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
∀ b. ∀ c. ∀ i. ∀ x. BetaAt(b,c,i,x) → Le(x,b)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
2 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall b c i x. ((exists h. h + S x = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + x) -> exists h. h + x = bProof 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.
01Fix variables and assumptionsL1–5
02Separate the logical casesL6–7
03Construct an explicit witnessL8–8
Supply the displayed value, then prove that it has the required property.
- L8
exists x1 * S ((S i) * c)
04Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
symm
05Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
exact hat_right_witness