bounded_euler_criterion_dichotomy

Exact expanded PA statement

forall p a n h A. p = S n -> ((~(p = 1) /\ forall esi_prime_left_ecb_prime esi_prime_right_ecb_prime. p = esi_prime_left_ecb_prime * esi_prime_right_ecb_prime -> esi_prime_left_ecb_prime = 1 \/ esi_prime_right_ecb_prime = 1)) -> ~(a = 0) -> (exists wpo_gap_ecb_a_lt_p. wpo_gap_ecb_a_lt_p + S (a) = p) -> n = h + h -> (exists ff_b_ecb_power ff_c_ecb_power. ((forall ff_i_ecb_power_repeat. (exists ff_lt_ecb_power_repeat_bound. ff_lt_ecb_power_repeat_bound + S ff_i_ecb_power_repeat = h) -> (((exists ff_h_ecb_power_repeat_decoded. ff_h_ecb_power_repeat_decoded + S (a) = S ((S (ff_i_ecb_power_repeat)) * ff_c_ecb_power)) /\ exists ff_q_ecb_power_repeat_decoded. ff_b_ecb_power = ff_q_ecb_power_repeat_decoded * S ((S (ff_i_ecb_power_repeat)) * ff_c_ecb_power) + (a)))) /\ (exists ff_u_ecb_power_product ff_v_ecb_power_product. ((((exists ff_h_ecb_power_product_start. ff_h_ecb_power_product_start + S (1) = S ((S (0)) * ff_v_ecb_power_product)) /\ exists ff_q_ecb_power_product_start. ff_u_ecb_power_product = ff_q_ecb_power_product_start * S ((S (0)) * ff_v_ecb_power_product) + (1))) /\ ((((exists ff_h_ecb_power_product_terminal. ff_h_ecb_power_product_terminal + S (A) = S ((S (h)) * ff_v_ecb_power_product)) /\ exists ff_q_ecb_power_product_terminal. ff_u_ecb_power_product = ff_q_ecb_power_product_terminal * S ((S (h)) * ff_v_ecb_power_product) + (A))) /\ forall ff_i_ecb_power_product. (exists ff_lt_ecb_power_product_bound. ff_lt_ecb_power_product_bound + S ff_i_ecb_power_product = h) -> exists ff_p_ecb_power_product ff_r_ecb_power_product ff_s_ecb_power_product. ((((exists ff_h_ecb_power_product_factor. ff_h_ecb_power_product_factor + S (ff_p_ecb_power_product) = S ((S (ff_i_ecb_power_product)) * ff_c_ecb_power)) /\ exists ff_q_ecb_power_product_factor. ff_b_ecb_power = ff_q_ecb_power_product_factor * S ((S (ff_i_ecb_power_product)) * ff_c_ecb_power) + (ff_p_ecb_power_product))) /\ ((((exists ff_h_ecb_power_product_partial. ff_h_ecb_power_product_partial + S (ff_r_ecb_power_product) = S ((S (ff_i_ecb_power_product)) * ff_v_ecb_power_product)) /\ exists ff_q_ecb_power_product_partial. ff_u_ecb_power_product = ff_q_ecb_power_product_partial * S ((S (ff_i_ecb_power_product)) * ff_v_ecb_power_product) + (ff_r_ecb_power_product))) /\ ((((exists ff_h_ecb_power_product_successor. ff_h_ecb_power_product_successor + S (ff_s_ecb_power_product) = S ((S (S ff_i_ecb_power_product)) * ff_v_ecb_power_product)) /\ exists ff_q_ecb_power_product_successor. ff_u_ecb_power_product = ff_q_ecb_power_product_successor * S ((S (S ff_i_ecb_power_product)) * ff_v_ecb_power_product) + (ff_s_ecb_power_product))) /\ ff_s_ecb_power_product = ff_r_ecb_power_product * ff_p_ecb_power_product)))))))) -> ((((exists qr_x_ecb_qres. exists qr_u_ecb_qres qr_v_ecb_qres. qr_x_ecb_qres * qr_x_ecb_qres + p * qr_u_ecb_qres = a + p * qr_v_ecb_qres) /\ (exists wpp_mod_left_ecb_mod_one wpp_mod_right_ecb_mod_one. (A) + p * wpp_mod_left_ecb_mod_one = (1) + p * wpp_mod_right_ecb_mod_one)) \/ ((~(exists qr_x_ecb_qres. exists qr_u_ecb_qres qr_v_ecb_qres. qr_x_ecb_qres * qr_x_ecb_qres + p * qr_u_ecb_qres = a + p * qr_v_ecb_qres)) /\ (exists wpp_mod_left_ecb_mod_predecessor wpp_mod_right_ecb_mod_predecessor. (A) + p * wpp_mod_left_ecb_mod_predecessor = (n) + p * wpp_mod_right_ecb_mod_predecessor))))