eisenstein_successor_row_split_reduced_rectangle_prefix

Exact expanded PA statement

forall p q h sh bb bc db dc tb tc l. (forall efrd_row_index_fubini_reduced_projection_split. (exists efrd_lt_gap_fubini_reduced_projection_split_bound. efrd_lt_gap_fubini_reduced_projection_split_bound + S (efrd_row_index_fubini_reduced_projection_split) = l) -> exists efrd_count_fubini_reduced_projection_split efrd_reduced_count_fubini_reduced_projection_split efrd_terminal_bit_fubini_reduced_projection_split. (((((((exists ff_h_efrd_fubini_reduced_projection_split_entry_outer_entry. ff_h_efrd_fubini_reduced_projection_split_entry_outer_entry + S (efrd_count_fubini_reduced_projection_split) = S ((S (efrd_row_index_fubini_reduced_projection_split)) * bc)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_outer_entry. bb = ff_q_efrd_fubini_reduced_projection_split_entry_outer_entry * S ((S (efrd_row_index_fubini_reduced_projection_split)) * bc) + (efrd_count_fubini_reduced_projection_split))) /\ (((exists ff_h_efrd_fubini_reduced_projection_split_entry_reduced_entry. ff_h_efrd_fubini_reduced_projection_split_entry_reduced_entry + S (efrd_reduced_count_fubini_reduced_projection_split) = S ((S (efrd_row_index_fubini_reduced_projection_split)) * dc)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_reduced_entry. db = ff_q_efrd_fubini_reduced_projection_split_entry_reduced_entry * S ((S (efrd_row_index_fubini_reduced_projection_split)) * dc) + (efrd_reduced_count_fubini_reduced_projection_split)))) /\ (((exists ff_h_efrd_fubini_reduced_projection_split_entry_terminal_entry. ff_h_efrd_fubini_reduced_projection_split_entry_terminal_entry + S (efrd_terminal_bit_fubini_reduced_projection_split) = S ((S (efrd_row_index_fubini_reduced_projection_split)) * tc)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_terminal_entry. tb = ff_q_efrd_fubini_reduced_projection_split_entry_terminal_entry * S ((S (efrd_row_index_fubini_reduced_projection_split)) * tc) + (efrd_terminal_bit_fubini_reduced_projection_split)))) /\ (exists efrd_row_code_fubini_reduced_projection_split_entry_split efrd_row_scale_fubini_reduced_projection_split_entry_split. (((((forall eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix. (exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_bound. eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_bound + S (eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix) = sh) -> exists eri_bit_efrd_fubini_reduced_projection_split_entry_split_successor_prefix. ((((exists ff_h_eri_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_decoded. ff_h_eri_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_decoded + S (eri_bit_efrd_fubini_reduced_projection_split_entry_split_successor_prefix) = S ((S (eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_eri_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_decoded. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_eri_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_decoded * S ((S (eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (eri_bit_efrd_fubini_reduced_projection_split_entry_split_successor_prefix))) /\ (((eri_bit_efrd_fubini_reduced_projection_split_entry_split_successor_prefix = 0 /\ ((exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_left. eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_left + S (q * S efrd_row_index_fubini_reduced_projection_split) = p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix) /\ ~(exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_right. eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix) = q * S efrd_row_index_fubini_reduced_projection_split))) \/ (eri_bit_efrd_fubini_reduced_projection_split_entry_split_successor_prefix = 1 /\ ((exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_right. eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix) = q * S efrd_row_index_fubini_reduced_projection_split) /\ ~(exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_left. eri_gap_efrd_fubini_reduced_projection_split_entry_split_successor_prefix_choice_left + S (q * S efrd_row_index_fubini_reduced_projection_split) = p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_successor_prefix))))))) /\ (((exists ff_u_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum. ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_start. ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_start. ff_u_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_terminal. ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_terminal + S (efrd_count_fubini_reduced_projection_split) = S ((S (sh)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_terminal. ff_u_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_terminal * S ((S (sh)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) + (efrd_count_fubini_reduced_projection_split))) /\ forall ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum. (exists ff_lt_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_bound. ff_lt_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_bound + S ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum = sh) -> exists ff_a_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum ff_r_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum ff_s_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum. ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_summand. ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_summand + S (ff_a_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) = S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_summand. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_summand * S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (ff_a_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_partial. ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_partial + S (ff_r_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) = S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_partial. ff_u_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_partial * S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) + (ff_r_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_successor. ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_successor + S (ff_s_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) = S ((S (S ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_successor. ff_u_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum_successor * S ((S (S ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum) + (ff_s_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum))) /\ ff_s_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum = ff_r_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum + ff_a_efrd_fubini_reduced_projection_split_entry_split_successor_count_sum)))))) /\ (forall ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits. (exists ff_lt_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits_bound. ff_lt_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits_bound + S ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits = sh) -> exists ff_bit_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits. ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits_decoded. ff_h_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits_decoded + S (ff_bit_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits) = S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits_decoded. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits_decoded * S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (ff_bit_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits))) /\ (ff_bit_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits = 0 \/ ff_bit_efrd_fubini_reduced_projection_split_entry_split_successor_count_bits = 1)))))) /\ ((forall eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix. (exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_bound. eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_bound + S (eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix) = h) -> exists eri_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix. ((((exists ff_h_eri_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_decoded. ff_h_eri_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_decoded + S (eri_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix) = S ((S (eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_eri_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_decoded. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_eri_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_decoded * S ((S (eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (eri_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix))) /\ (((eri_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix = 0 /\ ((exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_left. eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_left + S (q * S efrd_row_index_fubini_reduced_projection_split) = p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix) /\ ~(exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_right. eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix) = q * S efrd_row_index_fubini_reduced_projection_split))) \/ (eri_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix = 1 /\ ((exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_right. eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix) = q * S efrd_row_index_fubini_reduced_projection_split) /\ ~(exists eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_left. eri_gap_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix_choice_left + S (q * S efrd_row_index_fubini_reduced_projection_split) = p * S eri_column_efrd_fubini_reduced_projection_split_entry_split_reduced_prefix))))))) /\ (((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_terminal_entry. ff_h_efrd_fubini_reduced_projection_split_entry_split_terminal_entry + S (efrd_terminal_bit_fubini_reduced_projection_split) = S ((S (h)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_terminal_entry. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_efrd_fubini_reduced_projection_split_entry_split_terminal_entry * S ((S (h)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (efrd_terminal_bit_fubini_reduced_projection_split))))) /\ (((((exists ff_u_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum. ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_start. ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_start. ff_u_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_terminal. ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_terminal + S (efrd_reduced_count_fubini_reduced_projection_split) = S ((S (h)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_terminal. ff_u_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_terminal * S ((S (h)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) + (efrd_reduced_count_fubini_reduced_projection_split))) /\ forall ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum. (exists ff_lt_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_bound. ff_lt_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_bound + S ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum = h) -> exists ff_a_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum ff_r_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum ff_s_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum. ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_summand. ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_summand + S (ff_a_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) = S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_summand. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_summand * S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (ff_a_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_partial. ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_partial + S (ff_r_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) = S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_partial. ff_u_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_partial * S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) + (ff_r_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_successor. ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_successor + S (ff_s_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) = S ((S (S ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_successor. ff_u_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum = ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum_successor * S ((S (S ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum) + (ff_s_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum))) /\ ff_s_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum = ff_r_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum + ff_a_efrd_fubini_reduced_projection_split_entry_split_reduced_count_sum)))))) /\ (forall ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits. (exists ff_lt_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits_bound. ff_lt_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits_bound + S ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits = h) -> exists ff_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits. ((((exists ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits_decoded. ff_h_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits_decoded + S (ff_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits) = S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits)) * efrd_row_scale_fubini_reduced_projection_split_entry_split)) /\ exists ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits_decoded. efrd_row_code_fubini_reduced_projection_split_entry_split = ff_q_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits_decoded * S ((S (ff_i_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits)) * efrd_row_scale_fubini_reduced_projection_split_entry_split) + (ff_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits))) /\ (ff_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits = 0 \/ ff_bit_efrd_fubini_reduced_projection_split_entry_split_reduced_count_bits = 1))))) /\ (efrd_terminal_bit_fubini_reduced_projection_split = 0 \/ efrd_terminal_bit_fubini_reduced_projection_split = 1)) /\ efrd_count_fubini_reduced_projection_split = efrd_reduced_count_fubini_reduced_projection_split + efrd_terminal_bit_fubini_reduced_projection_split))))))) -> (forall erc_row_fubini_reduced_projection_rectangle. (exists erc_lt_gap_fubini_reduced_projection_rectangle_bound. erc_lt_gap_fubini_reduced_projection_rectangle_bound + S (erc_row_fubini_reduced_projection_rectangle) = l) -> exists erc_count_fubini_reduced_projection_rectangle. ((((exists ff_h_erc_fubini_reduced_projection_rectangle_decoded. ff_h_erc_fubini_reduced_projection_rectangle_decoded + S (erc_count_fubini_reduced_projection_rectangle) = S ((S (erc_row_fubini_reduced_projection_rectangle)) * dc)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_decoded. db = ff_q_erc_fubini_reduced_projection_rectangle_decoded * S ((S (erc_row_fubini_reduced_projection_rectangle)) * dc) + (erc_count_fubini_reduced_projection_rectangle))) /\ (exists erc_row_code_fubini_reduced_projection_rectangle_witness erc_row_scale_fubini_reduced_projection_rectangle_witness. ((forall eri_column_erc_fubini_reduced_projection_rectangle_witness_row. (exists eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_bound. eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_bound + S (eri_column_erc_fubini_reduced_projection_rectangle_witness_row) = h) -> exists eri_bit_erc_fubini_reduced_projection_rectangle_witness_row. ((((exists ff_h_eri_erc_fubini_reduced_projection_rectangle_witness_row_decoded. ff_h_eri_erc_fubini_reduced_projection_rectangle_witness_row_decoded + S (eri_bit_erc_fubini_reduced_projection_rectangle_witness_row) = S ((S (eri_column_erc_fubini_reduced_projection_rectangle_witness_row)) * erc_row_scale_fubini_reduced_projection_rectangle_witness)) /\ exists ff_q_eri_erc_fubini_reduced_projection_rectangle_witness_row_decoded. erc_row_code_fubini_reduced_projection_rectangle_witness = ff_q_eri_erc_fubini_reduced_projection_rectangle_witness_row_decoded * S ((S (eri_column_erc_fubini_reduced_projection_rectangle_witness_row)) * erc_row_scale_fubini_reduced_projection_rectangle_witness) + (eri_bit_erc_fubini_reduced_projection_rectangle_witness_row))) /\ (((eri_bit_erc_fubini_reduced_projection_rectangle_witness_row = 0 /\ ((exists eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_left. eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_left + S (q * S erc_row_fubini_reduced_projection_rectangle) = p * S eri_column_erc_fubini_reduced_projection_rectangle_witness_row) /\ ~(exists eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_right. eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_right + S (p * S eri_column_erc_fubini_reduced_projection_rectangle_witness_row) = q * S erc_row_fubini_reduced_projection_rectangle))) \/ (eri_bit_erc_fubini_reduced_projection_rectangle_witness_row = 1 /\ ((exists eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_right. eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_right + S (p * S eri_column_erc_fubini_reduced_projection_rectangle_witness_row) = q * S erc_row_fubini_reduced_projection_rectangle) /\ ~(exists eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_left. eri_gap_erc_fubini_reduced_projection_rectangle_witness_row_choice_left + S (q * S erc_row_fubini_reduced_projection_rectangle) = p * S eri_column_erc_fubini_reduced_projection_rectangle_witness_row))))))) /\ (((exists ff_u_erc_fubini_reduced_projection_rectangle_witness_count_sum ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum. ((((exists ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_start. ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_start + S (0) = S ((S (0)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_start. ff_u_erc_fubini_reduced_projection_rectangle_witness_count_sum = ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_start * S ((S (0)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum) + (0))) /\ ((((exists ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_terminal. ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_terminal + S (erc_count_fubini_reduced_projection_rectangle) = S ((S (h)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_terminal. ff_u_erc_fubini_reduced_projection_rectangle_witness_count_sum = ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_terminal * S ((S (h)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum) + (erc_count_fubini_reduced_projection_rectangle))) /\ forall ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum. (exists ff_lt_erc_fubini_reduced_projection_rectangle_witness_count_sum_bound. ff_lt_erc_fubini_reduced_projection_rectangle_witness_count_sum_bound + S ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum = h) -> exists ff_a_erc_fubini_reduced_projection_rectangle_witness_count_sum ff_r_erc_fubini_reduced_projection_rectangle_witness_count_sum ff_s_erc_fubini_reduced_projection_rectangle_witness_count_sum. ((((exists ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_summand. ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_summand + S (ff_a_erc_fubini_reduced_projection_rectangle_witness_count_sum) = S ((S (ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum)) * erc_row_scale_fubini_reduced_projection_rectangle_witness)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_summand. erc_row_code_fubini_reduced_projection_rectangle_witness = ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_summand * S ((S (ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum)) * erc_row_scale_fubini_reduced_projection_rectangle_witness) + (ff_a_erc_fubini_reduced_projection_rectangle_witness_count_sum))) /\ ((((exists ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_partial. ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_partial + S (ff_r_erc_fubini_reduced_projection_rectangle_witness_count_sum) = S ((S (ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_partial. ff_u_erc_fubini_reduced_projection_rectangle_witness_count_sum = ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_partial * S ((S (ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum) + (ff_r_erc_fubini_reduced_projection_rectangle_witness_count_sum))) /\ ((((exists ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_successor. ff_h_erc_fubini_reduced_projection_rectangle_witness_count_sum_successor + S (ff_s_erc_fubini_reduced_projection_rectangle_witness_count_sum) = S ((S (S ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_successor. ff_u_erc_fubini_reduced_projection_rectangle_witness_count_sum = ff_q_erc_fubini_reduced_projection_rectangle_witness_count_sum_successor * S ((S (S ff_i_erc_fubini_reduced_projection_rectangle_witness_count_sum)) * ff_v_erc_fubini_reduced_projection_rectangle_witness_count_sum) + (ff_s_erc_fubini_reduced_projection_rectangle_witness_count_sum))) /\ ff_s_erc_fubini_reduced_projection_rectangle_witness_count_sum = ff_r_erc_fubini_reduced_projection_rectangle_witness_count_sum + ff_a_erc_fubini_reduced_projection_rectangle_witness_count_sum)))))) /\ (forall ff_i_erc_fubini_reduced_projection_rectangle_witness_count_bits. (exists ff_lt_erc_fubini_reduced_projection_rectangle_witness_count_bits_bound. ff_lt_erc_fubini_reduced_projection_rectangle_witness_count_bits_bound + S ff_i_erc_fubini_reduced_projection_rectangle_witness_count_bits = h) -> exists ff_bit_erc_fubini_reduced_projection_rectangle_witness_count_bits. ((((exists ff_h_erc_fubini_reduced_projection_rectangle_witness_count_bits_decoded. ff_h_erc_fubini_reduced_projection_rectangle_witness_count_bits_decoded + S (ff_bit_erc_fubini_reduced_projection_rectangle_witness_count_bits) = S ((S (ff_i_erc_fubini_reduced_projection_rectangle_witness_count_bits)) * erc_row_scale_fubini_reduced_projection_rectangle_witness)) /\ exists ff_q_erc_fubini_reduced_projection_rectangle_witness_count_bits_decoded. erc_row_code_fubini_reduced_projection_rectangle_witness = ff_q_erc_fubini_reduced_projection_rectangle_witness_count_bits_decoded * S ((S (ff_i_erc_fubini_reduced_projection_rectangle_witness_count_bits)) * erc_row_scale_fubini_reduced_projection_rectangle_witness) + (ff_bit_erc_fubini_reduced_projection_rectangle_witness_count_bits))) /\ (ff_bit_erc_fubini_reduced_projection_rectangle_witness_count_bits = 0 \/ ff_bit_erc_fubini_reduced_projection_rectangle_witness_count_bits = 1)))))))))