image_equal_at1 * S ((S (ics_index_span_add_result_image_equal)) * ics_raw_negative_scale_span_add_result_image) + (ics_value1_span_add_result_image_equal))) -> (((exists fs_h_ics_span_add_result_image_equal_at2. fs_h_ics_span_add_result_image_equal_at2 + S (ics_value2_span_add_result_image_equal) = S ((S (ics_index_span_add_result_image_equal)) * rc)) /\ exists fs_q_ics_span_add_result_image_equal_at2. rb = fs_q_ics_span_add_result_image_equal_at2 * S ((S (ics_index_span_add_result_image_equal)) * rc) + (ics_value2_span_add_result_image_equal))) -> (((exists fs_h_ics_span_add_result_image_equal_at3. fs_h_ics_span_add_result_image_equal_at3 + S (ics_value3_span_add_result_image_equal) = S ((S (ics_index_span_add_result_image_equal)) * sc)) /\ exists fs_q_ics_span_add_result_image_equal_at3. sb = fs_q_ics_span_add_result_image_equal_at3 * S ((S (ics_index_span_add_result_image_equal)) * sc) + (ics_value3_span_add_result_image_equal))) -> ics_value0_span_add_result_image_equal + ics_value3_span_add_result_image_equal = ics_value2_span_add_result_image_equal + ics_value1_span_add_result_image_equal)))))Constructive proof overview
Generated structural guide
Every actual integer sum of two arbitrary column-span vectors lies in the same span, with the constructed finite sums of their actual coefficient streams as witnesses.
The unchanged tactic script uses 1 declared prerequisite and contains 71 exact native proof lines.
Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (1)
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–20
03Fix variables and assumptionsL21–21
Work with arbitrary variables or the premises of the current implication.
- L21
intro hadd
04Separate the logical casesL22–29
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
05Establish hcoeffL30–39
Establish this local claim before using it. It is not an additional assumption.
- L30
have hcoeff : ∃ ib. ∃ ic. ∃ jb. ∃ jc. MatrixPointwiseAdd(x,x1,x4,x5,ib,ic,w) ∧ (MatrixPointwiseAdd(x2,x3,x6,x7,jb,jc,w) ∧ IntegerMatrixVectorProduct(ab,ac,db,dc,ib,ic,jb,jc,w,r,rb,rc,sb,sc))Definitions: MatrixPointwiseAddIntegerMatrixVectorProduct - L31
specialize integer_matrix_vector_add_constructive (ab) - L32
specialize integer_matrix_vector_add_constructive (ac) - L33
specialize integer_matrix_vector_add_constructive (db) - L34
specialize integer_matrix_vector_add_constructive (dc) - L35
specialize integer_matrix_vector_add_constructive (x) - L36
specialize integer_matrix_vector_add_constructive (x1) - L37
specialize integer_matrix_vector_add_constructive (x2) - L38
specialize integer_matrix_vector_add_constructive (x3) - L39
specialize integer_matrix_vector_add_constructive (x4)
06Use earlier factsL40–49
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L40
specialize integer_matrix_vector_add_constructive (x5) - L41
specialize integer_matrix_vector_add_constructive (x6) - L42
specialize integer_matrix_vector_add_constructive (x7) - L43
specialize integer_matrix_vector_add_constructive (w) - L44
specialize integer_matrix_vector_add_constructive (r) - L45
specialize integer_matrix_vector_add_constructive (pb) - L46
specialize integer_matrix_vector_add_constructive (pc) - L47
specialize integer_matrix_vector_add_constructive (nb) - L48
specialize integer_matrix_vector_add_constructive (nc) - L49
specialize integer_matrix_vector_add_constructive (qb)
07Use earlier factsL50–59
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L50
specialize integer_matrix_vector_add_constructive (qc) - L51
specialize integer_matrix_vector_add_constructive (mb) - L52
specialize integer_matrix_vector_add_constructive (mc) - L53
specialize integer_matrix_vector_add_constructive (rb) - L54
specialize integer_matrix_vector_add_constructive (rc) - L55
specialize integer_matrix_vector_add_constructive (sb) - L56
specialize integer_matrix_vector_add_constructive (sc) - L57
apply integer_matrix_vector_add_constructive - L58
exact hfirst_witness_witness_witness_witness - L59
exact hsecond_witness_witness_witness_witness
08Use earlier factsL60–60
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L60
exact hadd
09Separate the logical casesL61–66
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
10Construct an explicit witnessL67–70
11Use earlier factsL71–71
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L71
exact hcoeff_witness_witness_witness_witness_right_right
Original exact command ledger · 71 lines
- 0001
intro ab - 0002
intro ac - 0003
intro db - 0004
intro dc - 0005
intro w - 0006
intro r - 0007
intro pb - 0008
intro pc - 0009
intro nb - 0010
intro nc - 0011
intro qb - 0012
intro qc - 0013
intro mb - 0014
intro mc - 0015
intro rb - 0016
intro rc - 0017
intro sb - 0018
intro sc - 0019
intro hfirst - 0020
intro hsecond - 0021
intro hadd - 0022
cases hfirst - 0023
cases hfirst_witness - 0024
cases hfirst_witness_witness - 0025
cases hfirst_witness_witness_witness - 0026
cases hsecond - 0027
cases hsecond_witness - 0028
cases hsecond_witness_witness - 0029
cases hsecond_witness_witness_witness - 0030
have hcoeff : exists ib ic jb jc. (((forall ff_index_mcp_add_ics_span_new_coeffp ff_left_mcp_add_ics_span_new_coeffp ff_right_mcp_add_ics_span_new_coeffp ff_target_mcp_add_ics_span_new_coeffp. (exists mcp_gap_ics_span_new_coeffp_bound. mcp_gap_ics_span_new_coeffp_bound + S (ff_index_mcp_add_ics_span_new_coeffp) = (w)) -> (((exists fs_h_mcp_ics_span_new_coeffp_left. fs_h_mcp_ics_span_new_coeffp_left + S (ff_left_mcp_add_ics_span_new_coeffp) = S ((S (ff_index_mcp_add_ics_span_new_coeffp)) * x1)) /\ exists fs_q_mcp_ics_span_new_coeffp_left. x = fs_q_mcp_ics_span_new_coeffp_left * S ((S (ff_index_mcp_add_ics_span_new_coeffp)) * x1) + (ff_left_mcp_add_ics_span_new_coeffp))) -> (((exists fs_h_mcp_ics_span_new_coeffp_right. fs_h_mcp_ics_span_new_coeffp_right + S (ff_right_mcp_add_ics_span_new_coeffp) = S ((S (ff_index_mcp_add_ics_span_new_coeffp)) * x5)) /\ exists fs_q_mcp_ics_span_new_coeffp_right. x4 = fs_q_mcp_ics_span_new_coeffp_right * S ((S (ff_index_mcp_add_ics_span_new_coeffp)) * x5) + (ff_right_mcp_add_ics_span_new_coeffp))) -> (((exists fs_h_mcp_ics_span_new_coeffp_target. fs_h_mcp_ics_span_new_coeffp_target + S (ff_target_mcp_add_ics_span_new_coeffp) = S ((S (ff_index_mcp_add_ics_span_new_coeffp)) * ic)) /\ exists fs_q_mcp_ics_span_new_coeffp_target. ib = fs_q_mcp_ics_span_new_coeffp_target * S ((S (ff_index_mcp_add_ics_span_new_coeffp)) * ic) + (ff_target_mcp_add_ics_span_new_coeffp))) -> ff_target_mcp_add_ics_span_new_coeffp = ff_left_mcp_add_ics_span_new_coeffp + ff_right_mcp_add_ics_span_new_coeffp) /\ (((forall ff_index_mcp_add_ics_span_new_coeffn ff_left_mcp_add_ics_span_new_coeffn ff_right_mcp_add_ics_span_new_coeffn ff_target_mcp_add_ics_span_new_coeffn. (exists mcp_gap_ics_span_new_coeffn_bound. mcp_gap_ics_span_new_coeffn_bound + S (ff_index_mcp_add_ics_span_new_coeffn) = (w)) -> (((exists fs_h_mcp_ics_span_new_coeffn_left. fs_h_mcp_ics_span_new_coeffn_left + S (ff_left_mcp_add_ics_span_new_coeffn) = S ((S (ff_index_mcp_add_ics_span_new_coeffn)) * x3)) /\ exists fs_q_mcp_ics_span_new_coeffn_left. x2 = fs_q_mcp_ics_span_new_coeffn_left * S ((S (ff_index_mcp_add_ics_span_new_coeffn)) * x3) + (ff_left_mcp_add_ics_span_new_coeffn))) -> (((exists fs_h_mcp_ics_span_new_coeffn_right. fs_h_mcp_ics_span_new_coeffn_right + S (ff_right_mcp_add_ics_span_new_coeffn) = S ((S (ff_index_mcp_add_ics_span_new_coeffn)) * x7)) /\ exists fs_q_mcp_ics_span_new_coeffn_right. x6 = fs_q_mcp_ics_span_new_coeffn_right * S ((S (ff_index_mcp_add_ics_span_new_coeffn)) * x7) + (ff_right_mcp_add_ics_span_new_coeffn))) -> (((exists fs_h_mcp_ics_span_new_coeffn_target. fs_h_mcp_ics_span_new_coeffn_target + S (ff_target_mcp_add_ics_span_new_coeffn) = S ((S (ff_index_mcp_add_ics_span_new_coeffn)) * jc)) /\ exists fs_q_mcp_ics_span_new_coeffn_target. jb = fs_q_mcp_ics_span_new_coeffn_target * S ((S (ff_index_mcp_add_ics_span_new_coeffn)) * jc) + (ff_target_mcp_add_ics_span_new_coeffn))) -> ff_target_mcp_add_ics_span_new_coeffn = ff_left_mcp_add_ics_span_new_coeffn + ff_right_mcp_add_ics_span_new_coeffn) /\ (exists ics_raw_positive_span_new_image ics_raw_positive_scale_span_new_image ics_raw_negative_span_new_image ics_raw_negative_scale_span_new_image. (((exists ff_pp_mcp_smatrix_ics_span_new_image_raw ff_pps_mcp_smatrix_ics_span_new_image_raw ff_nn_mcp_smatrix_ics_span_new_image_raw ff_nns_mcp_smatrix_ics_span_new_image_raw ff_pn_mcp_smatrix_ics_span_new_image_raw ff_pns_mcp_smatrix_ics_span_new_image_raw ff_np_mcp_smatrix_ics_span_new_image_raw ff_nps_mcp_smatrix_ics_span_new_image_raw. ((forall ff_index_mcp_prefix_ics_span_new_image_raw_pp. (exists mcp_gap_ics_span_new_image_raw_pp_index. mcp_gap_ics_span_new_image_raw_pp_index + S (ff_index_mcp_prefix_ics_span_new_image_raw_pp) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_new_image_raw_pp ff_column_mcp_prefix_ics_span_new_image_raw_pp ff_value_mcp_prefix_ics_span_new_image_raw_pp. ((ff_index_mcp_prefix_ics_span_new_image_raw_pp) = (1) * ff_row_mcp_prefix_ics_span_new_image_raw_pp + ff_column_mcp_prefix_ics_span_new_image_raw_pp /\ ((exists mcp_gap_ics_span_new_image_raw_pp_column. mcp_gap_ics_span_new_image_raw_pp_column + S (ff_column_mcp_prefix_ics_span_new_image_raw_pp) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_new_image_raw_pp_cell ff_left_scale_mcp_cell_ics_span_new_image_raw_pp_cell ff_right_mcp_cell_ics_span_new_image_raw_pp_cell ff_right_scale_mcp_cell_ics_span_new_image_raw_pp_cell. ((forall ff_index_mcp_ics_span_new_image_raw_pp_cell_row ff_source_mcp_ics_span_new_image_raw_pp_cell_row ff_target_mcp_ics_span_new_image_raw_pp_cell_row. (exists mcp_gap_ics_span_new_image_raw_pp_cell_row_bound. mcp_gap_ics_span_new_image_raw_pp_cell_row_bound + S (ff_index_mcp_ics_span_new_image_raw_pp_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_pp_cell_row_source. fs_h_mcp_ics_span_new_image_raw_pp_cell_row_source + S (ff_source_mcp_ics_span_new_image_raw_pp_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_pp_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_new_image_raw_pp_cell_row_source. ab = fs_q_mcp_ics_span_new_image_raw_pp_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_pp) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_pp_cell_row)) * ac) + (ff_source_mcp_ics_span_new_image_raw_pp_cell_row))) -> (((exists fs_h_mcp_ics_span_new_image_raw_pp_cell_row_target. fs_h_mcp_ics_span_new_image_raw_pp_cell_row_target + S (ff_target_mcp_ics_span_new_image_raw_pp_cell_row) = S ((S (ff_index_mcp_ics_span_new_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_pp_cell_row_target. ff_left_mcp_cell_ics_span_new_image_raw_pp_cell = fs_q_mcp_ics_span_new_image_raw_pp_cell_row_target * S ((S (ff_index_mcp_ics_span_new_image_raw_pp_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pp_cell) + (ff_target_mcp_ics_span_new_image_raw_pp_cell_row))) -> ff_target_mcp_ics_span_new_image_raw_pp_cell_row = ff_source_mcp_ics_span_new_image_raw_pp_cell_row) /\ ((forall ff_index_mcp_ics_span_new_image_raw_pp_cell_column ff_source_mcp_ics_span_new_image_raw_pp_cell_column ff_target_mcp_ics_span_new_image_raw_pp_cell_column. (exists mcp_gap_ics_span_new_image_raw_pp_cell_column_bound. mcp_gap_ics_span_new_image_raw_pp_cell_column_bound + S (ff_index_mcp_ics_span_new_image_raw_pp_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_pp_cell_column_source. fs_h_mcp_ics_span_new_image_raw_pp_cell_column_source + S (ff_source_mcp_ics_span_new_image_raw_pp_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_pp) + (1) * ff_index_mcp_ics_span_new_image_raw_pp_cell_column)) * ic)) /\ exists fs_q_mcp_ics_span_new_image_raw_pp_cell_column_source. ib = fs_q_mcp_ics_span_new_image_raw_pp_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_pp) + (1) * ff_index_mcp_ics_span_new_image_raw_pp_cell_column)) * ic) + (ff_source_mcp_ics_span_new_image_raw_pp_cell_column))) -> (((exists fs_h_mcp_ics_span_new_image_raw_pp_cell_column_target. fs_h_mcp_ics_span_new_image_raw_pp_cell_column_target + S (ff_target_mcp_ics_span_new_image_raw_pp_cell_column) = S ((S (ff_index_mcp_ics_span_new_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pp_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_pp_cell_column_target. ff_right_mcp_cell_ics_span_new_image_raw_pp_cell = fs_q_mcp_ics_span_new_image_raw_pp_cell_column_target * S ((S (ff_index_mcp_ics_span_new_image_raw_pp_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pp_cell) + (ff_target_mcp_ics_span_new_image_raw_pp_cell_column))) -> ff_target_mcp_ics_span_new_image_raw_pp_cell_column = ff_source_mcp_ics_span_new_image_raw_pp_cell_column) /\ (exists ff_code_dot_mcp_ics_span_new_image_raw_pp_cell_dot ff_scale_dot_mcp_ics_span_new_image_raw_pp_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_new_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pp_cell) + (fpmp_left_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pp_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_new_image_raw_pp_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pp_cell) + (fpmp_right_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_pp_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_new_image_raw_pp_cell_dot = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_pp_cell_dot) + (fpmp_target_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_new_image_raw_pp_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_start. ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_start. ff_u_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_new_image_raw_pp) = S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_new_image_raw_pp))) /\ forall ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum ff_r_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum ff_s_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_pp_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_new_image_raw_pp_cell_dot = ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_pp_cell_dot) + (ff_a_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) + (ff_r_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum) + (ff_s_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum = ff_r_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum + ff_a_dot_mcp_ics_span_new_image_raw_pp_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_new_image_raw_pp_entry. fs_h_mcp_ics_span_new_image_raw_pp_entry + S (ff_value_mcp_prefix_ics_span_new_image_raw_pp) = S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_pp_entry. ff_pp_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_pp_entry * S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_pp)) * ff_pps_mcp_smatrix_ics_span_new_image_raw) + (ff_value_mcp_prefix_ics_span_new_image_raw_pp))))))) /\ ((forall ff_index_mcp_prefix_ics_span_new_image_raw_nn. (exists mcp_gap_ics_span_new_image_raw_nn_index. mcp_gap_ics_span_new_image_raw_nn_index + S (ff_index_mcp_prefix_ics_span_new_image_raw_nn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_new_image_raw_nn ff_column_mcp_prefix_ics_span_new_image_raw_nn ff_value_mcp_prefix_ics_span_new_image_raw_nn. ((ff_index_mcp_prefix_ics_span_new_image_raw_nn) = (1) * ff_row_mcp_prefix_ics_span_new_image_raw_nn + ff_column_mcp_prefix_ics_span_new_image_raw_nn /\ ((exists mcp_gap_ics_span_new_image_raw_nn_column. mcp_gap_ics_span_new_image_raw_nn_column + S (ff_column_mcp_prefix_ics_span_new_image_raw_nn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_new_image_raw_nn_cell ff_left_scale_mcp_cell_ics_span_new_image_raw_nn_cell ff_right_mcp_cell_ics_span_new_image_raw_nn_cell ff_right_scale_mcp_cell_ics_span_new_image_raw_nn_cell. ((forall ff_index_mcp_ics_span_new_image_raw_nn_cell_row ff_source_mcp_ics_span_new_image_raw_nn_cell_row ff_target_mcp_ics_span_new_image_raw_nn_cell_row. (exists mcp_gap_ics_span_new_image_raw_nn_cell_row_bound. mcp_gap_ics_span_new_image_raw_nn_cell_row_bound + S (ff_index_mcp_ics_span_new_image_raw_nn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_nn_cell_row_source. fs_h_mcp_ics_span_new_image_raw_nn_cell_row_source + S (ff_source_mcp_ics_span_new_image_raw_nn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_nn_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_new_image_raw_nn_cell_row_source. db = fs_q_mcp_ics_span_new_image_raw_nn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_nn) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_nn_cell_row)) * dc) + (ff_source_mcp_ics_span_new_image_raw_nn_cell_row))) -> (((exists fs_h_mcp_ics_span_new_image_raw_nn_cell_row_target. fs_h_mcp_ics_span_new_image_raw_nn_cell_row_target + S (ff_target_mcp_ics_span_new_image_raw_nn_cell_row) = S ((S (ff_index_mcp_ics_span_new_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_nn_cell_row_target. ff_left_mcp_cell_ics_span_new_image_raw_nn_cell = fs_q_mcp_ics_span_new_image_raw_nn_cell_row_target * S ((S (ff_index_mcp_ics_span_new_image_raw_nn_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_nn_cell) + (ff_target_mcp_ics_span_new_image_raw_nn_cell_row))) -> ff_target_mcp_ics_span_new_image_raw_nn_cell_row = ff_source_mcp_ics_span_new_image_raw_nn_cell_row) /\ ((forall ff_index_mcp_ics_span_new_image_raw_nn_cell_column ff_source_mcp_ics_span_new_image_raw_nn_cell_column ff_target_mcp_ics_span_new_image_raw_nn_cell_column. (exists mcp_gap_ics_span_new_image_raw_nn_cell_column_bound. mcp_gap_ics_span_new_image_raw_nn_cell_column_bound + S (ff_index_mcp_ics_span_new_image_raw_nn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_nn_cell_column_source. fs_h_mcp_ics_span_new_image_raw_nn_cell_column_source + S (ff_source_mcp_ics_span_new_image_raw_nn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_nn) + (1) * ff_index_mcp_ics_span_new_image_raw_nn_cell_column)) * jc)) /\ exists fs_q_mcp_ics_span_new_image_raw_nn_cell_column_source. jb = fs_q_mcp_ics_span_new_image_raw_nn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_nn) + (1) * ff_index_mcp_ics_span_new_image_raw_nn_cell_column)) * jc) + (ff_source_mcp_ics_span_new_image_raw_nn_cell_column))) -> (((exists fs_h_mcp_ics_span_new_image_raw_nn_cell_column_target. fs_h_mcp_ics_span_new_image_raw_nn_cell_column_target + S (ff_target_mcp_ics_span_new_image_raw_nn_cell_column) = S ((S (ff_index_mcp_ics_span_new_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_nn_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_nn_cell_column_target. ff_right_mcp_cell_ics_span_new_image_raw_nn_cell = fs_q_mcp_ics_span_new_image_raw_nn_cell_column_target * S ((S (ff_index_mcp_ics_span_new_image_raw_nn_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_nn_cell) + (ff_target_mcp_ics_span_new_image_raw_nn_cell_column))) -> ff_target_mcp_ics_span_new_image_raw_nn_cell_column = ff_source_mcp_ics_span_new_image_raw_nn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_new_image_raw_nn_cell_dot ff_scale_dot_mcp_ics_span_new_image_raw_nn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_new_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_nn_cell) + (fpmp_left_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_nn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_new_image_raw_nn_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_nn_cell) + (fpmp_right_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_nn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_new_image_raw_nn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_nn_cell_dot) + (fpmp_target_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_new_image_raw_nn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_new_image_raw_nn) = S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_new_image_raw_nn))) /\ forall ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum ff_r_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum ff_s_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_nn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_new_image_raw_nn_cell_dot = ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_nn_cell_dot) + (ff_a_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum = ff_r_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum + ff_a_dot_mcp_ics_span_new_image_raw_nn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_new_image_raw_nn_entry. fs_h_mcp_ics_span_new_image_raw_nn_entry + S (ff_value_mcp_prefix_ics_span_new_image_raw_nn) = S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_nn_entry. ff_nn_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_nn_entry * S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_nn)) * ff_nns_mcp_smatrix_ics_span_new_image_raw) + (ff_value_mcp_prefix_ics_span_new_image_raw_nn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_new_image_raw_pn. (exists mcp_gap_ics_span_new_image_raw_pn_index. mcp_gap_ics_span_new_image_raw_pn_index + S (ff_index_mcp_prefix_ics_span_new_image_raw_pn) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_new_image_raw_pn ff_column_mcp_prefix_ics_span_new_image_raw_pn ff_value_mcp_prefix_ics_span_new_image_raw_pn. ((ff_index_mcp_prefix_ics_span_new_image_raw_pn) = (1) * ff_row_mcp_prefix_ics_span_new_image_raw_pn + ff_column_mcp_prefix_ics_span_new_image_raw_pn /\ ((exists mcp_gap_ics_span_new_image_raw_pn_column. mcp_gap_ics_span_new_image_raw_pn_column + S (ff_column_mcp_prefix_ics_span_new_image_raw_pn) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_new_image_raw_pn_cell ff_left_scale_mcp_cell_ics_span_new_image_raw_pn_cell ff_right_mcp_cell_ics_span_new_image_raw_pn_cell ff_right_scale_mcp_cell_ics_span_new_image_raw_pn_cell. ((forall ff_index_mcp_ics_span_new_image_raw_pn_cell_row ff_source_mcp_ics_span_new_image_raw_pn_cell_row ff_target_mcp_ics_span_new_image_raw_pn_cell_row. (exists mcp_gap_ics_span_new_image_raw_pn_cell_row_bound. mcp_gap_ics_span_new_image_raw_pn_cell_row_bound + S (ff_index_mcp_ics_span_new_image_raw_pn_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_pn_cell_row_source. fs_h_mcp_ics_span_new_image_raw_pn_cell_row_source + S (ff_source_mcp_ics_span_new_image_raw_pn_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_pn_cell_row)) * ac)) /\ exists fs_q_mcp_ics_span_new_image_raw_pn_cell_row_source. ab = fs_q_mcp_ics_span_new_image_raw_pn_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_pn) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_pn_cell_row)) * ac) + (ff_source_mcp_ics_span_new_image_raw_pn_cell_row))) -> (((exists fs_h_mcp_ics_span_new_image_raw_pn_cell_row_target. fs_h_mcp_ics_span_new_image_raw_pn_cell_row_target + S (ff_target_mcp_ics_span_new_image_raw_pn_cell_row) = S ((S (ff_index_mcp_ics_span_new_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_pn_cell_row_target. ff_left_mcp_cell_ics_span_new_image_raw_pn_cell = fs_q_mcp_ics_span_new_image_raw_pn_cell_row_target * S ((S (ff_index_mcp_ics_span_new_image_raw_pn_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pn_cell) + (ff_target_mcp_ics_span_new_image_raw_pn_cell_row))) -> ff_target_mcp_ics_span_new_image_raw_pn_cell_row = ff_source_mcp_ics_span_new_image_raw_pn_cell_row) /\ ((forall ff_index_mcp_ics_span_new_image_raw_pn_cell_column ff_source_mcp_ics_span_new_image_raw_pn_cell_column ff_target_mcp_ics_span_new_image_raw_pn_cell_column. (exists mcp_gap_ics_span_new_image_raw_pn_cell_column_bound. mcp_gap_ics_span_new_image_raw_pn_cell_column_bound + S (ff_index_mcp_ics_span_new_image_raw_pn_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_pn_cell_column_source. fs_h_mcp_ics_span_new_image_raw_pn_cell_column_source + S (ff_source_mcp_ics_span_new_image_raw_pn_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_pn) + (1) * ff_index_mcp_ics_span_new_image_raw_pn_cell_column)) * jc)) /\ exists fs_q_mcp_ics_span_new_image_raw_pn_cell_column_source. jb = fs_q_mcp_ics_span_new_image_raw_pn_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_pn) + (1) * ff_index_mcp_ics_span_new_image_raw_pn_cell_column)) * jc) + (ff_source_mcp_ics_span_new_image_raw_pn_cell_column))) -> (((exists fs_h_mcp_ics_span_new_image_raw_pn_cell_column_target. fs_h_mcp_ics_span_new_image_raw_pn_cell_column_target + S (ff_target_mcp_ics_span_new_image_raw_pn_cell_column) = S ((S (ff_index_mcp_ics_span_new_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pn_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_pn_cell_column_target. ff_right_mcp_cell_ics_span_new_image_raw_pn_cell = fs_q_mcp_ics_span_new_image_raw_pn_cell_column_target * S ((S (ff_index_mcp_ics_span_new_image_raw_pn_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pn_cell) + (ff_target_mcp_ics_span_new_image_raw_pn_cell_column))) -> ff_target_mcp_ics_span_new_image_raw_pn_cell_column = ff_source_mcp_ics_span_new_image_raw_pn_cell_column) /\ (exists ff_code_dot_mcp_ics_span_new_image_raw_pn_cell_dot ff_scale_dot_mcp_ics_span_new_image_raw_pn_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_new_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_pn_cell) + (fpmp_left_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pn_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_new_image_raw_pn_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_pn_cell) + (fpmp_right_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_pn_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_new_image_raw_pn_cell_dot = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_pn_cell_dot) + (fpmp_target_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_new_image_raw_pn_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_start. ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_start. ff_u_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_new_image_raw_pn) = S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_new_image_raw_pn))) /\ forall ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum ff_r_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum ff_s_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_pn_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_new_image_raw_pn_cell_dot = ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_pn_cell_dot) + (ff_a_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) + (ff_r_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum) + (ff_s_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum = ff_r_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum + ff_a_dot_mcp_ics_span_new_image_raw_pn_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_new_image_raw_pn_entry. fs_h_mcp_ics_span_new_image_raw_pn_entry + S (ff_value_mcp_prefix_ics_span_new_image_raw_pn) = S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_pn_entry. ff_pn_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_pn_entry * S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_pn)) * ff_pns_mcp_smatrix_ics_span_new_image_raw) + (ff_value_mcp_prefix_ics_span_new_image_raw_pn))))))) /\ ((forall ff_index_mcp_prefix_ics_span_new_image_raw_np. (exists mcp_gap_ics_span_new_image_raw_np_index. mcp_gap_ics_span_new_image_raw_np_index + S (ff_index_mcp_prefix_ics_span_new_image_raw_np) = ((r) * (1))) -> exists ff_row_mcp_prefix_ics_span_new_image_raw_np ff_column_mcp_prefix_ics_span_new_image_raw_np ff_value_mcp_prefix_ics_span_new_image_raw_np. ((ff_index_mcp_prefix_ics_span_new_image_raw_np) = (1) * ff_row_mcp_prefix_ics_span_new_image_raw_np + ff_column_mcp_prefix_ics_span_new_image_raw_np /\ ((exists mcp_gap_ics_span_new_image_raw_np_column. mcp_gap_ics_span_new_image_raw_np_column + S (ff_column_mcp_prefix_ics_span_new_image_raw_np) = (1)) /\ ((exists ff_left_mcp_cell_ics_span_new_image_raw_np_cell ff_left_scale_mcp_cell_ics_span_new_image_raw_np_cell ff_right_mcp_cell_ics_span_new_image_raw_np_cell ff_right_scale_mcp_cell_ics_span_new_image_raw_np_cell. ((forall ff_index_mcp_ics_span_new_image_raw_np_cell_row ff_source_mcp_ics_span_new_image_raw_np_cell_row ff_target_mcp_ics_span_new_image_raw_np_cell_row. (exists mcp_gap_ics_span_new_image_raw_np_cell_row_bound. mcp_gap_ics_span_new_image_raw_np_cell_row_bound + S (ff_index_mcp_ics_span_new_image_raw_np_cell_row) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_np_cell_row_source. fs_h_mcp_ics_span_new_image_raw_np_cell_row_source + S (ff_source_mcp_ics_span_new_image_raw_np_cell_row) = S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_np_cell_row)) * dc)) /\ exists fs_q_mcp_ics_span_new_image_raw_np_cell_row_source. db = fs_q_mcp_ics_span_new_image_raw_np_cell_row_source * S ((S (((ff_row_mcp_prefix_ics_span_new_image_raw_np) * (w)) + (1) * ff_index_mcp_ics_span_new_image_raw_np_cell_row)) * dc) + (ff_source_mcp_ics_span_new_image_raw_np_cell_row))) -> (((exists fs_h_mcp_ics_span_new_image_raw_np_cell_row_target. fs_h_mcp_ics_span_new_image_raw_np_cell_row_target + S (ff_target_mcp_ics_span_new_image_raw_np_cell_row) = S ((S (ff_index_mcp_ics_span_new_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_np_cell_row_target. ff_left_mcp_cell_ics_span_new_image_raw_np_cell = fs_q_mcp_ics_span_new_image_raw_np_cell_row_target * S ((S (ff_index_mcp_ics_span_new_image_raw_np_cell_row)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_np_cell) + (ff_target_mcp_ics_span_new_image_raw_np_cell_row))) -> ff_target_mcp_ics_span_new_image_raw_np_cell_row = ff_source_mcp_ics_span_new_image_raw_np_cell_row) /\ ((forall ff_index_mcp_ics_span_new_image_raw_np_cell_column ff_source_mcp_ics_span_new_image_raw_np_cell_column ff_target_mcp_ics_span_new_image_raw_np_cell_column. (exists mcp_gap_ics_span_new_image_raw_np_cell_column_bound. mcp_gap_ics_span_new_image_raw_np_cell_column_bound + S (ff_index_mcp_ics_span_new_image_raw_np_cell_column) = (w)) -> (((exists fs_h_mcp_ics_span_new_image_raw_np_cell_column_source. fs_h_mcp_ics_span_new_image_raw_np_cell_column_source + S (ff_source_mcp_ics_span_new_image_raw_np_cell_column) = S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_np) + (1) * ff_index_mcp_ics_span_new_image_raw_np_cell_column)) * ic)) /\ exists fs_q_mcp_ics_span_new_image_raw_np_cell_column_source. ib = fs_q_mcp_ics_span_new_image_raw_np_cell_column_source * S ((S ((ff_column_mcp_prefix_ics_span_new_image_raw_np) + (1) * ff_index_mcp_ics_span_new_image_raw_np_cell_column)) * ic) + (ff_source_mcp_ics_span_new_image_raw_np_cell_column))) -> (((exists fs_h_mcp_ics_span_new_image_raw_np_cell_column_target. fs_h_mcp_ics_span_new_image_raw_np_cell_column_target + S (ff_target_mcp_ics_span_new_image_raw_np_cell_column) = S ((S (ff_index_mcp_ics_span_new_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_np_cell)) /\ exists fs_q_mcp_ics_span_new_image_raw_np_cell_column_target. ff_right_mcp_cell_ics_span_new_image_raw_np_cell = fs_q_mcp_ics_span_new_image_raw_np_cell_column_target * S ((S (ff_index_mcp_ics_span_new_image_raw_np_cell_column)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_np_cell) + (ff_target_mcp_ics_span_new_image_raw_np_cell_column))) -> ff_target_mcp_ics_span_new_image_raw_np_cell_column = ff_source_mcp_ics_span_new_image_raw_np_cell_column) /\ (exists ff_code_dot_mcp_ics_span_new_image_raw_np_cell_dot ff_scale_dot_mcp_ics_span_new_image_raw_np_cell_dot. ((forall fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise fpmp_left_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise fpmp_right_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise fpmp_target_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise. (exists fpmp_gap_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise. fpmp_gap_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise + S fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise = w) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_left. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_left + S (fpmp_left_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_left. ff_left_mcp_cell_ics_span_new_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_left * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise)) * ff_left_scale_mcp_cell_ics_span_new_image_raw_np_cell) + (fpmp_left_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_right. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_right + S (fpmp_right_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_np_cell)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_right. ff_right_mcp_cell_ics_span_new_image_raw_np_cell = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_right * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise)) * ff_right_scale_mcp_cell_ics_span_new_image_raw_np_cell) + (fpmp_right_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise))) -> (((exists ff_h_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_target. ff_h_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_target + S (fpmp_target_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise) = S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_np_cell_dot)) /\ exists ff_q_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_target. ff_code_dot_mcp_ics_span_new_image_raw_np_cell_dot = ff_q_fpmp_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise_target * S ((S (fpmp_index_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise)) * ff_scale_dot_mcp_ics_span_new_image_raw_np_cell_dot) + (fpmp_target_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise))) -> fpmp_target_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise = fpmp_left_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise * fpmp_right_dot_mcp_ics_span_new_image_raw_np_cell_dot_pointwise) /\ (exists ff_u_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_start. ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_start + S (0) = S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_start. ff_u_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_start * S ((S (0)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) + (0))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_terminal. ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_terminal + S (ff_value_mcp_prefix_ics_span_new_image_raw_np) = S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_terminal. ff_u_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_terminal * S ((S (w)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) + (ff_value_mcp_prefix_ics_span_new_image_raw_np))) /\ forall ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum. (exists ff_lt_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_bound. ff_lt_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_bound + S ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum = w) -> exists ff_a_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum ff_r_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum ff_s_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum. ((((exists ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_summand. ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_summand + S (ff_a_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_np_cell_dot)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_summand. ff_code_dot_mcp_ics_span_new_image_raw_np_cell_dot = ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_summand * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) * ff_scale_dot_mcp_ics_span_new_image_raw_np_cell_dot) + (ff_a_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_partial. ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_partial + S (ff_r_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) = S ((S (ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_partial. ff_u_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_partial * S ((S (ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) + (ff_r_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum))) /\ ((((exists ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_successor. ff_h_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_successor + S (ff_s_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) = S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) /\ exists ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_successor. ff_u_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum = ff_q_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum_successor * S ((S (S ff_i_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum)) * ff_v_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum) + (ff_s_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum))) /\ ff_s_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum = ff_r_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum + ff_a_dot_mcp_ics_span_new_image_raw_np_cell_dot_sum))))))))))) /\ (((exists fs_h_mcp_ics_span_new_image_raw_np_entry. fs_h_mcp_ics_span_new_image_raw_np_entry + S (ff_value_mcp_prefix_ics_span_new_image_raw_np) = S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_np_entry. ff_np_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_np_entry * S ((S (ff_index_mcp_prefix_ics_span_new_image_raw_np)) * ff_nps_mcp_smatrix_ics_span_new_image_raw) + (ff_value_mcp_prefix_ics_span_new_image_raw_np))))))) /\ ((forall ff_index_mcp_add_ics_span_new_image_raw_positive ff_left_mcp_add_ics_span_new_image_raw_positive ff_right_mcp_add_ics_span_new_image_raw_positive ff_target_mcp_add_ics_span_new_image_raw_positive. (exists mcp_gap_ics_span_new_image_raw_positive_bound. mcp_gap_ics_span_new_image_raw_positive_bound + S (ff_index_mcp_add_ics_span_new_image_raw_positive) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_new_image_raw_positive_left. fs_h_mcp_ics_span_new_image_raw_positive_left + S (ff_left_mcp_add_ics_span_new_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_new_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_positive_left. ff_pp_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_positive_left * S ((S (ff_index_mcp_add_ics_span_new_image_raw_positive)) * ff_pps_mcp_smatrix_ics_span_new_image_raw) + (ff_left_mcp_add_ics_span_new_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_new_image_raw_positive_right. fs_h_mcp_ics_span_new_image_raw_positive_right + S (ff_right_mcp_add_ics_span_new_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_new_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_positive_right. ff_nn_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_positive_right * S ((S (ff_index_mcp_add_ics_span_new_image_raw_positive)) * ff_nns_mcp_smatrix_ics_span_new_image_raw) + (ff_right_mcp_add_ics_span_new_image_raw_positive))) -> (((exists fs_h_mcp_ics_span_new_image_raw_positive_target. fs_h_mcp_ics_span_new_image_raw_positive_target + S (ff_target_mcp_add_ics_span_new_image_raw_positive) = S ((S (ff_index_mcp_add_ics_span_new_image_raw_positive)) * ics_raw_positive_scale_span_new_image)) /\ exists fs_q_mcp_ics_span_new_image_raw_positive_target. ics_raw_positive_span_new_image = fs_q_mcp_ics_span_new_image_raw_positive_target * S ((S (ff_index_mcp_add_ics_span_new_image_raw_positive)) * ics_raw_positive_scale_span_new_image) + (ff_target_mcp_add_ics_span_new_image_raw_positive))) -> ff_target_mcp_add_ics_span_new_image_raw_positive = ff_left_mcp_add_ics_span_new_image_raw_positive + ff_right_mcp_add_ics_span_new_image_raw_positive) /\ (forall ff_index_mcp_add_ics_span_new_image_raw_negative ff_left_mcp_add_ics_span_new_image_raw_negative ff_right_mcp_add_ics_span_new_image_raw_negative ff_target_mcp_add_ics_span_new_image_raw_negative. (exists mcp_gap_ics_span_new_image_raw_negative_bound. mcp_gap_ics_span_new_image_raw_negative_bound + S (ff_index_mcp_add_ics_span_new_image_raw_negative) = ((r) * (1))) -> (((exists fs_h_mcp_ics_span_new_image_raw_negative_left. fs_h_mcp_ics_span_new_image_raw_negative_left + S (ff_left_mcp_add_ics_span_new_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_new_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_negative_left. ff_pn_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_negative_left * S ((S (ff_index_mcp_add_ics_span_new_image_raw_negative)) * ff_pns_mcp_smatrix_ics_span_new_image_raw) + (ff_left_mcp_add_ics_span_new_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_new_image_raw_negative_right. fs_h_mcp_ics_span_new_image_raw_negative_right + S (ff_right_mcp_add_ics_span_new_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_new_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_new_image_raw)) /\ exists fs_q_mcp_ics_span_new_image_raw_negative_right. ff_np_mcp_smatrix_ics_span_new_image_raw = fs_q_mcp_ics_span_new_image_raw_negative_right * S ((S (ff_index_mcp_add_ics_span_new_image_raw_negative)) * ff_nps_mcp_smatrix_ics_span_new_image_raw) + (ff_right_mcp_add_ics_span_new_image_raw_negative))) -> (((exists fs_h_mcp_ics_span_new_image_raw_negative_target. fs_h_mcp_ics_span_new_image_raw_negative_target + S (ff_target_mcp_add_ics_span_new_image_raw_negative) = S ((S (ff_index_mcp_add_ics_span_new_image_raw_negative)) * ics_raw_negative_scale_span_new_image)) /\ exists fs_q_mcp_ics_span_new_image_raw_negative_target. ics_raw_negative_span_new_image = fs_q_mcp_ics_span_new_image_raw_negative_target * S ((S (ff_index_mcp_add_ics_span_new_image_raw_negative)) * ics_raw_negative_scale_span_new_image) + (ff_target_mcp_add_ics_span_new_image_raw_negative))) -> ff_target_mcp_add_ics_span_new_image_raw_negative = ff_left_mcp_add_ics_span_new_image_raw_negative + ff_right_mcp_add_ics_span_new_image_raw_negative))))))) /\ (forall ics_index_span_new_image_equal ics_value0_span_new_image_equal ics_value1_span_new_image_equal ics_value2_span_new_image_equal ics_value3_span_new_image_equal. (exists ics_gap_span_new_image_equal_bound. ics_gap_span_new_image_equal_bound + S (ics_index_span_new_image_equal) = (r)) -> (((exists fs_h_ics_span_new_image_equal_at0. fs_h_ics_span_new_image_equal_at0 + S (ics_value0_span_new_image_equal) = S ((S (ics_index_span_new_image_equal)) * ics_raw_positive_scale_span_new_image)) /\ exists fs_q_ics_span_new_image_equal_at0. ics_raw_positive_span_new_image = fs_q_ics_span_new_image_equal_at0 * S ((S (ics_index_span_new_image_equal)) * ics_raw_positive_scale_span_new_image) + (ics_value0_span_new_image_equal))) -> (((exists fs_h_ics_span_new_image_equal_at1. fs_h_ics_span_new_image_equal_at1 + S (ics_value1_span_new_image_equal) = S ((S (ics_index_span_new_image_equal)) * ics_raw_negative_scale_span_new_image)) /\ exists fs_q_ics_span_new_image_equal_at1. ics_raw_negative_span_new_image = fs_q_ics_span_new_image_equal_at1 * S ((S (ics_index_span_new_image_equal)) * ics_raw_negative_scale_span_new_image) + (ics_value1_span_new_image_equal))) -> (((exists fs_h_ics_span_new_image_equal_at2. fs_h_ics_span_new_image_equal_at2 + S (ics_value2_span_new_image_equal) = S ((S (ics_index_span_new_image_equal)) * rc)) /\ exists fs_q_ics_span_new_image_equal_at2. rb = fs_q_ics_span_new_image_equal_at2 * S ((S (ics_index_span_new_image_equal)) * rc) + (ics_value2_span_new_image_equal))) -> (((exists fs_h_ics_span_new_image_equal_at3. fs_h_ics_span_new_image_equal_at3 + S (ics_value3_span_new_image_equal) = S ((S (ics_index_span_new_image_equal)) * sc)) /\ exists fs_q_ics_span_new_image_equal_at3. sb = fs_q_ics_span_new_image_equal_at3 * S ((S (ics_index_span_new_image_equal)) * sc) + (ics_value3_span_new_image_equal))) -> ics_value0_span_new_image_equal + ics_value3_span_new_image_equal = ics_value2_span_new_image_equal + ics_value1_span_new_image_equal)))))))) - 0031
specialize integer_matrix_vector_add_constructive (ab) - 0032
specialize integer_matrix_vector_add_constructive (ac) - 0033
specialize integer_matrix_vector_add_constructive (db) - 0034
specialize integer_matrix_vector_add_constructive (dc) - 0035
specialize integer_matrix_vector_add_constructive (x) - 0036
specialize integer_matrix_vector_add_constructive (x1) - 0037
specialize integer_matrix_vector_add_constructive (x2) - 0038
specialize integer_matrix_vector_add_constructive (x3) - 0039
specialize integer_matrix_vector_add_constructive (x4) - 0040
specialize integer_matrix_vector_add_constructive (x5) - 0041
specialize integer_matrix_vector_add_constructive (x6) - 0042
specialize integer_matrix_vector_add_constructive (x7) - 0043
specialize integer_matrix_vector_add_constructive (w) - 0044
specialize integer_matrix_vector_add_constructive (r) - 0045
specialize integer_matrix_vector_add_constructive (pb) - 0046
specialize integer_matrix_vector_add_constructive (pc) - 0047
specialize integer_matrix_vector_add_constructive (nb) - 0048
specialize integer_matrix_vector_add_constructive (nc) - 0049
specialize integer_matrix_vector_add_constructive (qb) - 0050
specialize integer_matrix_vector_add_constructive (qc) - 0051
specialize integer_matrix_vector_add_constructive (mb) - 0052
specialize integer_matrix_vector_add_constructive (mc) - 0053
specialize integer_matrix_vector_add_constructive (rb) - 0054
specialize integer_matrix_vector_add_constructive (rc) - 0055
specialize integer_matrix_vector_add_constructive (sb) - 0056
specialize integer_matrix_vector_add_constructive (sc) - 0057
apply integer_matrix_vector_add_constructive - 0058
exact hfirst_witness_witness_witness_witness - 0059
exact hsecond_witness_witness_witness_witness - 0060
exact hadd - 0061
cases hcoeff - 0062
cases hcoeff_witness - 0063
cases hcoeff_witness_witness - 0064
cases hcoeff_witness_witness_witness - 0065
cases hcoeff_witness_witness_witness_witness - 0066
cases hcoeff_witness_witness_witness_witness_right - 0067
exists x8 - 0068
exists x9 - 0069
exists x10 - 0070
exists x11 - 0071
exact hcoeff_witness_witness_witness_witness_right_right