Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Definition in prerequisite notation
¬d = 0 ∧ (Dvd(d,n) ∧ PrimeFactorToggle(p,d,e)) ∨ (d = 0 ∨ ¬Dvd(d,n)) ∧ e = dOnly definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
(((~(((d))=0)) /\ (((exists pvs_factor_lowercontinuationdivisor. ((n)) = ((d)) * pvs_factor_lowercontinuationdivisor) /\ ((((~(exists pvs_factor_lowercontinuationtogglefresh_input. ((d)) = ((p)) * pvs_factor_lowercontinuationtogglefresh_input)) /\ (((e))=((p))*((d))))) \/ ((((((d))=((p))*((e))) /\ (~(exists pvs_factor_lowercontinuationtogglefresh_output. ((e)) = ((p)) * pvs_factor_lowercontinuationtogglefresh_output)))) \/ (((exists pvs_factor_lowercontinuationtogglesquare. ((d)) = (((p))*((p))) * pvs_factor_lowercontinuationtogglesquare) /\ (((e))=((d))))))))))) \/ (((((d))=0 \/ ~(exists pvs_factor_lowercontinuationnondivisor. ((n)) = ((d)) * pvs_factor_lowercontinuationnondivisor)) /\ (((e))=((d)))))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
MC0008 · divisor_prime_toggle_existsMC0009 · divisor_prime_toggle_functionalMC000A · divisor_prime_toggle_symmetricMC000B · divisor_prime_toggle_boundedMC000C · divisor_prime_toggle_prefix_existsMC000D · divisor_prime_toggle_prefix_lookupMC000E · divisor_prime_toggle_prefix_permutationMC0012 · mobius_divisor_mask_prime_toggle_negatesMC0016 · mobius_divisor_mask_prime_factor_sum_zero