fermat_predecessor_exponent_mod_one

Exact expanded PA statement

forall p n a A. p = S n -> ((~(p = 1) /\ forall frm_prime_left_predecessor_prime frm_prime_right_predecessor_prime. p = frm_prime_left_predecessor_prime * frm_prime_right_predecessor_prime -> frm_prime_left_predecessor_prime = 1 \/ frm_prime_right_predecessor_prime = 1)) -> (~(exists frm_factor_predecessor_multiplier. a = p * frm_factor_predecessor_multiplier)) -> (exists ff_b_predecessor_power ff_c_predecessor_power. ((forall ff_i_predecessor_power_repeat. (exists ff_lt_predecessor_power_repeat_bound. ff_lt_predecessor_power_repeat_bound + S ff_i_predecessor_power_repeat = n) -> (((exists ff_h_predecessor_power_repeat_decoded. ff_h_predecessor_power_repeat_decoded + S (a) = S ((S (ff_i_predecessor_power_repeat)) * ff_c_predecessor_power)) /\ exists ff_q_predecessor_power_repeat_decoded. ff_b_predecessor_power = ff_q_predecessor_power_repeat_decoded * S ((S (ff_i_predecessor_power_repeat)) * ff_c_predecessor_power) + (a)))) /\ (exists ff_u_predecessor_power_product ff_v_predecessor_power_product. ((((exists ff_h_predecessor_power_product_start. ff_h_predecessor_power_product_start + S (1) = S ((S (0)) * ff_v_predecessor_power_product)) /\ exists ff_q_predecessor_power_product_start. ff_u_predecessor_power_product = ff_q_predecessor_power_product_start * S ((S (0)) * ff_v_predecessor_power_product) + (1))) /\ ((((exists ff_h_predecessor_power_product_terminal. ff_h_predecessor_power_product_terminal + S (A) = S ((S (n)) * ff_v_predecessor_power_product)) /\ exists ff_q_predecessor_power_product_terminal. ff_u_predecessor_power_product = ff_q_predecessor_power_product_terminal * S ((S (n)) * ff_v_predecessor_power_product) + (A))) /\ forall ff_i_predecessor_power_product. (exists ff_lt_predecessor_power_product_bound. ff_lt_predecessor_power_product_bound + S ff_i_predecessor_power_product = n) -> exists ff_p_predecessor_power_product ff_r_predecessor_power_product ff_s_predecessor_power_product. ((((exists ff_h_predecessor_power_product_factor. ff_h_predecessor_power_product_factor + S (ff_p_predecessor_power_product) = S ((S (ff_i_predecessor_power_product)) * ff_c_predecessor_power)) /\ exists ff_q_predecessor_power_product_factor. ff_b_predecessor_power = ff_q_predecessor_power_product_factor * S ((S (ff_i_predecessor_power_product)) * ff_c_predecessor_power) + (ff_p_predecessor_power_product))) /\ ((((exists ff_h_predecessor_power_product_partial. ff_h_predecessor_power_product_partial + S (ff_r_predecessor_power_product) = S ((S (ff_i_predecessor_power_product)) * ff_v_predecessor_power_product)) /\ exists ff_q_predecessor_power_product_partial. ff_u_predecessor_power_product = ff_q_predecessor_power_product_partial * S ((S (ff_i_predecessor_power_product)) * ff_v_predecessor_power_product) + (ff_r_predecessor_power_product))) /\ ((((exists ff_h_predecessor_power_product_successor. ff_h_predecessor_power_product_successor + S (ff_s_predecessor_power_product) = S ((S (S ff_i_predecessor_power_product)) * ff_v_predecessor_power_product)) /\ exists ff_q_predecessor_power_product_successor. ff_u_predecessor_power_product = ff_q_predecessor_power_product_successor * S ((S (S ff_i_predecessor_power_product)) * ff_v_predecessor_power_product) + (ff_s_predecessor_power_product))) /\ ff_s_predecessor_power_product = ff_r_predecessor_power_product * ff_p_predecessor_power_product)))))))) -> (exists fep_mod_left_predecessor_result fep_mod_right_predecessor_result. A + p * fep_mod_left_predecessor_result = 1 + p * fep_mod_right_predecessor_result)