primorial_index_eq_transport

Exact expanded PA statement

forall n m z. n = m -> (exists bpr_code_bpmit_source bpr_scale_bpmit_source. ((forall bpr_index_bpmit_source_mask. (exists bpr_gap_bpmit_source_mask_bound. bpr_gap_bpmit_source_mask_bound + S (bpr_index_bpmit_source_mask) = n) -> exists bpr_value_bpmit_source_mask. ((((exists bpr_height_bpmit_source_mask_decoded. bpr_height_bpmit_source_mask_decoded + S (bpr_value_bpmit_source_mask) = S ((S (bpr_index_bpmit_source_mask)) * bpr_scale_bpmit_source)) /\ exists bpr_quotient_bpmit_source_mask_decoded. bpr_code_bpmit_source = bpr_quotient_bpmit_source_mask_decoded * S ((S (bpr_index_bpmit_source_mask)) * bpr_scale_bpmit_source) + (bpr_value_bpmit_source_mask))) /\ (((((~(S (bpr_index_bpmit_source_mask) = 1) /\ forall bpr_left_bpmit_source_mask_choice_prime bpr_right_bpmit_source_mask_choice_prime. S (bpr_index_bpmit_source_mask) = bpr_left_bpmit_source_mask_choice_prime * bpr_right_bpmit_source_mask_choice_prime -> bpr_left_bpmit_source_mask_choice_prime = 1 \/ bpr_right_bpmit_source_mask_choice_prime = 1)) /\ bpr_value_bpmit_source_mask = S (bpr_index_bpmit_source_mask)) \/ (~((~(S (bpr_index_bpmit_source_mask) = 1) /\ forall bpr_left_bpmit_source_mask_choice_prime bpr_right_bpmit_source_mask_choice_prime. S (bpr_index_bpmit_source_mask) = bpr_left_bpmit_source_mask_choice_prime * bpr_right_bpmit_source_mask_choice_prime -> bpr_left_bpmit_source_mask_choice_prime = 1 \/ bpr_right_bpmit_source_mask_choice_prime = 1)) /\ bpr_value_bpmit_source_mask = 1))))) /\ (exists ff_u_bpmit_source_product ff_v_bpmit_source_product. ((((exists ff_h_bpmit_source_product_start. ff_h_bpmit_source_product_start + S (1) = S ((S (0)) * ff_v_bpmit_source_product)) /\ exists ff_q_bpmit_source_product_start. ff_u_bpmit_source_product = ff_q_bpmit_source_product_start * S ((S (0)) * ff_v_bpmit_source_product) + (1))) /\ ((((exists ff_h_bpmit_source_product_terminal. ff_h_bpmit_source_product_terminal + S (z) = S ((S (n)) * ff_v_bpmit_source_product)) /\ exists ff_q_bpmit_source_product_terminal. ff_u_bpmit_source_product = ff_q_bpmit_source_product_terminal * S ((S (n)) * ff_v_bpmit_source_product) + (z))) /\ forall ff_i_bpmit_source_product. (exists ff_lt_bpmit_source_product_bound. ff_lt_bpmit_source_product_bound + S ff_i_bpmit_source_product = n) -> exists ff_p_bpmit_source_product ff_r_bpmit_source_product ff_s_bpmit_source_product. ((((exists ff_h_bpmit_source_product_factor. ff_h_bpmit_source_product_factor + S (ff_p_bpmit_source_product) = S ((S (ff_i_bpmit_source_product)) * bpr_scale_bpmit_source)) /\ exists ff_q_bpmit_source_product_factor. bpr_code_bpmit_source = ff_q_bpmit_source_product_factor * S ((S (ff_i_bpmit_source_product)) * bpr_scale_bpmit_source) + (ff_p_bpmit_source_product))) /\ ((((exists ff_h_bpmit_source_product_partial. ff_h_bpmit_source_product_partial + S (ff_r_bpmit_source_product) = S ((S (ff_i_bpmit_source_product)) * ff_v_bpmit_source_product)) /\ exists ff_q_bpmit_source_product_partial. ff_u_bpmit_source_product = ff_q_bpmit_source_product_partial * S ((S (ff_i_bpmit_source_product)) * ff_v_bpmit_source_product) + (ff_r_bpmit_source_product))) /\ ((((exists ff_h_bpmit_source_product_successor. ff_h_bpmit_source_product_successor + S (ff_s_bpmit_source_product) = S ((S (S ff_i_bpmit_source_product)) * ff_v_bpmit_source_product)) /\ exists ff_q_bpmit_source_product_successor. ff_u_bpmit_source_product = ff_q_bpmit_source_product_successor * S ((S (S ff_i_bpmit_source_product)) * ff_v_bpmit_source_product) + (ff_s_bpmit_source_product))) /\ ff_s_bpmit_source_product = ff_r_bpmit_source_product * ff_p_bpmit_source_product)))))))) -> (exists bpr_code_bpmit_target bpr_scale_bpmit_target. ((forall bpr_index_bpmit_target_mask. (exists bpr_gap_bpmit_target_mask_bound. bpr_gap_bpmit_target_mask_bound + S (bpr_index_bpmit_target_mask) = m) -> exists bpr_value_bpmit_target_mask. ((((exists bpr_height_bpmit_target_mask_decoded. bpr_height_bpmit_target_mask_decoded + S (bpr_value_bpmit_target_mask) = S ((S (bpr_index_bpmit_target_mask)) * bpr_scale_bpmit_target)) /\ exists bpr_quotient_bpmit_target_mask_decoded. bpr_code_bpmit_target = bpr_quotient_bpmit_target_mask_decoded * S ((S (bpr_index_bpmit_target_mask)) * bpr_scale_bpmit_target) + (bpr_value_bpmit_target_mask))) /\ (((((~(S (bpr_index_bpmit_target_mask) = 1) /\ forall bpr_left_bpmit_target_mask_choice_prime bpr_right_bpmit_target_mask_choice_prime. S (bpr_index_bpmit_target_mask) = bpr_left_bpmit_target_mask_choice_prime * bpr_right_bpmit_target_mask_choice_prime -> bpr_left_bpmit_target_mask_choice_prime = 1 \/ bpr_right_bpmit_target_mask_choice_prime = 1)) /\ bpr_value_bpmit_target_mask = S (bpr_index_bpmit_target_mask)) \/ (~((~(S (bpr_index_bpmit_target_mask) = 1) /\ forall bpr_left_bpmit_target_mask_choice_prime bpr_right_bpmit_target_mask_choice_prime. S (bpr_index_bpmit_target_mask) = bpr_left_bpmit_target_mask_choice_prime * bpr_right_bpmit_target_mask_choice_prime -> bpr_left_bpmit_target_mask_choice_prime = 1 \/ bpr_right_bpmit_target_mask_choice_prime = 1)) /\ bpr_value_bpmit_target_mask = 1))))) /\ (exists ff_u_bpmit_target_product ff_v_bpmit_target_product. ((((exists ff_h_bpmit_target_product_start. ff_h_bpmit_target_product_start + S (1) = S ((S (0)) * ff_v_bpmit_target_product)) /\ exists ff_q_bpmit_target_product_start. ff_u_bpmit_target_product = ff_q_bpmit_target_product_start * S ((S (0)) * ff_v_bpmit_target_product) + (1))) /\ ((((exists ff_h_bpmit_target_product_terminal. ff_h_bpmit_target_product_terminal + S (z) = S ((S (m)) * ff_v_bpmit_target_product)) /\ exists ff_q_bpmit_target_product_terminal. ff_u_bpmit_target_product = ff_q_bpmit_target_product_terminal * S ((S (m)) * ff_v_bpmit_target_product) + (z))) /\ forall ff_i_bpmit_target_product. (exists ff_lt_bpmit_target_product_bound. ff_lt_bpmit_target_product_bound + S ff_i_bpmit_target_product = m) -> exists ff_p_bpmit_target_product ff_r_bpmit_target_product ff_s_bpmit_target_product. ((((exists ff_h_bpmit_target_product_factor. ff_h_bpmit_target_product_factor + S (ff_p_bpmit_target_product) = S ((S (ff_i_bpmit_target_product)) * bpr_scale_bpmit_target)) /\ exists ff_q_bpmit_target_product_factor. bpr_code_bpmit_target = ff_q_bpmit_target_product_factor * S ((S (ff_i_bpmit_target_product)) * bpr_scale_bpmit_target) + (ff_p_bpmit_target_product))) /\ ((((exists ff_h_bpmit_target_product_partial. ff_h_bpmit_target_product_partial + S (ff_r_bpmit_target_product) = S ((S (ff_i_bpmit_target_product)) * ff_v_bpmit_target_product)) /\ exists ff_q_bpmit_target_product_partial. ff_u_bpmit_target_product = ff_q_bpmit_target_product_partial * S ((S (ff_i_bpmit_target_product)) * ff_v_bpmit_target_product) + (ff_r_bpmit_target_product))) /\ ((((exists ff_h_bpmit_target_product_successor. ff_h_bpmit_target_product_successor + S (ff_s_bpmit_target_product) = S ((S (S ff_i_bpmit_target_product)) * ff_v_bpmit_target_product)) /\ exists ff_q_bpmit_target_product_successor. ff_u_bpmit_target_product = ff_q_bpmit_target_product_successor * S ((S (S ff_i_bpmit_target_product)) * ff_v_bpmit_target_product) + (ff_s_bpmit_target_product))) /\ ff_s_bpmit_target_product = ff_r_bpmit_target_product * ff_p_bpmit_target_product))))))))