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.
Exact expanded PA statement
forall a. (((exists x. a = a * x) /\ (exists y. 0 = a * y)) /\ forall c. (exists u. a = c * u) -> (exists v. 0 = c * v) -> exists w. a = c * w)Structural proof guide
Every natural is the relational gcd of itself and zero.
Direct prerequisites: multiple_refl, multiple_zero. The authored body proceeds by direct introduction and elimination.
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing Stable membership.
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 assumptionsL1–1
Work with arbitrary variables or the premises of the current implication.
- L1
intro a
02Separate the logical casesL2–3
03Use earlier factsL4–7
04Fix variables and assumptionsL8–10
05Use earlier factsL11–11
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L11
exact ha
Original exact command ledger · 11 lines
- 0001
intro a - 0002
split - 0003
split - 0004
specialize multiple_refl a - 0005
exact multiple_refl - 0006
specialize multiple_zero a - 0007
exact multiple_zero - 0008
intro c - 0009
intro ha - 0010
intro hz - 0011
exact ha