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 m n q. n = m * q + 0 -> exists k. n = m * kStructural proof guide
A quotient decomposition with zero remainder supplies a divisibility witness.
Direct prerequisites: none. The authored body proceeds by equality transport (1).
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.
01Fix variables and assumptionsL1–4
02Construct an explicit witnessL5–5
Supply the displayed value, then prove that it has the required property.
- L5
exists q