factorial_length_eq_transport

Exact expanded PA statement

forall n m z. n = m -> (exists ff_b_bcflet_source ff_c_bcflet_source. ((forall ff_i_bcflet_source_range. (exists ff_lt_bcflet_source_range_bound. ff_lt_bcflet_source_range_bound + S ff_i_bcflet_source_range = n) -> (((exists ff_h_bcflet_source_range_decoded. ff_h_bcflet_source_range_decoded + S (1 + ff_i_bcflet_source_range) = S ((S (ff_i_bcflet_source_range)) * ff_c_bcflet_source)) /\ exists ff_q_bcflet_source_range_decoded. ff_b_bcflet_source = ff_q_bcflet_source_range_decoded * S ((S (ff_i_bcflet_source_range)) * ff_c_bcflet_source) + (1 + ff_i_bcflet_source_range)))) /\ (exists ff_u_bcflet_source_product ff_v_bcflet_source_product. ((((exists ff_h_bcflet_source_product_start. ff_h_bcflet_source_product_start + S (1) = S ((S (0)) * ff_v_bcflet_source_product)) /\ exists ff_q_bcflet_source_product_start. ff_u_bcflet_source_product = ff_q_bcflet_source_product_start * S ((S (0)) * ff_v_bcflet_source_product) + (1))) /\ ((((exists ff_h_bcflet_source_product_terminal. ff_h_bcflet_source_product_terminal + S (z) = S ((S (n)) * ff_v_bcflet_source_product)) /\ exists ff_q_bcflet_source_product_terminal. ff_u_bcflet_source_product = ff_q_bcflet_source_product_terminal * S ((S (n)) * ff_v_bcflet_source_product) + (z))) /\ forall ff_i_bcflet_source_product. (exists ff_lt_bcflet_source_product_bound. ff_lt_bcflet_source_product_bound + S ff_i_bcflet_source_product = n) -> exists ff_p_bcflet_source_product ff_r_bcflet_source_product ff_s_bcflet_source_product. ((((exists ff_h_bcflet_source_product_factor. ff_h_bcflet_source_product_factor + S (ff_p_bcflet_source_product) = S ((S (ff_i_bcflet_source_product)) * ff_c_bcflet_source)) /\ exists ff_q_bcflet_source_product_factor. ff_b_bcflet_source = ff_q_bcflet_source_product_factor * S ((S (ff_i_bcflet_source_product)) * ff_c_bcflet_source) + (ff_p_bcflet_source_product))) /\ ((((exists ff_h_bcflet_source_product_partial. ff_h_bcflet_source_product_partial + S (ff_r_bcflet_source_product) = S ((S (ff_i_bcflet_source_product)) * ff_v_bcflet_source_product)) /\ exists ff_q_bcflet_source_product_partial. ff_u_bcflet_source_product = ff_q_bcflet_source_product_partial * S ((S (ff_i_bcflet_source_product)) * ff_v_bcflet_source_product) + (ff_r_bcflet_source_product))) /\ ((((exists ff_h_bcflet_source_product_successor. ff_h_bcflet_source_product_successor + S (ff_s_bcflet_source_product) = S ((S (S ff_i_bcflet_source_product)) * ff_v_bcflet_source_product)) /\ exists ff_q_bcflet_source_product_successor. ff_u_bcflet_source_product = ff_q_bcflet_source_product_successor * S ((S (S ff_i_bcflet_source_product)) * ff_v_bcflet_source_product) + (ff_s_bcflet_source_product))) /\ ff_s_bcflet_source_product = ff_r_bcflet_source_product * ff_p_bcflet_source_product)))))))) -> (exists ff_b_bcflet_target ff_c_bcflet_target. ((forall ff_i_bcflet_target_range. (exists ff_lt_bcflet_target_range_bound. ff_lt_bcflet_target_range_bound + S ff_i_bcflet_target_range = m) -> (((exists ff_h_bcflet_target_range_decoded. ff_h_bcflet_target_range_decoded + S (1 + ff_i_bcflet_target_range) = S ((S (ff_i_bcflet_target_range)) * ff_c_bcflet_target)) /\ exists ff_q_bcflet_target_range_decoded. ff_b_bcflet_target = ff_q_bcflet_target_range_decoded * S ((S (ff_i_bcflet_target_range)) * ff_c_bcflet_target) + (1 + ff_i_bcflet_target_range)))) /\ (exists ff_u_bcflet_target_product ff_v_bcflet_target_product. ((((exists ff_h_bcflet_target_product_start. ff_h_bcflet_target_product_start + S (1) = S ((S (0)) * ff_v_bcflet_target_product)) /\ exists ff_q_bcflet_target_product_start. ff_u_bcflet_target_product = ff_q_bcflet_target_product_start * S ((S (0)) * ff_v_bcflet_target_product) + (1))) /\ ((((exists ff_h_bcflet_target_product_terminal. ff_h_bcflet_target_product_terminal + S (z) = S ((S (m)) * ff_v_bcflet_target_product)) /\ exists ff_q_bcflet_target_product_terminal. ff_u_bcflet_target_product = ff_q_bcflet_target_product_terminal * S ((S (m)) * ff_v_bcflet_target_product) + (z))) /\ forall ff_i_bcflet_target_product. (exists ff_lt_bcflet_target_product_bound. ff_lt_bcflet_target_product_bound + S ff_i_bcflet_target_product = m) -> exists ff_p_bcflet_target_product ff_r_bcflet_target_product ff_s_bcflet_target_product. ((((exists ff_h_bcflet_target_product_factor. ff_h_bcflet_target_product_factor + S (ff_p_bcflet_target_product) = S ((S (ff_i_bcflet_target_product)) * ff_c_bcflet_target)) /\ exists ff_q_bcflet_target_product_factor. ff_b_bcflet_target = ff_q_bcflet_target_product_factor * S ((S (ff_i_bcflet_target_product)) * ff_c_bcflet_target) + (ff_p_bcflet_target_product))) /\ ((((exists ff_h_bcflet_target_product_partial. ff_h_bcflet_target_product_partial + S (ff_r_bcflet_target_product) = S ((S (ff_i_bcflet_target_product)) * ff_v_bcflet_target_product)) /\ exists ff_q_bcflet_target_product_partial. ff_u_bcflet_target_product = ff_q_bcflet_target_product_partial * S ((S (ff_i_bcflet_target_product)) * ff_v_bcflet_target_product) + (ff_r_bcflet_target_product))) /\ ((((exists ff_h_bcflet_target_product_successor. ff_h_bcflet_target_product_successor + S (ff_s_bcflet_target_product) = S ((S (S ff_i_bcflet_target_product)) * ff_v_bcflet_target_product)) /\ exists ff_q_bcflet_target_product_successor. ff_u_bcflet_target_product = ff_q_bcflet_target_product_successor * S ((S (S ff_i_bcflet_target_product)) * ff_v_bcflet_target_product) + (ff_s_bcflet_target_product))) /\ ff_s_bcflet_target_product = ff_r_bcflet_target_product * ff_p_bcflet_target_product))))))))