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 c i x. (exists h. h + S x = S ((S i) * c)) -> ((exists h. h + S x = S ((S i) * c)) /\ exists q. x = q * S ((S i) * c) + x)Structural proof guide
A value below a Gödel-beta modulus decodes to itself when used as the code.
Direct prerequisites: mul_zero_left, zero_add. The authored body proceeds by equality transport (2).
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 assumptionsL1–4
02Separate the logical casesL5–5
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L5
split
03Use earlier factsL6–6
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L6
exact hx
04Construct an explicit witnessL7–7
Supply the displayed value, then prove that it has the required property.
- L7
exists 0
05Use earlier factsL8–8
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L8
specialize mul_zero_left (S ((S i) * c))
06Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
rewrite mul_zero_left
07Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
specialize zero_add x