PD0028

AllPrime(b,c,l)

Public research checkpoint, not admitted to Alpha or Stable. Alpha v30 remains 3222 checked-use theorems; Stable remains 432. The on-demand Alpha Lean service does not yet expose these checkpoint theorems; their independently checked literal bundles and unchanged sources are available below.

Every decoded factor below l is prime.

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

Definition in prerequisite notation

∀ dp_i. Lt(dp_i,l) → ∃ x. BetaAt(b,c,dp_i,x) ∧ Prime(x)

Only definitions earlier in this acyclic notation graph are used here.

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

Lt(a,b)Prime(p)BetaAt(b,c,i,x)

Definitions depending on this notation

PrimeFactorList(n,b,c,l)

Checked theorems using this definition

none directly; see definition consumers