prime_power_divides_exponent_le_value

Exact expanded PA statement

forall p e a. ((~(p = 1) /\ forall frm_prime_left_bpvl_prime frm_prime_right_bpvl_prime. p = frm_prime_left_bpvl_prime * frm_prime_right_bpvl_prime -> frm_prime_left_bpvl_prime = 1 \/ frm_prime_right_bpvl_prime = 1)) -> ~(a = 0) -> (exists bpv_result_bpvl_bound_divides. ((exists ff_b_bpvl_bound_divides_power ff_c_bpvl_bound_divides_power. ((forall ff_i_bpvl_bound_divides_power_repeat. (exists ff_lt_bpvl_bound_divides_power_repeat_bound. ff_lt_bpvl_bound_divides_power_repeat_bound + S ff_i_bpvl_bound_divides_power_repeat = e) -> (((exists ff_h_bpvl_bound_divides_power_repeat_decoded. ff_h_bpvl_bound_divides_power_repeat_decoded + S (p) = S ((S (ff_i_bpvl_bound_divides_power_repeat)) * ff_c_bpvl_bound_divides_power)) /\ exists ff_q_bpvl_bound_divides_power_repeat_decoded. ff_b_bpvl_bound_divides_power = ff_q_bpvl_bound_divides_power_repeat_decoded * S ((S (ff_i_bpvl_bound_divides_power_repeat)) * ff_c_bpvl_bound_divides_power) + (p)))) /\ (exists ff_u_bpvl_bound_divides_power_product ff_v_bpvl_bound_divides_power_product. ((((exists ff_h_bpvl_bound_divides_power_product_start. ff_h_bpvl_bound_divides_power_product_start + S (1) = S ((S (0)) * ff_v_bpvl_bound_divides_power_product)) /\ exists ff_q_bpvl_bound_divides_power_product_start. ff_u_bpvl_bound_divides_power_product = ff_q_bpvl_bound_divides_power_product_start * S ((S (0)) * ff_v_bpvl_bound_divides_power_product) + (1))) /\ ((((exists ff_h_bpvl_bound_divides_power_product_terminal. ff_h_bpvl_bound_divides_power_product_terminal + S (bpv_result_bpvl_bound_divides) = S ((S (e)) * ff_v_bpvl_bound_divides_power_product)) /\ exists ff_q_bpvl_bound_divides_power_product_terminal. ff_u_bpvl_bound_divides_power_product = ff_q_bpvl_bound_divides_power_product_terminal * S ((S (e)) * ff_v_bpvl_bound_divides_power_product) + (bpv_result_bpvl_bound_divides))) /\ forall ff_i_bpvl_bound_divides_power_product. (exists ff_lt_bpvl_bound_divides_power_product_bound. ff_lt_bpvl_bound_divides_power_product_bound + S ff_i_bpvl_bound_divides_power_product = e) -> exists ff_p_bpvl_bound_divides_power_product ff_r_bpvl_bound_divides_power_product ff_s_bpvl_bound_divides_power_product. ((((exists ff_h_bpvl_bound_divides_power_product_factor. ff_h_bpvl_bound_divides_power_product_factor + S (ff_p_bpvl_bound_divides_power_product) = S ((S (ff_i_bpvl_bound_divides_power_product)) * ff_c_bpvl_bound_divides_power)) /\ exists ff_q_bpvl_bound_divides_power_product_factor. ff_b_bpvl_bound_divides_power = ff_q_bpvl_bound_divides_power_product_factor * S ((S (ff_i_bpvl_bound_divides_power_product)) * ff_c_bpvl_bound_divides_power) + (ff_p_bpvl_bound_divides_power_product))) /\ ((((exists ff_h_bpvl_bound_divides_power_product_partial. ff_h_bpvl_bound_divides_power_product_partial + S (ff_r_bpvl_bound_divides_power_product) = S ((S (ff_i_bpvl_bound_divides_power_product)) * ff_v_bpvl_bound_divides_power_product)) /\ exists ff_q_bpvl_bound_divides_power_product_partial. ff_u_bpvl_bound_divides_power_product = ff_q_bpvl_bound_divides_power_product_partial * S ((S (ff_i_bpvl_bound_divides_power_product)) * ff_v_bpvl_bound_divides_power_product) + (ff_r_bpvl_bound_divides_power_product))) /\ ((((exists ff_h_bpvl_bound_divides_power_product_successor. ff_h_bpvl_bound_divides_power_product_successor + S (ff_s_bpvl_bound_divides_power_product) = S ((S (S ff_i_bpvl_bound_divides_power_product)) * ff_v_bpvl_bound_divides_power_product)) /\ exists ff_q_bpvl_bound_divides_power_product_successor. ff_u_bpvl_bound_divides_power_product = ff_q_bpvl_bound_divides_power_product_successor * S ((S (S ff_i_bpvl_bound_divides_power_product)) * ff_v_bpvl_bound_divides_power_product) + (ff_s_bpvl_bound_divides_power_product))) /\ ff_s_bpvl_bound_divides_power_product = ff_r_bpvl_bound_divides_power_product * ff_p_bpvl_bound_divides_power_product)))))))) /\ (exists bpv_factor_bpvl_bound_divides_divides. a = bpv_result_bpvl_bound_divides * bpv_factor_bpvl_bound_divides_divides))) -> (exists bpv_gap_divides_exponent_value. bpv_gap_divides_exponent_value + e = a)