eisenstein_successor_row_split_prefix_extend

Exact expanded PA statement

forall p q h sh bb bc db dc tb tc l. (forall efrd_row_index_fubini_row_split_extend_before. (exists efrd_lt_gap_fubini_row_split_extend_before_bound. efrd_lt_gap_fubini_row_split_extend_before_bound + S (efrd_row_index_fubini_row_split_extend_before) = l) -> exists efrd_count_fubini_row_split_extend_before efrd_reduced_count_fubini_row_split_extend_before efrd_terminal_bit_fubini_row_split_extend_before. (((((((exists ff_h_efrd_fubini_row_split_extend_before_entry_outer_entry. ff_h_efrd_fubini_row_split_extend_before_entry_outer_entry + S (efrd_count_fubini_row_split_extend_before) = S ((S (efrd_row_index_fubini_row_split_extend_before)) * bc)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_outer_entry. bb = ff_q_efrd_fubini_row_split_extend_before_entry_outer_entry * S ((S (efrd_row_index_fubini_row_split_extend_before)) * bc) + (efrd_count_fubini_row_split_extend_before))) /\ (((exists ff_h_efrd_fubini_row_split_extend_before_entry_reduced_entry. ff_h_efrd_fubini_row_split_extend_before_entry_reduced_entry + S (efrd_reduced_count_fubini_row_split_extend_before) = S ((S (efrd_row_index_fubini_row_split_extend_before)) * dc)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_reduced_entry. db = ff_q_efrd_fubini_row_split_extend_before_entry_reduced_entry * S ((S (efrd_row_index_fubini_row_split_extend_before)) * dc) + (efrd_reduced_count_fubini_row_split_extend_before)))) /\ (((exists ff_h_efrd_fubini_row_split_extend_before_entry_terminal_entry. ff_h_efrd_fubini_row_split_extend_before_entry_terminal_entry + S (efrd_terminal_bit_fubini_row_split_extend_before) = S ((S (efrd_row_index_fubini_row_split_extend_before)) * tc)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_terminal_entry. tb = ff_q_efrd_fubini_row_split_extend_before_entry_terminal_entry * S ((S (efrd_row_index_fubini_row_split_extend_before)) * tc) + (efrd_terminal_bit_fubini_row_split_extend_before)))) /\ (exists efrd_row_code_fubini_row_split_extend_before_entry_split efrd_row_scale_fubini_row_split_extend_before_entry_split. (((((forall eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix. (exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_bound. eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_bound + S (eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix) = sh) -> exists eri_bit_efrd_fubini_row_split_extend_before_entry_split_successor_prefix. ((((exists ff_h_eri_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_decoded. ff_h_eri_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_decoded + S (eri_bit_efrd_fubini_row_split_extend_before_entry_split_successor_prefix) = S ((S (eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_eri_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_decoded. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_eri_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_decoded * S ((S (eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (eri_bit_efrd_fubini_row_split_extend_before_entry_split_successor_prefix))) /\ (((eri_bit_efrd_fubini_row_split_extend_before_entry_split_successor_prefix = 0 /\ ((exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_before) = p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix) = q * S efrd_row_index_fubini_row_split_extend_before))) \/ (eri_bit_efrd_fubini_row_split_extend_before_entry_split_successor_prefix = 1 /\ ((exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix) = q * S efrd_row_index_fubini_row_split_extend_before) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_before_entry_split_successor_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_before) = p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_successor_prefix))))))) /\ (((exists ff_u_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_start. ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_start. ff_u_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_terminal. ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_terminal + S (efrd_count_fubini_row_split_extend_before) = S ((S (sh)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_terminal. ff_u_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_terminal * S ((S (sh)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) + (efrd_count_fubini_row_split_extend_before))) /\ forall ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum. (exists ff_lt_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_bound. ff_lt_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_bound + S ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum = sh) -> exists ff_a_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum ff_r_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum ff_s_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_summand. ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_summand + S (ff_a_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_summand. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_summand * S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (ff_a_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_partial. ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_partial + S (ff_r_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_partial. ff_u_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_partial * S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) + (ff_r_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_successor. ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_successor + S (ff_s_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) = S ((S (S ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_successor. ff_u_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum_successor * S ((S (S ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum) + (ff_s_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum))) /\ ff_s_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum = ff_r_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum + ff_a_efrd_fubini_row_split_extend_before_entry_split_successor_count_sum)))))) /\ (forall ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits. (exists ff_lt_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits_bound. ff_lt_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits_bound + S ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits = sh) -> exists ff_bit_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits. ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits_decoded. ff_h_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits_decoded + S (ff_bit_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits) = S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits_decoded. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits_decoded * S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (ff_bit_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits))) /\ (ff_bit_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits = 0 \/ ff_bit_efrd_fubini_row_split_extend_before_entry_split_successor_count_bits = 1)))))) /\ ((forall eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix. (exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_bound. eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_bound + S (eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix) = h) -> exists eri_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix. ((((exists ff_h_eri_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_decoded. ff_h_eri_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_decoded + S (eri_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix) = S ((S (eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_eri_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_decoded. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_eri_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_decoded * S ((S (eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (eri_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix))) /\ (((eri_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix = 0 /\ ((exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_before) = p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix) = q * S efrd_row_index_fubini_row_split_extend_before))) \/ (eri_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix = 1 /\ ((exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix) = q * S efrd_row_index_fubini_row_split_extend_before) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_before) = p * S eri_column_efrd_fubini_row_split_extend_before_entry_split_reduced_prefix))))))) /\ (((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_terminal_entry. ff_h_efrd_fubini_row_split_extend_before_entry_split_terminal_entry + S (efrd_terminal_bit_fubini_row_split_extend_before) = S ((S (h)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_terminal_entry. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_efrd_fubini_row_split_extend_before_entry_split_terminal_entry * S ((S (h)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (efrd_terminal_bit_fubini_row_split_extend_before))))) /\ (((((exists ff_u_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_start. ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_start. ff_u_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_terminal. ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_terminal + S (efrd_reduced_count_fubini_row_split_extend_before) = S ((S (h)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_terminal. ff_u_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_terminal * S ((S (h)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) + (efrd_reduced_count_fubini_row_split_extend_before))) /\ forall ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum. (exists ff_lt_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_bound. ff_lt_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_bound + S ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum = h) -> exists ff_a_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum ff_r_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum ff_s_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_summand. ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_summand + S (ff_a_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_summand. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_summand * S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (ff_a_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_partial. ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_partial + S (ff_r_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_partial. ff_u_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_partial * S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) + (ff_r_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_successor. ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_successor + S (ff_s_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) = S ((S (S ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_successor. ff_u_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum_successor * S ((S (S ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum) + (ff_s_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum))) /\ ff_s_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum = ff_r_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum + ff_a_efrd_fubini_row_split_extend_before_entry_split_reduced_count_sum)))))) /\ (forall ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits. (exists ff_lt_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits_bound. ff_lt_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits_bound + S ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits = h) -> exists ff_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits. ((((exists ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits_decoded. ff_h_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits_decoded + S (ff_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits) = S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits)) * efrd_row_scale_fubini_row_split_extend_before_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits_decoded. efrd_row_code_fubini_row_split_extend_before_entry_split = ff_q_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits_decoded * S ((S (ff_i_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits)) * efrd_row_scale_fubini_row_split_extend_before_entry_split) + (ff_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits))) /\ (ff_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits = 0 \/ ff_bit_efrd_fubini_row_split_extend_before_entry_split_reduced_count_bits = 1))))) /\ (efrd_terminal_bit_fubini_row_split_extend_before = 0 \/ efrd_terminal_bit_fubini_row_split_extend_before = 1)) /\ efrd_count_fubini_row_split_extend_before = efrd_reduced_count_fubini_row_split_extend_before + efrd_terminal_bit_fubini_row_split_extend_before))))))) -> (exists n r a. ((((exists ff_h_fubini_row_split_extend_last_source. ff_h_fubini_row_split_extend_last_source + S (n) = S ((S (l)) * bc)) /\ exists ff_q_fubini_row_split_extend_last_source. bb = ff_q_fubini_row_split_extend_last_source * S ((S (l)) * bc) + (n))) /\ (exists efrd_row_code_fubini_row_split_extend_last_witness efrd_row_scale_fubini_row_split_extend_last_witness. (((((forall eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix. (exists eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_bound. eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_bound + S (eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix) = sh) -> exists eri_bit_efrd_fubini_row_split_extend_last_witness_successor_prefix. ((((exists ff_h_eri_efrd_fubini_row_split_extend_last_witness_successor_prefix_decoded. ff_h_eri_efrd_fubini_row_split_extend_last_witness_successor_prefix_decoded + S (eri_bit_efrd_fubini_row_split_extend_last_witness_successor_prefix) = S ((S (eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_eri_efrd_fubini_row_split_extend_last_witness_successor_prefix_decoded. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_eri_efrd_fubini_row_split_extend_last_witness_successor_prefix_decoded * S ((S (eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (eri_bit_efrd_fubini_row_split_extend_last_witness_successor_prefix))) /\ (((eri_bit_efrd_fubini_row_split_extend_last_witness_successor_prefix = 0 /\ ((exists eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_left + S (q * S l) = p * S eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix) = q * S l))) \/ (eri_bit_efrd_fubini_row_split_extend_last_witness_successor_prefix = 1 /\ ((exists eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix) = q * S l) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_last_witness_successor_prefix_choice_left + S (q * S l) = p * S eri_column_efrd_fubini_row_split_extend_last_witness_successor_prefix))))))) /\ (((exists ff_u_efrd_fubini_row_split_extend_last_witness_successor_count_sum ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_start. ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_start. ff_u_efrd_fubini_row_split_extend_last_witness_successor_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_terminal. ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_terminal + S (n) = S ((S (sh)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_terminal. ff_u_efrd_fubini_row_split_extend_last_witness_successor_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_terminal * S ((S (sh)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum) + (n))) /\ forall ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum. (exists ff_lt_efrd_fubini_row_split_extend_last_witness_successor_count_sum_bound. ff_lt_efrd_fubini_row_split_extend_last_witness_successor_count_sum_bound + S ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum = sh) -> exists ff_a_efrd_fubini_row_split_extend_last_witness_successor_count_sum ff_r_efrd_fubini_row_split_extend_last_witness_successor_count_sum ff_s_efrd_fubini_row_split_extend_last_witness_successor_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_summand. ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_summand + S (ff_a_efrd_fubini_row_split_extend_last_witness_successor_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_summand. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_summand * S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (ff_a_efrd_fubini_row_split_extend_last_witness_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_partial. ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_partial + S (ff_r_efrd_fubini_row_split_extend_last_witness_successor_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_partial. ff_u_efrd_fubini_row_split_extend_last_witness_successor_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_partial * S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum) + (ff_r_efrd_fubini_row_split_extend_last_witness_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_successor. ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_sum_successor + S (ff_s_efrd_fubini_row_split_extend_last_witness_successor_count_sum) = S ((S (S ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_successor. ff_u_efrd_fubini_row_split_extend_last_witness_successor_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_sum_successor * S ((S (S ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_successor_count_sum) + (ff_s_efrd_fubini_row_split_extend_last_witness_successor_count_sum))) /\ ff_s_efrd_fubini_row_split_extend_last_witness_successor_count_sum = ff_r_efrd_fubini_row_split_extend_last_witness_successor_count_sum + ff_a_efrd_fubini_row_split_extend_last_witness_successor_count_sum)))))) /\ (forall ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_bits. (exists ff_lt_efrd_fubini_row_split_extend_last_witness_successor_count_bits_bound. ff_lt_efrd_fubini_row_split_extend_last_witness_successor_count_bits_bound + S ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_bits = sh) -> exists ff_bit_efrd_fubini_row_split_extend_last_witness_successor_count_bits. ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_bits_decoded. ff_h_efrd_fubini_row_split_extend_last_witness_successor_count_bits_decoded + S (ff_bit_efrd_fubini_row_split_extend_last_witness_successor_count_bits) = S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_bits)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_bits_decoded. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_efrd_fubini_row_split_extend_last_witness_successor_count_bits_decoded * S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_successor_count_bits)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (ff_bit_efrd_fubini_row_split_extend_last_witness_successor_count_bits))) /\ (ff_bit_efrd_fubini_row_split_extend_last_witness_successor_count_bits = 0 \/ ff_bit_efrd_fubini_row_split_extend_last_witness_successor_count_bits = 1)))))) /\ ((forall eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix. (exists eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_bound. eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_bound + S (eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix) = h) -> exists eri_bit_efrd_fubini_row_split_extend_last_witness_reduced_prefix. ((((exists ff_h_eri_efrd_fubini_row_split_extend_last_witness_reduced_prefix_decoded. ff_h_eri_efrd_fubini_row_split_extend_last_witness_reduced_prefix_decoded + S (eri_bit_efrd_fubini_row_split_extend_last_witness_reduced_prefix) = S ((S (eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_eri_efrd_fubini_row_split_extend_last_witness_reduced_prefix_decoded. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_eri_efrd_fubini_row_split_extend_last_witness_reduced_prefix_decoded * S ((S (eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (eri_bit_efrd_fubini_row_split_extend_last_witness_reduced_prefix))) /\ (((eri_bit_efrd_fubini_row_split_extend_last_witness_reduced_prefix = 0 /\ ((exists eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_left + S (q * S l) = p * S eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix) = q * S l))) \/ (eri_bit_efrd_fubini_row_split_extend_last_witness_reduced_prefix = 1 /\ ((exists eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix) = q * S l) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_last_witness_reduced_prefix_choice_left + S (q * S l) = p * S eri_column_efrd_fubini_row_split_extend_last_witness_reduced_prefix))))))) /\ (((exists ff_h_efrd_fubini_row_split_extend_last_witness_terminal_entry. ff_h_efrd_fubini_row_split_extend_last_witness_terminal_entry + S (a) = S ((S (h)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_terminal_entry. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_efrd_fubini_row_split_extend_last_witness_terminal_entry * S ((S (h)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (a))))) /\ (((((exists ff_u_efrd_fubini_row_split_extend_last_witness_reduced_count_sum ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_start. ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_start. ff_u_efrd_fubini_row_split_extend_last_witness_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_terminal. ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_terminal + S (r) = S ((S (h)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_terminal. ff_u_efrd_fubini_row_split_extend_last_witness_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_terminal * S ((S (h)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) + (r))) /\ forall ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum. (exists ff_lt_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_bound. ff_lt_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_bound + S ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum = h) -> exists ff_a_efrd_fubini_row_split_extend_last_witness_reduced_count_sum ff_r_efrd_fubini_row_split_extend_last_witness_reduced_count_sum ff_s_efrd_fubini_row_split_extend_last_witness_reduced_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_summand. ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_summand + S (ff_a_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_summand. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_summand * S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (ff_a_efrd_fubini_row_split_extend_last_witness_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_partial. ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_partial + S (ff_r_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_partial. ff_u_efrd_fubini_row_split_extend_last_witness_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_partial * S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) + (ff_r_efrd_fubini_row_split_extend_last_witness_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_successor. ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_successor + S (ff_s_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) = S ((S (S ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_successor. ff_u_efrd_fubini_row_split_extend_last_witness_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_sum_successor * S ((S (S ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_last_witness_reduced_count_sum) + (ff_s_efrd_fubini_row_split_extend_last_witness_reduced_count_sum))) /\ ff_s_efrd_fubini_row_split_extend_last_witness_reduced_count_sum = ff_r_efrd_fubini_row_split_extend_last_witness_reduced_count_sum + ff_a_efrd_fubini_row_split_extend_last_witness_reduced_count_sum)))))) /\ (forall ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_bits. (exists ff_lt_efrd_fubini_row_split_extend_last_witness_reduced_count_bits_bound. ff_lt_efrd_fubini_row_split_extend_last_witness_reduced_count_bits_bound + S ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_bits = h) -> exists ff_bit_efrd_fubini_row_split_extend_last_witness_reduced_count_bits. ((((exists ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_bits_decoded. ff_h_efrd_fubini_row_split_extend_last_witness_reduced_count_bits_decoded + S (ff_bit_efrd_fubini_row_split_extend_last_witness_reduced_count_bits) = S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_bits)) * efrd_row_scale_fubini_row_split_extend_last_witness)) /\ exists ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_bits_decoded. efrd_row_code_fubini_row_split_extend_last_witness = ff_q_efrd_fubini_row_split_extend_last_witness_reduced_count_bits_decoded * S ((S (ff_i_efrd_fubini_row_split_extend_last_witness_reduced_count_bits)) * efrd_row_scale_fubini_row_split_extend_last_witness) + (ff_bit_efrd_fubini_row_split_extend_last_witness_reduced_count_bits))) /\ (ff_bit_efrd_fubini_row_split_extend_last_witness_reduced_count_bits = 0 \/ ff_bit_efrd_fubini_row_split_extend_last_witness_reduced_count_bits = 1))))) /\ (a = 0 \/ a = 1)) /\ n = r + a)))))) -> exists eb ec ub uc. (forall efrd_row_index_fubini_row_split_extend_after. (exists efrd_lt_gap_fubini_row_split_extend_after_bound. efrd_lt_gap_fubini_row_split_extend_after_bound + S (efrd_row_index_fubini_row_split_extend_after) = S l) -> exists efrd_count_fubini_row_split_extend_after efrd_reduced_count_fubini_row_split_extend_after efrd_terminal_bit_fubini_row_split_extend_after. (((((((exists ff_h_efrd_fubini_row_split_extend_after_entry_outer_entry. ff_h_efrd_fubini_row_split_extend_after_entry_outer_entry + S (efrd_count_fubini_row_split_extend_after) = S ((S (efrd_row_index_fubini_row_split_extend_after)) * bc)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_outer_entry. bb = ff_q_efrd_fubini_row_split_extend_after_entry_outer_entry * S ((S (efrd_row_index_fubini_row_split_extend_after)) * bc) + (efrd_count_fubini_row_split_extend_after))) /\ (((exists ff_h_efrd_fubini_row_split_extend_after_entry_reduced_entry. ff_h_efrd_fubini_row_split_extend_after_entry_reduced_entry + S (efrd_reduced_count_fubini_row_split_extend_after) = S ((S (efrd_row_index_fubini_row_split_extend_after)) * ec)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_reduced_entry. eb = ff_q_efrd_fubini_row_split_extend_after_entry_reduced_entry * S ((S (efrd_row_index_fubini_row_split_extend_after)) * ec) + (efrd_reduced_count_fubini_row_split_extend_after)))) /\ (((exists ff_h_efrd_fubini_row_split_extend_after_entry_terminal_entry. ff_h_efrd_fubini_row_split_extend_after_entry_terminal_entry + S (efrd_terminal_bit_fubini_row_split_extend_after) = S ((S (efrd_row_index_fubini_row_split_extend_after)) * uc)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_terminal_entry. ub = ff_q_efrd_fubini_row_split_extend_after_entry_terminal_entry * S ((S (efrd_row_index_fubini_row_split_extend_after)) * uc) + (efrd_terminal_bit_fubini_row_split_extend_after)))) /\ (exists efrd_row_code_fubini_row_split_extend_after_entry_split efrd_row_scale_fubini_row_split_extend_after_entry_split. (((((forall eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix. (exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_bound. eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_bound + S (eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix) = sh) -> exists eri_bit_efrd_fubini_row_split_extend_after_entry_split_successor_prefix. ((((exists ff_h_eri_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_decoded. ff_h_eri_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_decoded + S (eri_bit_efrd_fubini_row_split_extend_after_entry_split_successor_prefix) = S ((S (eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_eri_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_decoded. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_eri_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_decoded * S ((S (eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (eri_bit_efrd_fubini_row_split_extend_after_entry_split_successor_prefix))) /\ (((eri_bit_efrd_fubini_row_split_extend_after_entry_split_successor_prefix = 0 /\ ((exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_after) = p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix) = q * S efrd_row_index_fubini_row_split_extend_after))) \/ (eri_bit_efrd_fubini_row_split_extend_after_entry_split_successor_prefix = 1 /\ ((exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix) = q * S efrd_row_index_fubini_row_split_extend_after) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_after_entry_split_successor_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_after) = p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_successor_prefix))))))) /\ (((exists ff_u_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_start. ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_start. ff_u_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_terminal. ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_terminal + S (efrd_count_fubini_row_split_extend_after) = S ((S (sh)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_terminal. ff_u_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_terminal * S ((S (sh)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) + (efrd_count_fubini_row_split_extend_after))) /\ forall ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum. (exists ff_lt_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_bound. ff_lt_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_bound + S ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum = sh) -> exists ff_a_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum ff_r_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum ff_s_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_summand. ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_summand + S (ff_a_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_summand. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_summand * S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (ff_a_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_partial. ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_partial + S (ff_r_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_partial. ff_u_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_partial * S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) + (ff_r_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_successor. ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_successor + S (ff_s_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) = S ((S (S ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_successor. ff_u_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum_successor * S ((S (S ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum) + (ff_s_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum))) /\ ff_s_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum = ff_r_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum + ff_a_efrd_fubini_row_split_extend_after_entry_split_successor_count_sum)))))) /\ (forall ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits. (exists ff_lt_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits_bound. ff_lt_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits_bound + S ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits = sh) -> exists ff_bit_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits. ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits_decoded. ff_h_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits_decoded + S (ff_bit_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits) = S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits_decoded. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits_decoded * S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (ff_bit_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits))) /\ (ff_bit_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits = 0 \/ ff_bit_efrd_fubini_row_split_extend_after_entry_split_successor_count_bits = 1)))))) /\ ((forall eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix. (exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_bound. eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_bound + S (eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix) = h) -> exists eri_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix. ((((exists ff_h_eri_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_decoded. ff_h_eri_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_decoded + S (eri_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix) = S ((S (eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_eri_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_decoded. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_eri_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_decoded * S ((S (eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (eri_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix))) /\ (((eri_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix = 0 /\ ((exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_after) = p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix) = q * S efrd_row_index_fubini_row_split_extend_after))) \/ (eri_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix = 1 /\ ((exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_right. eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_right + S (p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix) = q * S efrd_row_index_fubini_row_split_extend_after) /\ ~(exists eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_left. eri_gap_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix_choice_left + S (q * S efrd_row_index_fubini_row_split_extend_after) = p * S eri_column_efrd_fubini_row_split_extend_after_entry_split_reduced_prefix))))))) /\ (((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_terminal_entry. ff_h_efrd_fubini_row_split_extend_after_entry_split_terminal_entry + S (efrd_terminal_bit_fubini_row_split_extend_after) = S ((S (h)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_terminal_entry. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_efrd_fubini_row_split_extend_after_entry_split_terminal_entry * S ((S (h)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (efrd_terminal_bit_fubini_row_split_extend_after))))) /\ (((((exists ff_u_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_start. ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_start + S (0) = S ((S (0)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_start. ff_u_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_start * S ((S (0)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) + (0))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_terminal. ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_terminal + S (efrd_reduced_count_fubini_row_split_extend_after) = S ((S (h)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_terminal. ff_u_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_terminal * S ((S (h)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) + (efrd_reduced_count_fubini_row_split_extend_after))) /\ forall ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum. (exists ff_lt_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_bound. ff_lt_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_bound + S ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum = h) -> exists ff_a_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum ff_r_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum ff_s_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum. ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_summand. ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_summand + S (ff_a_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_summand. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_summand * S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (ff_a_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_partial. ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_partial + S (ff_r_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) = S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_partial. ff_u_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_partial * S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) + (ff_r_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum))) /\ ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_successor. ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_successor + S (ff_s_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) = S ((S (S ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_successor. ff_u_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum = ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum_successor * S ((S (S ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)) * ff_v_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum) + (ff_s_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum))) /\ ff_s_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum = ff_r_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum + ff_a_efrd_fubini_row_split_extend_after_entry_split_reduced_count_sum)))))) /\ (forall ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits. (exists ff_lt_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits_bound. ff_lt_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits_bound + S ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits = h) -> exists ff_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits. ((((exists ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits_decoded. ff_h_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits_decoded + S (ff_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits) = S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits)) * efrd_row_scale_fubini_row_split_extend_after_entry_split)) /\ exists ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits_decoded. efrd_row_code_fubini_row_split_extend_after_entry_split = ff_q_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits_decoded * S ((S (ff_i_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits)) * efrd_row_scale_fubini_row_split_extend_after_entry_split) + (ff_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits))) /\ (ff_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits = 0 \/ ff_bit_efrd_fubini_row_split_extend_after_entry_split_reduced_count_bits = 1))))) /\ (efrd_terminal_bit_fubini_row_split_extend_after = 0 \/ efrd_terminal_bit_fubini_row_split_extend_after = 1)) /\ efrd_count_fubini_row_split_extend_after = efrd_reduced_count_fubini_row_split_extend_after + efrd_terminal_bit_fubini_row_split_extend_after)))))))