Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Definition in prerequisite notation
∃ ff_b_defined_power. ∃ ff_c_defined_power. Repeat(ff_b_defined_power,ff_c_defined_power,a,e) ∧ Product(ff_b_defined_power,ff_c_defined_power,e,z)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists ff_b_defined_power ff_c_defined_power. ((forall ff_i_defined_power_repeat. (exists ff_lt_defined_power_repeat_bound. ff_lt_defined_power_repeat_bound + S ff_i_defined_power_repeat = e) -> (((exists ff_h_defined_power_repeat_decoded. ff_h_defined_power_repeat_decoded + S (a) = S ((S (ff_i_defined_power_repeat)) * ff_c_defined_power)) /\ exists ff_q_defined_power_repeat_decoded. ff_b_defined_power = ff_q_defined_power_repeat_decoded * S ((S (ff_i_defined_power_repeat)) * ff_c_defined_power) + (a)))) /\ (exists ff_u_defined_power_product ff_v_defined_power_product. ((((exists ff_h_defined_power_product_start. ff_h_defined_power_product_start + S (1) = S ((S (0)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_start. ff_u_defined_power_product = ff_q_defined_power_product_start * S ((S (0)) * ff_v_defined_power_product) + (1))) /\ ((((exists ff_h_defined_power_product_terminal. ff_h_defined_power_product_terminal + S (z) = S ((S (e)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_terminal. ff_u_defined_power_product = ff_q_defined_power_product_terminal * S ((S (e)) * ff_v_defined_power_product) + (z))) /\ forall ff_i_defined_power_product. (exists ff_lt_defined_power_product_bound. ff_lt_defined_power_product_bound + S ff_i_defined_power_product = e) -> exists ff_p_defined_power_product ff_r_defined_power_product ff_s_defined_power_product. ((((exists ff_h_defined_power_product_factor. ff_h_defined_power_product_factor + S (ff_p_defined_power_product) = S ((S (ff_i_defined_power_product)) * ff_c_defined_power)) /\ exists ff_q_defined_power_product_factor. ff_b_defined_power = ff_q_defined_power_product_factor * S ((S (ff_i_defined_power_product)) * ff_c_defined_power) + (ff_p_defined_power_product))) /\ ((((exists ff_h_defined_power_product_partial. ff_h_defined_power_product_partial + S (ff_r_defined_power_product) = S ((S (ff_i_defined_power_product)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_partial. ff_u_defined_power_product = ff_q_defined_power_product_partial * S ((S (ff_i_defined_power_product)) * ff_v_defined_power_product) + (ff_r_defined_power_product))) /\ ((((exists ff_h_defined_power_product_successor. ff_h_defined_power_product_successor + S (ff_s_defined_power_product) = S ((S (S ff_i_defined_power_product)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_successor. ff_u_defined_power_product = ff_q_defined_power_product_successor * S ((S (S ff_i_defined_power_product)) * ff_v_defined_power_product) + (ff_s_defined_power_product))) /\ ff_s_defined_power_product = ff_r_defined_power_product * ff_p_defined_power_product)))))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.
Direct definition dependencies
Definitions depending on this notation
Checked theorems using this definition
SK0011 · power_value_eq_transportSK0012 · power_one_base_valueSK0013 · power_one_base_existsSK0014 · power_product_constructSK0015 · power_divisible_exponent_rootSK0016 · positive_power_nonzero_baseSK0017 · positive_power_prime_valuations_divisibleSK0018 · prime_valuation_divisibility_cofactorSK0019 · prime_valuation_divisible_power_root_boundedSK001A · prime_valuation_divisible_power_root_existsSK0023 · prime_valuation_support_exponent_gcd_nonzeroSK0024 · prime_exponent_entry_has_prime_valuationSK0025 · prime_support_common_divisor_implies_all_valuationsSK0028 · prime_support_perfect_power_iff_degree_dividesSK0029 · prime_support_exponent_gcd_roots_availableSK002A · perfect_power_root_table_prefix_appendSK002B · perfect_power_root_table_conditional_entrySK002C · perfect_power_root_table_prefix_existsSK002D · perfect_power_root_table_existsSK002F · perfect_power_profile_existsSK0030 · perfect_power_profile_data_degree_classificationSK0031 · perfect_power_profile_data_root_lookup