Readable signature
PowerDivides(p,e,n)Exact expansion
exists bpv_result_bertrand_defined_power_divides. ((exists ff_b_bertrand_defined_power_divides_power ff_c_bertrand_defined_power_divides_power. ((forall ff_i_bertrand_defined_power_divides_power_repeat. (exists ff_lt_bertrand_defined_power_divides_power_repeat_bound. ff_lt_bertrand_defined_power_divides_power_repeat_bound + S ff_i_bertrand_defined_power_divides_power_repeat = e) -> (((exists ff_h_bertrand_defined_power_divides_power_repeat_decoded. ff_h_bertrand_defined_power_divides_power_repeat_decoded + S (p) = S ((S (ff_i_bertrand_defined_power_divides_power_repeat)) * ff_c_bertrand_defined_power_divides_power)) /\ exists ff_q_bertrand_defined_power_divides_power_repeat_decoded. ff_b_bertrand_defined_power_divides_power = ff_q_bertrand_defined_power_divides_power_repeat_decoded * S ((S (ff_i_bertrand_defined_power_divides_power_repeat)) * ff_c_bertrand_defined_power_divides_power) + (p)))) /\ (exists ff_u_bertrand_defined_power_divides_power_product ff_v_bertrand_defined_power_divides_power_product. ((((exists ff_h_bertrand_defined_power_divides_power_product_start. ff_h_bertrand_defined_power_divides_power_product_start + S (1) = S ((S (0)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_start. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_start * S ((S (0)) * ff_v_bertrand_defined_power_divides_power_product) + (1))) /\ ((((exists ff_h_bertrand_defined_power_divides_power_product_terminal. ff_h_bertrand_defined_power_divides_power_product_terminal + S (bpv_result_bertrand_defined_power_divides) = S ((S (e)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_terminal. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_terminal * S ((S (e)) * ff_v_bertrand_defined_power_divides_power_product) + (bpv_result_bertrand_defined_power_divides))) /\ forall ff_i_bertrand_defined_power_divides_power_product. (exists ff_lt_bertrand_defined_power_divides_power_product_bound. ff_lt_bertrand_defined_power_divides_power_product_bound + S ff_i_bertrand_defined_power_divides_power_product = e) -> exists ff_p_bertrand_defined_power_divides_power_product ff_r_bertrand_defined_power_divides_power_product ff_s_bertrand_defined_power_divides_power_product. ((((exists ff_h_bertrand_defined_power_divides_power_product_factor. ff_h_bertrand_defined_power_divides_power_product_factor + S (ff_p_bertrand_defined_power_divides_power_product) = S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_c_bertrand_defined_power_divides_power)) /\ exists ff_q_bertrand_defined_power_divides_power_product_factor. ff_b_bertrand_defined_power_divides_power = ff_q_bertrand_defined_power_divides_power_product_factor * S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_c_bertrand_defined_power_divides_power) + (ff_p_bertrand_defined_power_divides_power_product))) /\ ((((exists ff_h_bertrand_defined_power_divides_power_product_partial. ff_h_bertrand_defined_power_divides_power_product_partial + S (ff_r_bertrand_defined_power_divides_power_product) = S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_partial. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_partial * S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product) + (ff_r_bertrand_defined_power_divides_power_product))) /\ ((((exists ff_h_bertrand_defined_power_divides_power_product_successor. ff_h_bertrand_defined_power_divides_power_product_successor + S (ff_s_bertrand_defined_power_divides_power_product) = S ((S (S ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_successor. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_successor * S ((S (S ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product) + (ff_s_bertrand_defined_power_divides_power_product))) /\ ff_s_bertrand_defined_power_divides_power_product = ff_r_bertrand_defined_power_divides_power_product * ff_p_bertrand_defined_power_divides_power_product)))))))) /\ (exists bpv_factor_bertrand_defined_power_divides_divides. n = bpv_result_bertrand_defined_power_divides * bpv_factor_bertrand_defined_power_divides_divides))This node is conservative notation, not a theorem, new axiom, predicate constant, or kernel rule. Its expansion is checked for exact first-order AST equivalence.
Definition neighborhood
Expands using
Used by definitions
Used by theorem statements or local proof propositions
BT00Q3 power_divides_decidable BT00Q4 power_divides_zero BT00Q5 bounded_power_valuation_search BT00Q6 bounded_power_valuation_exists BT00Q9 power_valuation_power_divides BT00QA power_valuation_dominates BT00QG prime_power_divides_exponent_le_value BT00QH power_valuation_successor_not_divides BT00QI power_valuation_selected_and_successor_not_divides BT00QK power_divides_exponent_antitone BT00QL power_divides_add_mul BT00QM power_divides_successor_of_cofactor BT00QN prime_power_successor_cancel_cofactor BT00QP power_valuation_exact_cofactor BT00QQ power_valuation_mul_successor_not_divides BT00QR power_valuation_mul_lower BT00QS power_valuation_mul_upper BT00RL prime_power_valuation_one_zero BT00SB prime_power_divides_exponent_le_valuation BT00SC power_divides_of_exponent_le_valuation BT00SI valuation_threshold_bit_decides_power_divides BT00SK power_quotient_successor_pointwise_add BT00W0 power_valuation_nonzero_exponent_divides_base BT00YX prime_contribution_factor_divides BT0101 prime_contribution_selected_successor_divides BT0102 prime_contribution_cofactor_prime_contradiction