PD0028

AllPrime(b,c,l)

Every decoded factor below l is prime.

Conservative notation; not a theorem, primitive, or axiom.

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.

Hygienic expanded first-order definition

forall dp_i. (exists dp_gap. dp_gap + S dp_i = l) -> exists dp_p. ((((exists ff_h_defined_all_prime_entry. ff_h_defined_all_prime_entry + S (dp_p) = S ((S (dp_i)) * c)) /\ exists ff_q_defined_all_prime_entry. b = ff_q_defined_all_prime_entry * S ((S (dp_i)) * c) + (dp_p))) /\ (~(dp_p = 1) /\ forall dp_a dp_d. dp_p = dp_a * dp_d -> dp_a = 1 \/ dp_d = 1))

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

none

Checked theorems using this definition