beta_product_uniform_le_pow

Exact expanded PA statement

forall b c a l n q. (forall i x. (exists bpulp_bound. bpulp_bound + S i = l) -> (((exists ff_h_bpulp_source. ff_h_bpulp_source + S (x) = S ((S (i)) * c)) /\ exists ff_q_bpulp_source. b = ff_q_bpulp_source * S ((S (i)) * c) + (x))) -> exists bpulp_factor_gap. bpulp_factor_gap + x = a) -> (exists ff_u_bpulp_source_product ff_v_bpulp_source_product. ((((exists ff_h_bpulp_source_product_start. ff_h_bpulp_source_product_start + S (1) = S ((S (0)) * ff_v_bpulp_source_product)) /\ exists ff_q_bpulp_source_product_start. ff_u_bpulp_source_product = ff_q_bpulp_source_product_start * S ((S (0)) * ff_v_bpulp_source_product) + (1))) /\ ((((exists ff_h_bpulp_source_product_terminal. ff_h_bpulp_source_product_terminal + S (n) = S ((S (l)) * ff_v_bpulp_source_product)) /\ exists ff_q_bpulp_source_product_terminal. ff_u_bpulp_source_product = ff_q_bpulp_source_product_terminal * S ((S (l)) * ff_v_bpulp_source_product) + (n))) /\ forall ff_i_bpulp_source_product. (exists ff_lt_bpulp_source_product_bound. ff_lt_bpulp_source_product_bound + S ff_i_bpulp_source_product = l) -> exists ff_p_bpulp_source_product ff_r_bpulp_source_product ff_s_bpulp_source_product. ((((exists ff_h_bpulp_source_product_factor. ff_h_bpulp_source_product_factor + S (ff_p_bpulp_source_product) = S ((S (ff_i_bpulp_source_product)) * c)) /\ exists ff_q_bpulp_source_product_factor. b = ff_q_bpulp_source_product_factor * S ((S (ff_i_bpulp_source_product)) * c) + (ff_p_bpulp_source_product))) /\ ((((exists ff_h_bpulp_source_product_partial. ff_h_bpulp_source_product_partial + S (ff_r_bpulp_source_product) = S ((S (ff_i_bpulp_source_product)) * ff_v_bpulp_source_product)) /\ exists ff_q_bpulp_source_product_partial. ff_u_bpulp_source_product = ff_q_bpulp_source_product_partial * S ((S (ff_i_bpulp_source_product)) * ff_v_bpulp_source_product) + (ff_r_bpulp_source_product))) /\ ((((exists ff_h_bpulp_source_product_successor. ff_h_bpulp_source_product_successor + S (ff_s_bpulp_source_product) = S ((S (S ff_i_bpulp_source_product)) * ff_v_bpulp_source_product)) /\ exists ff_q_bpulp_source_product_successor. ff_u_bpulp_source_product = ff_q_bpulp_source_product_successor * S ((S (S ff_i_bpulp_source_product)) * ff_v_bpulp_source_product) + (ff_s_bpulp_source_product))) /\ ff_s_bpulp_source_product = ff_r_bpulp_source_product * ff_p_bpulp_source_product)))))) -> (exists ff_b_bpulp_target_power ff_c_bpulp_target_power. ((forall ff_i_bpulp_target_power_repeat. (exists ff_lt_bpulp_target_power_repeat_bound. ff_lt_bpulp_target_power_repeat_bound + S ff_i_bpulp_target_power_repeat = l) -> (((exists ff_h_bpulp_target_power_repeat_decoded. ff_h_bpulp_target_power_repeat_decoded + S (a) = S ((S (ff_i_bpulp_target_power_repeat)) * ff_c_bpulp_target_power)) /\ exists ff_q_bpulp_target_power_repeat_decoded. ff_b_bpulp_target_power = ff_q_bpulp_target_power_repeat_decoded * S ((S (ff_i_bpulp_target_power_repeat)) * ff_c_bpulp_target_power) + (a)))) /\ (exists ff_u_bpulp_target_power_product ff_v_bpulp_target_power_product. ((((exists ff_h_bpulp_target_power_product_start. ff_h_bpulp_target_power_product_start + S (1) = S ((S (0)) * ff_v_bpulp_target_power_product)) /\ exists ff_q_bpulp_target_power_product_start. ff_u_bpulp_target_power_product = ff_q_bpulp_target_power_product_start * S ((S (0)) * ff_v_bpulp_target_power_product) + (1))) /\ ((((exists ff_h_bpulp_target_power_product_terminal. ff_h_bpulp_target_power_product_terminal + S (q) = S ((S (l)) * ff_v_bpulp_target_power_product)) /\ exists ff_q_bpulp_target_power_product_terminal. ff_u_bpulp_target_power_product = ff_q_bpulp_target_power_product_terminal * S ((S (l)) * ff_v_bpulp_target_power_product) + (q))) /\ forall ff_i_bpulp_target_power_product. (exists ff_lt_bpulp_target_power_product_bound. ff_lt_bpulp_target_power_product_bound + S ff_i_bpulp_target_power_product = l) -> exists ff_p_bpulp_target_power_product ff_r_bpulp_target_power_product ff_s_bpulp_target_power_product. ((((exists ff_h_bpulp_target_power_product_factor. ff_h_bpulp_target_power_product_factor + S (ff_p_bpulp_target_power_product) = S ((S (ff_i_bpulp_target_power_product)) * ff_c_bpulp_target_power)) /\ exists ff_q_bpulp_target_power_product_factor. ff_b_bpulp_target_power = ff_q_bpulp_target_power_product_factor * S ((S (ff_i_bpulp_target_power_product)) * ff_c_bpulp_target_power) + (ff_p_bpulp_target_power_product))) /\ ((((exists ff_h_bpulp_target_power_product_partial. ff_h_bpulp_target_power_product_partial + S (ff_r_bpulp_target_power_product) = S ((S (ff_i_bpulp_target_power_product)) * ff_v_bpulp_target_power_product)) /\ exists ff_q_bpulp_target_power_product_partial. ff_u_bpulp_target_power_product = ff_q_bpulp_target_power_product_partial * S ((S (ff_i_bpulp_target_power_product)) * ff_v_bpulp_target_power_product) + (ff_r_bpulp_target_power_product))) /\ ((((exists ff_h_bpulp_target_power_product_successor. ff_h_bpulp_target_power_product_successor + S (ff_s_bpulp_target_power_product) = S ((S (S ff_i_bpulp_target_power_product)) * ff_v_bpulp_target_power_product)) /\ exists ff_q_bpulp_target_power_product_successor. ff_u_bpulp_target_power_product = ff_q_bpulp_target_power_product_successor * S ((S (S ff_i_bpulp_target_power_product)) * ff_v_bpulp_target_power_product) + (ff_s_bpulp_target_power_product))) /\ ff_s_bpulp_target_power_product = ff_r_bpulp_target_power_product * ff_p_bpulp_target_power_product)))))))) -> exists bpulp_result_gap. bpulp_result_gap + n = q