eisenstein_transposed_column_decoded_choice

Exact expanded PA statement

forall p q h bb bc i z e k j a. (forall etc_row_index_fubini_total_decoded_choice_column. (exists edt_lt_gap_fubini_total_decoded_choice_column_bound. edt_lt_gap_fubini_total_decoded_choice_column_bound + S (etc_row_index_fubini_total_decoded_choice_column) = k) -> exists etc_bit_fubini_total_decoded_choice_column. ((((exists ff_h_etc_fubini_total_decoded_choice_column_decoded. ff_h_etc_fubini_total_decoded_choice_column_decoded + S (etc_bit_fubini_total_decoded_choice_column) = S ((S (etc_row_index_fubini_total_decoded_choice_column)) * e)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_decoded. z = ff_q_etc_fubini_total_decoded_choice_column_decoded * S ((S (etc_row_index_fubini_total_decoded_choice_column)) * e) + (etc_bit_fubini_total_decoded_choice_column))) /\ (exists etc_count_fubini_total_decoded_choice_column_witness etc_row_code_fubini_total_decoded_choice_column_witness etc_row_scale_fubini_total_decoded_choice_column_witness. ((((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_outer_entry. ff_h_etc_fubini_total_decoded_choice_column_witness_outer_entry + S (etc_count_fubini_total_decoded_choice_column_witness) = S ((S (etc_row_index_fubini_total_decoded_choice_column)) * bc)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_outer_entry. bb = ff_q_etc_fubini_total_decoded_choice_column_witness_outer_entry * S ((S (etc_row_index_fubini_total_decoded_choice_column)) * bc) + (etc_count_fubini_total_decoded_choice_column_witness))) /\ (forall eri_column_etc_fubini_total_decoded_choice_column_witness_row. (exists eri_gap_etc_fubini_total_decoded_choice_column_witness_row_bound. eri_gap_etc_fubini_total_decoded_choice_column_witness_row_bound + S (eri_column_etc_fubini_total_decoded_choice_column_witness_row) = h) -> exists eri_bit_etc_fubini_total_decoded_choice_column_witness_row. ((((exists ff_h_eri_etc_fubini_total_decoded_choice_column_witness_row_decoded. ff_h_eri_etc_fubini_total_decoded_choice_column_witness_row_decoded + S (eri_bit_etc_fubini_total_decoded_choice_column_witness_row) = S ((S (eri_column_etc_fubini_total_decoded_choice_column_witness_row)) * etc_row_scale_fubini_total_decoded_choice_column_witness)) /\ exists ff_q_eri_etc_fubini_total_decoded_choice_column_witness_row_decoded. etc_row_code_fubini_total_decoded_choice_column_witness = ff_q_eri_etc_fubini_total_decoded_choice_column_witness_row_decoded * S ((S (eri_column_etc_fubini_total_decoded_choice_column_witness_row)) * etc_row_scale_fubini_total_decoded_choice_column_witness) + (eri_bit_etc_fubini_total_decoded_choice_column_witness_row))) /\ (((eri_bit_etc_fubini_total_decoded_choice_column_witness_row = 0 /\ ((exists eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_left. eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_left + S (p * S etc_row_index_fubini_total_decoded_choice_column) = q * S eri_column_etc_fubini_total_decoded_choice_column_witness_row) /\ ~(exists eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_right. eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_right + S (q * S eri_column_etc_fubini_total_decoded_choice_column_witness_row) = p * S etc_row_index_fubini_total_decoded_choice_column))) \/ (eri_bit_etc_fubini_total_decoded_choice_column_witness_row = 1 /\ ((exists eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_right. eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_right + S (q * S eri_column_etc_fubini_total_decoded_choice_column_witness_row) = p * S etc_row_index_fubini_total_decoded_choice_column) /\ ~(exists eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_left. eri_gap_etc_fubini_total_decoded_choice_column_witness_row_choice_left + S (p * S etc_row_index_fubini_total_decoded_choice_column) = q * S eri_column_etc_fubini_total_decoded_choice_column_witness_row)))))))) /\ (((exists ff_u_etc_fubini_total_decoded_choice_column_witness_count_relation_sum ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum. ((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_start. ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_start + S (0) = S ((S (0)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_start. ff_u_etc_fubini_total_decoded_choice_column_witness_count_relation_sum = ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_start * S ((S (0)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) + (0))) /\ ((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_terminal. ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_terminal + S (etc_count_fubini_total_decoded_choice_column_witness) = S ((S (h)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_terminal. ff_u_etc_fubini_total_decoded_choice_column_witness_count_relation_sum = ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_terminal * S ((S (h)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) + (etc_count_fubini_total_decoded_choice_column_witness))) /\ forall ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum. (exists ff_lt_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_bound. ff_lt_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_bound + S ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum = h) -> exists ff_a_etc_fubini_total_decoded_choice_column_witness_count_relation_sum ff_r_etc_fubini_total_decoded_choice_column_witness_count_relation_sum ff_s_etc_fubini_total_decoded_choice_column_witness_count_relation_sum. ((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_summand. ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_summand + S (ff_a_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) = S ((S (ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) * etc_row_scale_fubini_total_decoded_choice_column_witness)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_summand. etc_row_code_fubini_total_decoded_choice_column_witness = ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_summand * S ((S (ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) * etc_row_scale_fubini_total_decoded_choice_column_witness) + (ff_a_etc_fubini_total_decoded_choice_column_witness_count_relation_sum))) /\ ((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_partial. ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_partial + S (ff_r_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) = S ((S (ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_partial. ff_u_etc_fubini_total_decoded_choice_column_witness_count_relation_sum = ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_partial * S ((S (ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) + (ff_r_etc_fubini_total_decoded_choice_column_witness_count_relation_sum))) /\ ((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_successor. ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_successor + S (ff_s_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) = S ((S (S ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_successor. ff_u_etc_fubini_total_decoded_choice_column_witness_count_relation_sum = ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_sum_successor * S ((S (S ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)) * ff_v_etc_fubini_total_decoded_choice_column_witness_count_relation_sum) + (ff_s_etc_fubini_total_decoded_choice_column_witness_count_relation_sum))) /\ ff_s_etc_fubini_total_decoded_choice_column_witness_count_relation_sum = ff_r_etc_fubini_total_decoded_choice_column_witness_count_relation_sum + ff_a_etc_fubini_total_decoded_choice_column_witness_count_relation_sum)))))) /\ (forall ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_bits. (exists ff_lt_etc_fubini_total_decoded_choice_column_witness_count_relation_bits_bound. ff_lt_etc_fubini_total_decoded_choice_column_witness_count_relation_bits_bound + S ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_bits = h) -> exists ff_bit_etc_fubini_total_decoded_choice_column_witness_count_relation_bits. ((((exists ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_bits_decoded. ff_h_etc_fubini_total_decoded_choice_column_witness_count_relation_bits_decoded + S (ff_bit_etc_fubini_total_decoded_choice_column_witness_count_relation_bits) = S ((S (ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_bits)) * etc_row_scale_fubini_total_decoded_choice_column_witness)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_bits_decoded. etc_row_code_fubini_total_decoded_choice_column_witness = ff_q_etc_fubini_total_decoded_choice_column_witness_count_relation_bits_decoded * S ((S (ff_i_etc_fubini_total_decoded_choice_column_witness_count_relation_bits)) * etc_row_scale_fubini_total_decoded_choice_column_witness) + (ff_bit_etc_fubini_total_decoded_choice_column_witness_count_relation_bits))) /\ (ff_bit_etc_fubini_total_decoded_choice_column_witness_count_relation_bits = 0 \/ ff_bit_etc_fubini_total_decoded_choice_column_witness_count_relation_bits = 1)))))) /\ (((exists ff_h_etc_fubini_total_decoded_choice_column_witness_inner_entry. ff_h_etc_fubini_total_decoded_choice_column_witness_inner_entry + S (etc_bit_fubini_total_decoded_choice_column) = S ((S (i)) * etc_row_scale_fubini_total_decoded_choice_column_witness)) /\ exists ff_q_etc_fubini_total_decoded_choice_column_witness_inner_entry. etc_row_code_fubini_total_decoded_choice_column_witness = ff_q_etc_fubini_total_decoded_choice_column_witness_inner_entry * S ((S (i)) * etc_row_scale_fubini_total_decoded_choice_column_witness) + (etc_bit_fubini_total_decoded_choice_column))))))) -> (exists edt_lt_gap_fubini_total_decoded_choice_fixed_bound. edt_lt_gap_fubini_total_decoded_choice_fixed_bound + S (i) = h) -> (exists edt_lt_gap_fubini_total_row_bound. edt_lt_gap_fubini_total_row_bound + S (j) = k) -> (((exists ff_h_fubini_total_decoded_choice_entry. ff_h_fubini_total_decoded_choice_entry + S (a) = S ((S (j)) * e)) /\ exists ff_q_fubini_total_decoded_choice_entry. z = ff_q_fubini_total_decoded_choice_entry * S ((S (j)) * e) + (a))) -> (((a = 0 /\ ((exists eri_gap_fubini_total_decoded_choice_result_left. eri_gap_fubini_total_decoded_choice_result_left + S (p * S j) = q * S i) /\ ~(exists eri_gap_fubini_total_decoded_choice_result_right. eri_gap_fubini_total_decoded_choice_result_right + S (q * S i) = p * S j))) \/ (a = 1 /\ ((exists eri_gap_fubini_total_decoded_choice_result_right. eri_gap_fubini_total_decoded_choice_result_right + S (q * S i) = p * S j) /\ ~(exists eri_gap_fubini_total_decoded_choice_result_left. eri_gap_fubini_total_decoded_choice_result_left + S (p * S j) = q * S i)))))