prime_contribution_selected_successor_divides

Exact expanded PA statement

forall p e a z q n. (exists bpr_power_code_bpcssd_power bpr_power_scale_bpcssd_power. ((forall bpr_power_index_bpcssd_power. (exists bpr_gap_bpcssd_power_repeat_bound. bpr_gap_bpcssd_power_repeat_bound + S (bpr_power_index_bpcssd_power) = e) -> (((exists bpr_height_bpcssd_power_repeat_entry. bpr_height_bpcssd_power_repeat_entry + S (p) = S ((S (bpr_power_index_bpcssd_power)) * bpr_power_scale_bpcssd_power)) /\ exists bpr_quotient_bpcssd_power_repeat_entry. bpr_power_code_bpcssd_power = bpr_quotient_bpcssd_power_repeat_entry * S ((S (bpr_power_index_bpcssd_power)) * bpr_power_scale_bpcssd_power) + (p)))) /\ (exists ff_u_bpcssd_power_product ff_v_bpcssd_power_product. ((((exists ff_h_bpcssd_power_product_start. ff_h_bpcssd_power_product_start + S (1) = S ((S (0)) * ff_v_bpcssd_power_product)) /\ exists ff_q_bpcssd_power_product_start. ff_u_bpcssd_power_product = ff_q_bpcssd_power_product_start * S ((S (0)) * ff_v_bpcssd_power_product) + (1))) /\ ((((exists ff_h_bpcssd_power_product_terminal. ff_h_bpcssd_power_product_terminal + S (a) = S ((S (e)) * ff_v_bpcssd_power_product)) /\ exists ff_q_bpcssd_power_product_terminal. ff_u_bpcssd_power_product = ff_q_bpcssd_power_product_terminal * S ((S (e)) * ff_v_bpcssd_power_product) + (a))) /\ forall ff_i_bpcssd_power_product. (exists ff_lt_bpcssd_power_product_bound. ff_lt_bpcssd_power_product_bound + S ff_i_bpcssd_power_product = e) -> exists ff_p_bpcssd_power_product ff_r_bpcssd_power_product ff_s_bpcssd_power_product. ((((exists ff_h_bpcssd_power_product_factor. ff_h_bpcssd_power_product_factor + S (ff_p_bpcssd_power_product) = S ((S (ff_i_bpcssd_power_product)) * bpr_power_scale_bpcssd_power)) /\ exists ff_q_bpcssd_power_product_factor. bpr_power_code_bpcssd_power = ff_q_bpcssd_power_product_factor * S ((S (ff_i_bpcssd_power_product)) * bpr_power_scale_bpcssd_power) + (ff_p_bpcssd_power_product))) /\ ((((exists ff_h_bpcssd_power_product_partial. ff_h_bpcssd_power_product_partial + S (ff_r_bpcssd_power_product) = S ((S (ff_i_bpcssd_power_product)) * ff_v_bpcssd_power_product)) /\ exists ff_q_bpcssd_power_product_partial. ff_u_bpcssd_power_product = ff_q_bpcssd_power_product_partial * S ((S (ff_i_bpcssd_power_product)) * ff_v_bpcssd_power_product) + (ff_r_bpcssd_power_product))) /\ ((((exists ff_h_bpcssd_power_product_successor. ff_h_bpcssd_power_product_successor + S (ff_s_bpcssd_power_product) = S ((S (S ff_i_bpcssd_power_product)) * ff_v_bpcssd_power_product)) /\ exists ff_q_bpcssd_power_product_successor. ff_u_bpcssd_power_product = ff_q_bpcssd_power_product_successor * S ((S (S ff_i_bpcssd_power_product)) * ff_v_bpcssd_power_product) + (ff_s_bpcssd_power_product))) /\ ff_s_bpcssd_power_product = ff_r_bpcssd_power_product * ff_p_bpcssd_power_product)))))))) -> (exists bpr_divides_quotient_bpcssd_factor. z = (a) * bpr_divides_quotient_bpcssd_factor) -> (exists bpr_divides_quotient_bpcssd_prime_factor. q = (p) * bpr_divides_quotient_bpcssd_prime_factor) -> n = z * q -> (exists bpr_power_value_bpcssd_result. ((exists bpr_power_code_bpcssd_result_power bpr_power_scale_bpcssd_result_power. ((forall bpr_power_index_bpcssd_result_power. (exists bpr_gap_bpcssd_result_power_repeat_bound. bpr_gap_bpcssd_result_power_repeat_bound + S (bpr_power_index_bpcssd_result_power) = S e) -> (((exists bpr_height_bpcssd_result_power_repeat_entry. bpr_height_bpcssd_result_power_repeat_entry + S (p) = S ((S (bpr_power_index_bpcssd_result_power)) * bpr_power_scale_bpcssd_result_power)) /\ exists bpr_quotient_bpcssd_result_power_repeat_entry. bpr_power_code_bpcssd_result_power = bpr_quotient_bpcssd_result_power_repeat_entry * S ((S (bpr_power_index_bpcssd_result_power)) * bpr_power_scale_bpcssd_result_power) + (p)))) /\ (exists ff_u_bpcssd_result_power_product ff_v_bpcssd_result_power_product. ((((exists ff_h_bpcssd_result_power_product_start. ff_h_bpcssd_result_power_product_start + S (1) = S ((S (0)) * ff_v_bpcssd_result_power_product)) /\ exists ff_q_bpcssd_result_power_product_start. ff_u_bpcssd_result_power_product = ff_q_bpcssd_result_power_product_start * S ((S (0)) * ff_v_bpcssd_result_power_product) + (1))) /\ ((((exists ff_h_bpcssd_result_power_product_terminal. ff_h_bpcssd_result_power_product_terminal + S (bpr_power_value_bpcssd_result) = S ((S (S e)) * ff_v_bpcssd_result_power_product)) /\ exists ff_q_bpcssd_result_power_product_terminal. ff_u_bpcssd_result_power_product = ff_q_bpcssd_result_power_product_terminal * S ((S (S e)) * ff_v_bpcssd_result_power_product) + (bpr_power_value_bpcssd_result))) /\ forall ff_i_bpcssd_result_power_product. (exists ff_lt_bpcssd_result_power_product_bound. ff_lt_bpcssd_result_power_product_bound + S ff_i_bpcssd_result_power_product = S e) -> exists ff_p_bpcssd_result_power_product ff_r_bpcssd_result_power_product ff_s_bpcssd_result_power_product. ((((exists ff_h_bpcssd_result_power_product_factor. ff_h_bpcssd_result_power_product_factor + S (ff_p_bpcssd_result_power_product) = S ((S (ff_i_bpcssd_result_power_product)) * bpr_power_scale_bpcssd_result_power)) /\ exists ff_q_bpcssd_result_power_product_factor. bpr_power_code_bpcssd_result_power = ff_q_bpcssd_result_power_product_factor * S ((S (ff_i_bpcssd_result_power_product)) * bpr_power_scale_bpcssd_result_power) + (ff_p_bpcssd_result_power_product))) /\ ((((exists ff_h_bpcssd_result_power_product_partial. ff_h_bpcssd_result_power_product_partial + S (ff_r_bpcssd_result_power_product) = S ((S (ff_i_bpcssd_result_power_product)) * ff_v_bpcssd_result_power_product)) /\ exists ff_q_bpcssd_result_power_product_partial. ff_u_bpcssd_result_power_product = ff_q_bpcssd_result_power_product_partial * S ((S (ff_i_bpcssd_result_power_product)) * ff_v_bpcssd_result_power_product) + (ff_r_bpcssd_result_power_product))) /\ ((((exists ff_h_bpcssd_result_power_product_successor. ff_h_bpcssd_result_power_product_successor + S (ff_s_bpcssd_result_power_product) = S ((S (S ff_i_bpcssd_result_power_product)) * ff_v_bpcssd_result_power_product)) /\ exists ff_q_bpcssd_result_power_product_successor. ff_u_bpcssd_result_power_product = ff_q_bpcssd_result_power_product_successor * S ((S (S ff_i_bpcssd_result_power_product)) * ff_v_bpcssd_result_power_product) + (ff_s_bpcssd_result_power_product))) /\ ff_s_bpcssd_result_power_product = ff_r_bpcssd_result_power_product * ff_p_bpcssd_result_power_product)))))))) /\ (exists bpr_divides_quotient_bpcssd_result_divides. n = (bpr_power_value_bpcssd_result) * bpr_divides_quotient_bpcssd_result_divides)))