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.
Statement with defined notation
∀ n. ¬n = 0 → ¬n = 1 → ∃ x. Prime(x) ∧ Dvd(x,n)Every purple notation token opens its conservative definition. Expanding the displayed statement recovers the exact first-order Peano-arithmetic formula checked by the unchanged kernel.
Definitions used by this theorem
In the theorem statement
2 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall n. ~(n = 0) -> ~(n = 1) -> exists p. ((~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1) /\ exists k. n = p * k)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. Every changed line has an exact-AST conservative-expansion receipt; the kernel still receives the immutable original tactic script.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (2)
01Fix variables and assumptionsL1–3
Original defined command ledger · 9 lines
- 0001
intro n - 0002
intro hn0 - 0003
intro hn1 - 0004
specialize prime_divisor_exists_up_to n - 0005
specialize prime_divisor_exists_up_to n - 0006
apply prime_divisor_exists_up_to - 0007
apply le_refl - 0008
exact hn0 - 0009
exact hn1