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 b c. (exists k. k + a = b) -> exists r. r + c * a = c * bStructural proof guide
Generated structural guide
Left multiplication preserves the witness-defined order.
Use the direct prerequisites mul_add as previously established PA formulas.
The proof proceeds by case analysis (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 assumptionsL1–4
02Separate the logical casesL5–5
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L5
cases h
03Construct an explicit witnessL6–6
Supply the displayed value, then prove that it has the required property.
- L6
exists c * x
04Calculate and transport equalitiesL7–8
05Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
apply mul_add
06Calculate and transport equalitiesL10–11
07Use earlier factsL12–12
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L12
exact h_witness