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
∀ a. IsGCD(a,a,0)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
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-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)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 assumptionsL1–1
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 defined 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