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. (exists b. n = 2 * b) -> exists c. m * n = 2 * cStructural proof guide
Generated structural guide
A product with an even right factor is even.
Use the direct prerequisites mul_double_right as previously established PA formulas.
The proof proceeds by case analysis (1), equality transport (1).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.
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 (1)
01Fix variables and assumptionsL1–3
02Separate the logical casesL4–4
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L4
cases hn
03Construct an explicit witnessL5–5
Supply the displayed value, then prove that it has the required property.
- L5
exists m * x
04Calculate and transport equalitiesL6–6
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L6
rewrite hn_witness
05Use earlier factsL7–7
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L7
apply mul_double_right