distinct_prime_factor_even_valuation_reflects_prefix

Statement with defined notation

forall p q n e f g. ((~(p = 1) /\ forall frm_prime_left_ftsp_p frm_prime_right_ftsp_p. p = frm_prime_left_ftsp_p * frm_prime_right_ftsp_p -> frm_prime_left_ftsp_p = 1 \/ frm_prime_right_ftsp_p = 1)) -> ((~(q = 1) /\ forall frm_prime_left_ftsp_q frm_prime_right_ftsp_q. q = frm_prime_left_ftsp_q * frm_prime_right_ftsp_q -> frm_prime_left_ftsp_q = 1 \/ frm_prime_right_ftsp_q = 1)) -> ~(p = q) -> ~(n = 0) -> (((exists bpv_gap_ftsp_reflected_value_exponent_bound. bpv_gap_ftsp_reflected_value_exponent_bound + e = n) /\ (exists bpv_result_ftsp_reflected_value_selected. ((exists ff_b_ftsp_reflected_value_selected_power ff_c_ftsp_reflected_value_selected_power. ((forall ff_i_ftsp_reflected_value_selected_power_repeat. (exists ff_lt_ftsp_reflected_value_selected_power_repeat_bound. ff_lt_ftsp_reflected_value_selected_power_repeat_bound + S ff_i_ftsp_reflected_value_selected_power_repeat = e) -> (((exists ff_h_ftsp_reflected_value_selected_power_repeat_decoded. ff_h_ftsp_reflected_value_selected_power_repeat_decoded + S (p) = S ((S (ff_i_ftsp_reflected_value_selected_power_repeat)) * ff_c_ftsp_reflected_value_selected_power)) /\ exists ff_q_ftsp_reflected_value_selected_power_repeat_decoded. ff_b_ftsp_reflected_value_selected_power = ff_q_ftsp_reflected_value_selected_power_repeat_decoded * S ((S (ff_i_ftsp_reflected_value_selected_power_repeat)) * ff_c_ftsp_reflected_value_selected_power) + (p)))) /\ (exists ff_u_ftsp_reflected_value_selected_power_product ff_v_ftsp_reflected_value_selected_power_product. ((((exists ff_h_ftsp_reflected_value_selected_power_product_start. ff_h_ftsp_reflected_value_selected_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_reflected_value_selected_power_product)) /\ exists ff_q_ftsp_reflected_value_selected_power_product_start. ff_u_ftsp_reflected_value_selected_power_product = ff_q_ftsp_reflected_value_selected_power_product_start * S ((S (0)) * ff_v_ftsp_reflected_value_selected_power_product) + (1))) /\ ((((exists ff_h_ftsp_reflected_value_selected_power_product_terminal. ff_h_ftsp_reflected_value_selected_power_product_terminal + S (bpv_result_ftsp_reflected_value_selected) = S ((S (e)) * ff_v_ftsp_reflected_value_selected_power_product)) /\ exists ff_q_ftsp_reflected_value_selected_power_product_terminal. ff_u_ftsp_reflected_value_selected_power_product = ff_q_ftsp_reflected_value_selected_power_product_terminal * S ((S (e)) * ff_v_ftsp_reflected_value_selected_power_product) + (bpv_result_ftsp_reflected_value_selected))) /\ forall ff_i_ftsp_reflected_value_selected_power_product. (exists ff_lt_ftsp_reflected_value_selected_power_product_bound. ff_lt_ftsp_reflected_value_selected_power_product_bound + S ff_i_ftsp_reflected_value_selected_power_product = e) -> exists ff_p_ftsp_reflected_value_selected_power_product ff_r_ftsp_reflected_value_selected_power_product ff_s_ftsp_reflected_value_selected_power_product. ((((exists ff_h_ftsp_reflected_value_selected_power_product_factor. ff_h_ftsp_reflected_value_selected_power_product_factor + S (ff_p_ftsp_reflected_value_selected_power_product) = S ((S (ff_i_ftsp_reflected_value_selected_power_product)) * ff_c_ftsp_reflected_value_selected_power)) /\ exists ff_q_ftsp_reflected_value_selected_power_product_factor. ff_b_ftsp_reflected_value_selected_power = ff_q_ftsp_reflected_value_selected_power_product_factor * S ((S (ff_i_ftsp_reflected_value_selected_power_product)) * ff_c_ftsp_reflected_value_selected_power) + (ff_p_ftsp_reflected_value_selected_power_product))) /\ ((((exists ff_h_ftsp_reflected_value_selected_power_product_partial. ff_h_ftsp_reflected_value_selected_power_product_partial + S (ff_r_ftsp_reflected_value_selected_power_product) = S ((S (ff_i_ftsp_reflected_value_selected_power_product)) * ff_v_ftsp_reflected_value_selected_power_product)) /\ exists ff_q_ftsp_reflected_value_selected_power_product_partial. ff_u_ftsp_reflected_value_selected_power_product = ff_q_ftsp_reflected_value_selected_power_product_partial * S ((S (ff_i_ftsp_reflected_value_selected_power_product)) * ff_v_ftsp_reflected_value_selected_power_product) + (ff_r_ftsp_reflected_value_selected_power_product))) /\ ((((exists ff_h_ftsp_reflected_value_selected_power_product_successor. ff_h_ftsp_reflected_value_selected_power_product_successor + S (ff_s_ftsp_reflected_value_selected_power_product) = S ((S (S ff_i_ftsp_reflected_value_selected_power_product)) * ff_v_ftsp_reflected_value_selected_power_product)) /\ exists ff_q_ftsp_reflected_value_selected_power_product_successor. ff_u_ftsp_reflected_value_selected_power_product = ff_q_ftsp_reflected_value_selected_power_product_successor * S ((S (S ff_i_ftsp_reflected_value_selected_power_product)) * ff_v_ftsp_reflected_value_selected_power_product) + (ff_s_ftsp_reflected_value_selected_power_product))) /\ ff_s_ftsp_reflected_value_selected_power_product = ff_r_ftsp_reflected_value_selected_power_product * ff_p_ftsp_reflected_value_selected_power_product)))))))) /\ (exists bpv_factor_ftsp_reflected_value_selected_divides. n = bpv_result_ftsp_reflected_value_selected * bpv_factor_ftsp_reflected_value_selected_divides)))) /\ forall bpv_candidate_ftsp_reflected_value. (exists bpv_gap_ftsp_reflected_value_candidate_bound. bpv_gap_ftsp_reflected_value_candidate_bound + bpv_candidate_ftsp_reflected_value = n) -> (exists bpv_result_ftsp_reflected_value_candidate. ((exists ff_b_ftsp_reflected_value_candidate_power ff_c_ftsp_reflected_value_candidate_power. ((forall ff_i_ftsp_reflected_value_candidate_power_repeat. (exists ff_lt_ftsp_reflected_value_candidate_power_repeat_bound. ff_lt_ftsp_reflected_value_candidate_power_repeat_bound + S ff_i_ftsp_reflected_value_candidate_power_repeat = bpv_candidate_ftsp_reflected_value) -> (((exists ff_h_ftsp_reflected_value_candidate_power_repeat_decoded. ff_h_ftsp_reflected_value_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_ftsp_reflected_value_candidate_power_repeat)) * ff_c_ftsp_reflected_value_candidate_power)) /\ exists ff_q_ftsp_reflected_value_candidate_power_repeat_decoded. ff_b_ftsp_reflected_value_candidate_power = ff_q_ftsp_reflected_value_candidate_power_repeat_decoded * S ((S (ff_i_ftsp_reflected_value_candidate_power_repeat)) * ff_c_ftsp_reflected_value_candidate_power) + (p)))) /\ (exists ff_u_ftsp_reflected_value_candidate_power_product ff_v_ftsp_reflected_value_candidate_power_product. ((((exists ff_h_ftsp_reflected_value_candidate_power_product_start. ff_h_ftsp_reflected_value_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_reflected_value_candidate_power_product)) /\ exists ff_q_ftsp_reflected_value_candidate_power_product_start. ff_u_ftsp_reflected_value_candidate_power_product = ff_q_ftsp_reflected_value_candidate_power_product_start * S ((S (0)) * ff_v_ftsp_reflected_value_candidate_power_product) + (1))) /\ ((((exists ff_h_ftsp_reflected_value_candidate_power_product_terminal. ff_h_ftsp_reflected_value_candidate_power_product_terminal + S (bpv_result_ftsp_reflected_value_candidate) = S ((S (bpv_candidate_ftsp_reflected_value)) * ff_v_ftsp_reflected_value_candidate_power_product)) /\ exists ff_q_ftsp_reflected_value_candidate_power_product_terminal. ff_u_ftsp_reflected_value_candidate_power_product = ff_q_ftsp_reflected_value_candidate_power_product_terminal * S ((S (bpv_candidate_ftsp_reflected_value)) * ff_v_ftsp_reflected_value_candidate_power_product) + (bpv_result_ftsp_reflected_value_candidate))) /\ forall ff_i_ftsp_reflected_value_candidate_power_product. (exists ff_lt_ftsp_reflected_value_candidate_power_product_bound. ff_lt_ftsp_reflected_value_candidate_power_product_bound + S ff_i_ftsp_reflected_value_candidate_power_product = bpv_candidate_ftsp_reflected_value) -> exists ff_p_ftsp_reflected_value_candidate_power_product ff_r_ftsp_reflected_value_candidate_power_product ff_s_ftsp_reflected_value_candidate_power_product. ((((exists ff_h_ftsp_reflected_value_candidate_power_product_factor. ff_h_ftsp_reflected_value_candidate_power_product_factor + S (ff_p_ftsp_reflected_value_candidate_power_product) = S ((S (ff_i_ftsp_reflected_value_candidate_power_product)) * ff_c_ftsp_reflected_value_candidate_power)) /\ exists ff_q_ftsp_reflected_value_candidate_power_product_factor. ff_b_ftsp_reflected_value_candidate_power = ff_q_ftsp_reflected_value_candidate_power_product_factor * S ((S (ff_i_ftsp_reflected_value_candidate_power_product)) * ff_c_ftsp_reflected_value_candidate_power) + (ff_p_ftsp_reflected_value_candidate_power_product))) /\ ((((exists ff_h_ftsp_reflected_value_candidate_power_product_partial. ff_h_ftsp_reflected_value_candidate_power_product_partial + S (ff_r_ftsp_reflected_value_candidate_power_product) = S ((S (ff_i_ftsp_reflected_value_candidate_power_product)) * ff_v_ftsp_reflected_value_candidate_power_product)) /\ exists ff_q_ftsp_reflected_value_candidate_power_product_partial. ff_u_ftsp_reflected_value_candidate_power_product = ff_q_ftsp_reflected_value_candidate_power_product_partial * S ((S (ff_i_ftsp_reflected_value_candidate_power_product)) * ff_v_ftsp_reflected_value_candidate_power_product) + (ff_r_ftsp_reflected_value_candidate_power_product))) /\ ((((exists ff_h_ftsp_reflected_value_candidate_power_product_successor. ff_h_ftsp_reflected_value_candidate_power_product_successor + S (ff_s_ftsp_reflected_value_candidate_power_product) = S ((S (S ff_i_ftsp_reflected_value_candidate_power_product)) * ff_v_ftsp_reflected_value_candidate_power_product)) /\ exists ff_q_ftsp_reflected_value_candidate_power_product_successor. ff_u_ftsp_reflected_value_candidate_power_product = ff_q_ftsp_reflected_value_candidate_power_product_successor * S ((S (S ff_i_ftsp_reflected_value_candidate_power_product)) * ff_v_ftsp_reflected_value_candidate_power_product) + (ff_s_ftsp_reflected_value_candidate_power_product))) /\ ff_s_ftsp_reflected_value_candidate_power_product = ff_r_ftsp_reflected_value_candidate_power_product * ff_p_ftsp_reflected_value_candidate_power_product)))))))) /\ (exists bpv_factor_ftsp_reflected_value_candidate_divides. n = bpv_result_ftsp_reflected_value_candidate * bpv_factor_ftsp_reflected_value_candidate_divides))) -> (exists bpv_gap_ftsp_reflected_value_maximal. bpv_gap_ftsp_reflected_value_maximal + bpv_candidate_ftsp_reflected_value = e)) -> (((exists bpv_gap_ftsp_reflected_prime_exponent_bound. bpv_gap_ftsp_reflected_prime_exponent_bound + f = q) /\ (exists bpv_result_ftsp_reflected_prime_selected. ((exists ff_b_ftsp_reflected_prime_selected_power ff_c_ftsp_reflected_prime_selected_power. ((forall ff_i_ftsp_reflected_prime_selected_power_repeat. (exists ff_lt_ftsp_reflected_prime_selected_power_repeat_bound. ff_lt_ftsp_reflected_prime_selected_power_repeat_bound + S ff_i_ftsp_reflected_prime_selected_power_repeat = f) -> (((exists ff_h_ftsp_reflected_prime_selected_power_repeat_decoded. ff_h_ftsp_reflected_prime_selected_power_repeat_decoded + S (p) = S ((S (ff_i_ftsp_reflected_prime_selected_power_repeat)) * ff_c_ftsp_reflected_prime_selected_power)) /\ exists ff_q_ftsp_reflected_prime_selected_power_repeat_decoded. ff_b_ftsp_reflected_prime_selected_power = ff_q_ftsp_reflected_prime_selected_power_repeat_decoded * S ((S (ff_i_ftsp_reflected_prime_selected_power_repeat)) * ff_c_ftsp_reflected_prime_selected_power) + (p)))) /\ (exists ff_u_ftsp_reflected_prime_selected_power_product ff_v_ftsp_reflected_prime_selected_power_product. ((((exists ff_h_ftsp_reflected_prime_selected_power_product_start. ff_h_ftsp_reflected_prime_selected_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_reflected_prime_selected_power_product)) /\ exists ff_q_ftsp_reflected_prime_selected_power_product_start. ff_u_ftsp_reflected_prime_selected_power_product = ff_q_ftsp_reflected_prime_selected_power_product_start * S ((S (0)) * ff_v_ftsp_reflected_prime_selected_power_product) + (1))) /\ ((((exists ff_h_ftsp_reflected_prime_selected_power_product_terminal. ff_h_ftsp_reflected_prime_selected_power_product_terminal + S (bpv_result_ftsp_reflected_prime_selected) = S ((S (f)) * ff_v_ftsp_reflected_prime_selected_power_product)) /\ exists ff_q_ftsp_reflected_prime_selected_power_product_terminal. ff_u_ftsp_reflected_prime_selected_power_product = ff_q_ftsp_reflected_prime_selected_power_product_terminal * S ((S (f)) * ff_v_ftsp_reflected_prime_selected_power_product) + (bpv_result_ftsp_reflected_prime_selected))) /\ forall ff_i_ftsp_reflected_prime_selected_power_product. (exists ff_lt_ftsp_reflected_prime_selected_power_product_bound. ff_lt_ftsp_reflected_prime_selected_power_product_bound + S ff_i_ftsp_reflected_prime_selected_power_product = f) -> exists ff_p_ftsp_reflected_prime_selected_power_product ff_r_ftsp_reflected_prime_selected_power_product ff_s_ftsp_reflected_prime_selected_power_product. ((((exists ff_h_ftsp_reflected_prime_selected_power_product_factor. ff_h_ftsp_reflected_prime_selected_power_product_factor + S (ff_p_ftsp_reflected_prime_selected_power_product) = S ((S (ff_i_ftsp_reflected_prime_selected_power_product)) * ff_c_ftsp_reflected_prime_selected_power)) /\ exists ff_q_ftsp_reflected_prime_selected_power_product_factor. ff_b_ftsp_reflected_prime_selected_power = ff_q_ftsp_reflected_prime_selected_power_product_factor * S ((S (ff_i_ftsp_reflected_prime_selected_power_product)) * ff_c_ftsp_reflected_prime_selected_power) + (ff_p_ftsp_reflected_prime_selected_power_product))) /\ ((((exists ff_h_ftsp_reflected_prime_selected_power_product_partial. ff_h_ftsp_reflected_prime_selected_power_product_partial + S (ff_r_ftsp_reflected_prime_selected_power_product) = S ((S (ff_i_ftsp_reflected_prime_selected_power_product)) * ff_v_ftsp_reflected_prime_selected_power_product)) /\ exists ff_q_ftsp_reflected_prime_selected_power_product_partial. ff_u_ftsp_reflected_prime_selected_power_product = ff_q_ftsp_reflected_prime_selected_power_product_partial * S ((S (ff_i_ftsp_reflected_prime_selected_power_product)) * ff_v_ftsp_reflected_prime_selected_power_product) + (ff_r_ftsp_reflected_prime_selected_power_product))) /\ ((((exists ff_h_ftsp_reflected_prime_selected_power_product_successor. ff_h_ftsp_reflected_prime_selected_power_product_successor + S (ff_s_ftsp_reflected_prime_selected_power_product) = S ((S (S ff_i_ftsp_reflected_prime_selected_power_product)) * ff_v_ftsp_reflected_prime_selected_power_product)) /\ exists ff_q_ftsp_reflected_prime_selected_power_product_successor. ff_u_ftsp_reflected_prime_selected_power_product = ff_q_ftsp_reflected_prime_selected_power_product_successor * S ((S (S ff_i_ftsp_reflected_prime_selected_power_product)) * ff_v_ftsp_reflected_prime_selected_power_product) + (ff_s_ftsp_reflected_prime_selected_power_product))) /\ ff_s_ftsp_reflected_prime_selected_power_product = ff_r_ftsp_reflected_prime_selected_power_product * ff_p_ftsp_reflected_prime_selected_power_product)))))))) /\ (exists bpv_factor_ftsp_reflected_prime_selected_divides. q = bpv_result_ftsp_reflected_prime_selected * bpv_factor_ftsp_reflected_prime_selected_divides)))) /\ forall bpv_candidate_ftsp_reflected_prime. (exists bpv_gap_ftsp_reflected_prime_candidate_bound. bpv_gap_ftsp_reflected_prime_candidate_bound + bpv_candidate_ftsp_reflected_prime = q) -> (exists bpv_result_ftsp_reflected_prime_candidate. ((exists ff_b_ftsp_reflected_prime_candidate_power ff_c_ftsp_reflected_prime_candidate_power. ((forall ff_i_ftsp_reflected_prime_candidate_power_repeat. (exists ff_lt_ftsp_reflected_prime_candidate_power_repeat_bound. ff_lt_ftsp_reflected_prime_candidate_power_repeat_bound + S ff_i_ftsp_reflected_prime_candidate_power_repeat = bpv_candidate_ftsp_reflected_prime) -> (((exists ff_h_ftsp_reflected_prime_candidate_power_repeat_decoded. ff_h_ftsp_reflected_prime_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_ftsp_reflected_prime_candidate_power_repeat)) * ff_c_ftsp_reflected_prime_candidate_power)) /\ exists ff_q_ftsp_reflected_prime_candidate_power_repeat_decoded. ff_b_ftsp_reflected_prime_candidate_power = ff_q_ftsp_reflected_prime_candidate_power_repeat_decoded * S ((S (ff_i_ftsp_reflected_prime_candidate_power_repeat)) * ff_c_ftsp_reflected_prime_candidate_power) + (p)))) /\ (exists ff_u_ftsp_reflected_prime_candidate_power_product ff_v_ftsp_reflected_prime_candidate_power_product. ((((exists ff_h_ftsp_reflected_prime_candidate_power_product_start. ff_h_ftsp_reflected_prime_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_reflected_prime_candidate_power_product)) /\ exists ff_q_ftsp_reflected_prime_candidate_power_product_start. ff_u_ftsp_reflected_prime_candidate_power_product = ff_q_ftsp_reflected_prime_candidate_power_product_start * S ((S (0)) * ff_v_ftsp_reflected_prime_candidate_power_product) + (1))) /\ ((((exists ff_h_ftsp_reflected_prime_candidate_power_product_terminal. ff_h_ftsp_reflected_prime_candidate_power_product_terminal + S (bpv_result_ftsp_reflected_prime_candidate) = S ((S (bpv_candidate_ftsp_reflected_prime)) * ff_v_ftsp_reflected_prime_candidate_power_product)) /\ exists ff_q_ftsp_reflected_prime_candidate_power_product_terminal. ff_u_ftsp_reflected_prime_candidate_power_product = ff_q_ftsp_reflected_prime_candidate_power_product_terminal * S ((S (bpv_candidate_ftsp_reflected_prime)) * ff_v_ftsp_reflected_prime_candidate_power_product) + (bpv_result_ftsp_reflected_prime_candidate))) /\ forall ff_i_ftsp_reflected_prime_candidate_power_product. (exists ff_lt_ftsp_reflected_prime_candidate_power_product_bound. ff_lt_ftsp_reflected_prime_candidate_power_product_bound + S ff_i_ftsp_reflected_prime_candidate_power_product = bpv_candidate_ftsp_reflected_prime) -> exists ff_p_ftsp_reflected_prime_candidate_power_product ff_r_ftsp_reflected_prime_candidate_power_product ff_s_ftsp_reflected_prime_candidate_power_product. ((((exists ff_h_ftsp_reflected_prime_candidate_power_product_factor. ff_h_ftsp_reflected_prime_candidate_power_product_factor + S (ff_p_ftsp_reflected_prime_candidate_power_product) = S ((S (ff_i_ftsp_reflected_prime_candidate_power_product)) * ff_c_ftsp_reflected_prime_candidate_power)) /\ exists ff_q_ftsp_reflected_prime_candidate_power_product_factor. ff_b_ftsp_reflected_prime_candidate_power = ff_q_ftsp_reflected_prime_candidate_power_product_factor * S ((S (ff_i_ftsp_reflected_prime_candidate_power_product)) * ff_c_ftsp_reflected_prime_candidate_power) + (ff_p_ftsp_reflected_prime_candidate_power_product))) /\ ((((exists ff_h_ftsp_reflected_prime_candidate_power_product_partial. ff_h_ftsp_reflected_prime_candidate_power_product_partial + S (ff_r_ftsp_reflected_prime_candidate_power_product) = S ((S (ff_i_ftsp_reflected_prime_candidate_power_product)) * ff_v_ftsp_reflected_prime_candidate_power_product)) /\ exists ff_q_ftsp_reflected_prime_candidate_power_product_partial. ff_u_ftsp_reflected_prime_candidate_power_product = ff_q_ftsp_reflected_prime_candidate_power_product_partial * S ((S (ff_i_ftsp_reflected_prime_candidate_power_product)) * ff_v_ftsp_reflected_prime_candidate_power_product) + (ff_r_ftsp_reflected_prime_candidate_power_product))) /\ ((((exists ff_h_ftsp_reflected_prime_candidate_power_product_successor. ff_h_ftsp_reflected_prime_candidate_power_product_successor + S (ff_s_ftsp_reflected_prime_candidate_power_product) = S ((S (S ff_i_ftsp_reflected_prime_candidate_power_product)) * ff_v_ftsp_reflected_prime_candidate_power_product)) /\ exists ff_q_ftsp_reflected_prime_candidate_power_product_successor. ff_u_ftsp_reflected_prime_candidate_power_product = ff_q_ftsp_reflected_prime_candidate_power_product_successor * S ((S (S ff_i_ftsp_reflected_prime_candidate_power_product)) * ff_v_ftsp_reflected_prime_candidate_power_product) + (ff_s_ftsp_reflected_prime_candidate_power_product))) /\ ff_s_ftsp_reflected_prime_candidate_power_product = ff_r_ftsp_reflected_prime_candidate_power_product * ff_p_ftsp_reflected_prime_candidate_power_product)))))))) /\ (exists bpv_factor_ftsp_reflected_prime_candidate_divides. q = bpv_result_ftsp_reflected_prime_candidate * bpv_factor_ftsp_reflected_prime_candidate_divides))) -> (exists bpv_gap_ftsp_reflected_prime_maximal. bpv_gap_ftsp_reflected_prime_maximal + bpv_candidate_ftsp_reflected_prime = f)) -> (((exists bpv_gap_ftsp_reflected_product_exponent_bound. bpv_gap_ftsp_reflected_product_exponent_bound + g = (n * q)) /\ (exists bpv_result_ftsp_reflected_product_selected. ((exists ff_b_ftsp_reflected_product_selected_power ff_c_ftsp_reflected_product_selected_power. ((forall ff_i_ftsp_reflected_product_selected_power_repeat. (exists ff_lt_ftsp_reflected_product_selected_power_repeat_bound. ff_lt_ftsp_reflected_product_selected_power_repeat_bound + S ff_i_ftsp_reflected_product_selected_power_repeat = g) -> (((exists ff_h_ftsp_reflected_product_selected_power_repeat_decoded. ff_h_ftsp_reflected_product_selected_power_repeat_decoded + S (p) = S ((S (ff_i_ftsp_reflected_product_selected_power_repeat)) * ff_c_ftsp_reflected_product_selected_power)) /\ exists ff_q_ftsp_reflected_product_selected_power_repeat_decoded. ff_b_ftsp_reflected_product_selected_power = ff_q_ftsp_reflected_product_selected_power_repeat_decoded * S ((S (ff_i_ftsp_reflected_product_selected_power_repeat)) * ff_c_ftsp_reflected_product_selected_power) + (p)))) /\ (exists ff_u_ftsp_reflected_product_selected_power_product ff_v_ftsp_reflected_product_selected_power_product. ((((exists ff_h_ftsp_reflected_product_selected_power_product_start. ff_h_ftsp_reflected_product_selected_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_reflected_product_selected_power_product)) /\ exists ff_q_ftsp_reflected_product_selected_power_product_start. ff_u_ftsp_reflected_product_selected_power_product = ff_q_ftsp_reflected_product_selected_power_product_start * S ((S (0)) * ff_v_ftsp_reflected_product_selected_power_product) + (1))) /\ ((((exists ff_h_ftsp_reflected_product_selected_power_product_terminal. ff_h_ftsp_reflected_product_selected_power_product_terminal + S (bpv_result_ftsp_reflected_product_selected) = S ((S (g)) * ff_v_ftsp_reflected_product_selected_power_product)) /\ exists ff_q_ftsp_reflected_product_selected_power_product_terminal. ff_u_ftsp_reflected_product_selected_power_product = ff_q_ftsp_reflected_product_selected_power_product_terminal * S ((S (g)) * ff_v_ftsp_reflected_product_selected_power_product) + (bpv_result_ftsp_reflected_product_selected))) /\ forall ff_i_ftsp_reflected_product_selected_power_product. (exists ff_lt_ftsp_reflected_product_selected_power_product_bound. ff_lt_ftsp_reflected_product_selected_power_product_bound + S ff_i_ftsp_reflected_product_selected_power_product = g) -> exists ff_p_ftsp_reflected_product_selected_power_product ff_r_ftsp_reflected_product_selected_power_product ff_s_ftsp_reflected_product_selected_power_product. ((((exists ff_h_ftsp_reflected_product_selected_power_product_factor. ff_h_ftsp_reflected_product_selected_power_product_factor + S (ff_p_ftsp_reflected_product_selected_power_product) = S ((S (ff_i_ftsp_reflected_product_selected_power_product)) * ff_c_ftsp_reflected_product_selected_power)) /\ exists ff_q_ftsp_reflected_product_selected_power_product_factor. ff_b_ftsp_reflected_product_selected_power = ff_q_ftsp_reflected_product_selected_power_product_factor * S ((S (ff_i_ftsp_reflected_product_selected_power_product)) * ff_c_ftsp_reflected_product_selected_power) + (ff_p_ftsp_reflected_product_selected_power_product))) /\ ((((exists ff_h_ftsp_reflected_product_selected_power_product_partial. ff_h_ftsp_reflected_product_selected_power_product_partial + S (ff_r_ftsp_reflected_product_selected_power_product) = S ((S (ff_i_ftsp_reflected_product_selected_power_product)) * ff_v_ftsp_reflected_product_selected_power_product)) /\ exists ff_q_ftsp_reflected_product_selected_power_product_partial. ff_u_ftsp_reflected_product_selected_power_product = ff_q_ftsp_reflected_product_selected_power_product_partial * S ((S (ff_i_ftsp_reflected_product_selected_power_product)) * ff_v_ftsp_reflected_product_selected_power_product) + (ff_r_ftsp_reflected_product_selected_power_product))) /\ ((((exists ff_h_ftsp_reflected_product_selected_power_product_successor. ff_h_ftsp_reflected_product_selected_power_product_successor + S (ff_s_ftsp_reflected_product_selected_power_product) = S ((S (S ff_i_ftsp_reflected_product_selected_power_product)) * ff_v_ftsp_reflected_product_selected_power_product)) /\ exists ff_q_ftsp_reflected_product_selected_power_product_successor. ff_u_ftsp_reflected_product_selected_power_product = ff_q_ftsp_reflected_product_selected_power_product_successor * S ((S (S ff_i_ftsp_reflected_product_selected_power_product)) * ff_v_ftsp_reflected_product_selected_power_product) + (ff_s_ftsp_reflected_product_selected_power_product))) /\ ff_s_ftsp_reflected_product_selected_power_product = ff_r_ftsp_reflected_product_selected_power_product * ff_p_ftsp_reflected_product_selected_power_product)))))))) /\ (exists bpv_factor_ftsp_reflected_product_selected_divides. (n * q) = bpv_result_ftsp_reflected_product_selected * bpv_factor_ftsp_reflected_product_selected_divides)))) /\ forall bpv_candidate_ftsp_reflected_product. (exists bpv_gap_ftsp_reflected_product_candidate_bound. bpv_gap_ftsp_reflected_product_candidate_bound + bpv_candidate_ftsp_reflected_product = (n * q)) -> (exists bpv_result_ftsp_reflected_product_candidate. ((exists ff_b_ftsp_reflected_product_candidate_power ff_c_ftsp_reflected_product_candidate_power. ((forall ff_i_ftsp_reflected_product_candidate_power_repeat. (exists ff_lt_ftsp_reflected_product_candidate_power_repeat_bound. ff_lt_ftsp_reflected_product_candidate_power_repeat_bound + S ff_i_ftsp_reflected_product_candidate_power_repeat = bpv_candidate_ftsp_reflected_product) -> (((exists ff_h_ftsp_reflected_product_candidate_power_repeat_decoded. ff_h_ftsp_reflected_product_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_ftsp_reflected_product_candidate_power_repeat)) * ff_c_ftsp_reflected_product_candidate_power)) /\ exists ff_q_ftsp_reflected_product_candidate_power_repeat_decoded. ff_b_ftsp_reflected_product_candidate_power = ff_q_ftsp_reflected_product_candidate_power_repeat_decoded * S ((S (ff_i_ftsp_reflected_product_candidate_power_repeat)) * ff_c_ftsp_reflected_product_candidate_power) + (p)))) /\ (exists ff_u_ftsp_reflected_product_candidate_power_product ff_v_ftsp_reflected_product_candidate_power_product. ((((exists ff_h_ftsp_reflected_product_candidate_power_product_start. ff_h_ftsp_reflected_product_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_reflected_product_candidate_power_product)) /\ exists ff_q_ftsp_reflected_product_candidate_power_product_start. ff_u_ftsp_reflected_product_candidate_power_product = ff_q_ftsp_reflected_product_candidate_power_product_start * S ((S (0)) * ff_v_ftsp_reflected_product_candidate_power_product) + (1))) /\ ((((exists ff_h_ftsp_reflected_product_candidate_power_product_terminal. ff_h_ftsp_reflected_product_candidate_power_product_terminal + S (bpv_result_ftsp_reflected_product_candidate) = S ((S (bpv_candidate_ftsp_reflected_product)) * ff_v_ftsp_reflected_product_candidate_power_product)) /\ exists ff_q_ftsp_reflected_product_candidate_power_product_terminal. ff_u_ftsp_reflected_product_candidate_power_product = ff_q_ftsp_reflected_product_candidate_power_product_terminal * S ((S (bpv_candidate_ftsp_reflected_product)) * ff_v_ftsp_reflected_product_candidate_power_product) + (bpv_result_ftsp_reflected_product_candidate))) /\ forall ff_i_ftsp_reflected_product_candidate_power_product. (exists ff_lt_ftsp_reflected_product_candidate_power_product_bound. ff_lt_ftsp_reflected_product_candidate_power_product_bound + S ff_i_ftsp_reflected_product_candidate_power_product = bpv_candidate_ftsp_reflected_product) -> exists ff_p_ftsp_reflected_product_candidate_power_product ff_r_ftsp_reflected_product_candidate_power_product ff_s_ftsp_reflected_product_candidate_power_product. ((((exists ff_h_ftsp_reflected_product_candidate_power_product_factor. ff_h_ftsp_reflected_product_candidate_power_product_factor + S (ff_p_ftsp_reflected_product_candidate_power_product) = S ((S (ff_i_ftsp_reflected_product_candidate_power_product)) * ff_c_ftsp_reflected_product_candidate_power)) /\ exists ff_q_ftsp_reflected_product_candidate_power_product_factor. ff_b_ftsp_reflected_product_candidate_power = ff_q_ftsp_reflected_product_candidate_power_product_factor * S ((S (ff_i_ftsp_reflected_product_candidate_power_product)) * ff_c_ftsp_reflected_product_candidate_power) + (ff_p_ftsp_reflected_product_candidate_power_product))) /\ ((((exists ff_h_ftsp_reflected_product_candidate_power_product_partial. ff_h_ftsp_reflected_product_candidate_power_product_partial + S (ff_r_ftsp_reflected_product_candidate_power_product) = S ((S (ff_i_ftsp_reflected_product_candidate_power_product)) * ff_v_ftsp_reflected_product_candidate_power_product)) /\ exists ff_q_ftsp_reflected_product_candidate_power_product_partial. ff_u_ftsp_reflected_product_candidate_power_product = ff_q_ftsp_reflected_product_candidate_power_product_partial * S ((S (ff_i_ftsp_reflected_product_candidate_power_product)) * ff_v_ftsp_reflected_product_candidate_power_product) + (ff_r_ftsp_reflected_product_candidate_power_product))) /\ ((((exists ff_h_ftsp_reflected_product_candidate_power_product_successor. ff_h_ftsp_reflected_product_candidate_power_product_successor + S (ff_s_ftsp_reflected_product_candidate_power_product) = S ((S (S ff_i_ftsp_reflected_product_candidate_power_product)) * ff_v_ftsp_reflected_product_candidate_power_product)) /\ exists ff_q_ftsp_reflected_product_candidate_power_product_successor. ff_u_ftsp_reflected_product_candidate_power_product = ff_q_ftsp_reflected_product_candidate_power_product_successor * S ((S (S ff_i_ftsp_reflected_product_candidate_power_product)) * ff_v_ftsp_reflected_product_candidate_power_product) + (ff_s_ftsp_reflected_product_candidate_power_product))) /\ ff_s_ftsp_reflected_product_candidate_power_product = ff_r_ftsp_reflected_product_candidate_power_product * ff_p_ftsp_reflected_product_candidate_power_product)))))))) /\ (exists bpv_factor_ftsp_reflected_product_candidate_divides. (n * q) = bpv_result_ftsp_reflected_product_candidate * bpv_factor_ftsp_reflected_product_candidate_divides))) -> (exists bpv_gap_ftsp_reflected_product_maximal. bpv_gap_ftsp_reflected_product_maximal + bpv_candidate_ftsp_reflected_product = g)) -> (exists h. g = h + h) -> exists h. e = h + h

Every purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.

Definitions used by this theorem

In the theorem statement

In local proof propositions

Proof neighborhood

Direct theorem prerequisites

Direct theorem dependents

Definition-aware tactic body

Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay command.