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.
This branch proves the finite determinant/rank/span substrate. It does not claim Smith or Hermite normal form, lattice index equals determinant, determinant multiplicativity, lattice reduction, or geometry-of-numbers theorems.
Exact theorem in conservative defined notation
∀ p. ∀ n. ∀ P. ∀ N. p + N = P + n → n + P = N + pEvery linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 11 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 assumptionsL1–5
02Calculate and transport equalitiesL6–6
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L6
trans P + n
03Use earlier factsL7–7
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L7
apply add_comm