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.
Sets are complete characteristic-bit codes with actual finite cardinality witnesses. The proof constructs translations and the sumset; no finite-choice oracle, supplied cardinality conclusion, or unproved polynomial-method premise is used.
Exact theorem in conservative defined notation
∀ i. BetaAt(0,0,i,0)Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 6 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay 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 assumptionsL1–1
Work with arbitrary variables or the premises of the current implication.
- L1
intro i
02Separate the logical casesL2–2
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L2
split
03Construct an explicit witnessL3–3
Supply the displayed value, then prove that it has the required property.
- L3
exists 0
04Calculate and transport equalitiesL4–4
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L4
simp
05Construct an explicit witnessL5–5
Supply the displayed value, then prove that it has the required property.
- L5
exists 0
06Calculate and transport equalitiesL6–6
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L6
simp