primorial_zero

Exact expanded PA statement

forall z. (exists bpr_code_bp_zero_source bpr_scale_bp_zero_source. ((forall bpr_index_bp_zero_source_mask. (exists bpr_gap_bp_zero_source_mask_bound. bpr_gap_bp_zero_source_mask_bound + S (bpr_index_bp_zero_source_mask) = 0) -> exists bpr_value_bp_zero_source_mask. ((((exists bpr_height_bp_zero_source_mask_decoded. bpr_height_bp_zero_source_mask_decoded + S (bpr_value_bp_zero_source_mask) = S ((S (bpr_index_bp_zero_source_mask)) * bpr_scale_bp_zero_source)) /\ exists bpr_quotient_bp_zero_source_mask_decoded. bpr_code_bp_zero_source = bpr_quotient_bp_zero_source_mask_decoded * S ((S (bpr_index_bp_zero_source_mask)) * bpr_scale_bp_zero_source) + (bpr_value_bp_zero_source_mask))) /\ (((((~(S (bpr_index_bp_zero_source_mask) = 1) /\ forall bpr_left_bp_zero_source_mask_choice_prime bpr_right_bp_zero_source_mask_choice_prime. S (bpr_index_bp_zero_source_mask) = bpr_left_bp_zero_source_mask_choice_prime * bpr_right_bp_zero_source_mask_choice_prime -> bpr_left_bp_zero_source_mask_choice_prime = 1 \/ bpr_right_bp_zero_source_mask_choice_prime = 1)) /\ bpr_value_bp_zero_source_mask = S (bpr_index_bp_zero_source_mask)) \/ (~((~(S (bpr_index_bp_zero_source_mask) = 1) /\ forall bpr_left_bp_zero_source_mask_choice_prime bpr_right_bp_zero_source_mask_choice_prime. S (bpr_index_bp_zero_source_mask) = bpr_left_bp_zero_source_mask_choice_prime * bpr_right_bp_zero_source_mask_choice_prime -> bpr_left_bp_zero_source_mask_choice_prime = 1 \/ bpr_right_bp_zero_source_mask_choice_prime = 1)) /\ bpr_value_bp_zero_source_mask = 1))))) /\ (exists ff_u_bp_zero_source_product ff_v_bp_zero_source_product. ((((exists ff_h_bp_zero_source_product_start. ff_h_bp_zero_source_product_start + S (1) = S ((S (0)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_start. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_start * S ((S (0)) * ff_v_bp_zero_source_product) + (1))) /\ ((((exists ff_h_bp_zero_source_product_terminal. ff_h_bp_zero_source_product_terminal + S (z) = S ((S (0)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_terminal. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_terminal * S ((S (0)) * ff_v_bp_zero_source_product) + (z))) /\ forall ff_i_bp_zero_source_product. (exists ff_lt_bp_zero_source_product_bound. ff_lt_bp_zero_source_product_bound + S ff_i_bp_zero_source_product = 0) -> exists ff_p_bp_zero_source_product ff_r_bp_zero_source_product ff_s_bp_zero_source_product. ((((exists ff_h_bp_zero_source_product_factor. ff_h_bp_zero_source_product_factor + S (ff_p_bp_zero_source_product) = S ((S (ff_i_bp_zero_source_product)) * bpr_scale_bp_zero_source)) /\ exists ff_q_bp_zero_source_product_factor. bpr_code_bp_zero_source = ff_q_bp_zero_source_product_factor * S ((S (ff_i_bp_zero_source_product)) * bpr_scale_bp_zero_source) + (ff_p_bp_zero_source_product))) /\ ((((exists ff_h_bp_zero_source_product_partial. ff_h_bp_zero_source_product_partial + S (ff_r_bp_zero_source_product) = S ((S (ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_partial. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_partial * S ((S (ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product) + (ff_r_bp_zero_source_product))) /\ ((((exists ff_h_bp_zero_source_product_successor. ff_h_bp_zero_source_product_successor + S (ff_s_bp_zero_source_product) = S ((S (S ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product)) /\ exists ff_q_bp_zero_source_product_successor. ff_u_bp_zero_source_product = ff_q_bp_zero_source_product_successor * S ((S (S ff_i_bp_zero_source_product)) * ff_v_bp_zero_source_product) + (ff_s_bp_zero_source_product))) /\ ff_s_bp_zero_source_product = ff_r_bp_zero_source_product * ff_p_bp_zero_source_product)))))))) -> z = 1