prime_range_product_coprime

Exact expanded PA statement

forall p n b c F. p = S n -> ((~(p = 1) /\ forall frp_prime_left_prime_p frp_prime_right_prime_p. p = frp_prime_left_prime_p * frp_prime_right_prime_p -> frp_prime_left_prime_p = 1 \/ frp_prime_right_prime_p = 1)) -> (forall ff_i_frp_range_prime_range. (exists ff_lt_frp_range_prime_range_bound. ff_lt_frp_range_prime_range_bound + S ff_i_frp_range_prime_range = n) -> (((exists ff_h_frp_range_prime_range_decoded. ff_h_frp_range_prime_range_decoded + S (1 + ff_i_frp_range_prime_range) = S ((S (ff_i_frp_range_prime_range)) * c)) /\ exists ff_q_frp_range_prime_range_decoded. b = ff_q_frp_range_prime_range_decoded * S ((S (ff_i_frp_range_prime_range)) * c) + (1 + ff_i_frp_range_prime_range)))) -> (exists ff_u_prime_product ff_v_prime_product. ((((exists ff_h_prime_product_start. ff_h_prime_product_start + S (1) = S ((S (0)) * ff_v_prime_product)) /\ exists ff_q_prime_product_start. ff_u_prime_product = ff_q_prime_product_start * S ((S (0)) * ff_v_prime_product) + (1))) /\ ((((exists ff_h_prime_product_terminal. ff_h_prime_product_terminal + S (F) = S ((S (n)) * ff_v_prime_product)) /\ exists ff_q_prime_product_terminal. ff_u_prime_product = ff_q_prime_product_terminal * S ((S (n)) * ff_v_prime_product) + (F))) /\ forall ff_i_prime_product. (exists ff_lt_prime_product_bound. ff_lt_prime_product_bound + S ff_i_prime_product = n) -> exists ff_p_prime_product ff_r_prime_product ff_s_prime_product. ((((exists ff_h_prime_product_factor. ff_h_prime_product_factor + S (ff_p_prime_product) = S ((S (ff_i_prime_product)) * c)) /\ exists ff_q_prime_product_factor. b = ff_q_prime_product_factor * S ((S (ff_i_prime_product)) * c) + (ff_p_prime_product))) /\ ((((exists ff_h_prime_product_partial. ff_h_prime_product_partial + S (ff_r_prime_product) = S ((S (ff_i_prime_product)) * ff_v_prime_product)) /\ exists ff_q_prime_product_partial. ff_u_prime_product = ff_q_prime_product_partial * S ((S (ff_i_prime_product)) * ff_v_prime_product) + (ff_r_prime_product))) /\ ((((exists ff_h_prime_product_successor. ff_h_prime_product_successor + S (ff_s_prime_product) = S ((S (S ff_i_prime_product)) * ff_v_prime_product)) /\ exists ff_q_prime_product_successor. ff_u_prime_product = ff_q_prime_product_successor * S ((S (S ff_i_prime_product)) * ff_v_prime_product) + (ff_s_prime_product))) /\ ff_s_prime_product = ff_r_prime_product * ff_p_prime_product)))))) -> (forall frp_divisor_prime_product_result. (exists frp_left_factor_prime_product_result. F = frp_divisor_prime_product_result * frp_left_factor_prime_product_result) -> (exists frp_right_factor_prime_product_result. p = frp_divisor_prime_product_result * frp_right_factor_prime_product_result) -> frp_divisor_prime_product_result = 1)