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.
G101 and G102 were OPEN when these BitLen foundations were first admitted in Alpha v22. Both are now CLOSED in Alpha v23: complete canonical exponent digits and both exact logarithmic execution bounds are proved.
Exact theorem in conservative defined notation
∀ b. b = 0 ∨ b = 1 → Lt(b,2)Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete unchanged native tactic proof
All 9 lines are the exact independently kernel-checked original 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 assumptionsL1–2
02Separate the logical casesL3–3
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L3
cases hbit
03Construct an explicit witnessL4–4
Supply the displayed value, then prove that it has the required property.
- L4
exists 1
04Calculate and transport equalitiesL5–6
05Construct an explicit witnessL7–7
Supply the displayed value, then prove that it has the required property.
- L7
exists 0