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.
The natural-code carrier consists of genuine pairs of the existing signed integers; no new primitive arithmetic is trusted. The theorem constructs quotient, remainder, and actual norm witnesses. Gaussian gcd, unique factorization, and prime classification are separate targets.
Exact theorem in conservative defined notation
∀ a. ∀ b. ∀ c. ∀ d. ∀ e. ∀ f. ∀ g. ∀ h. ∀ i. ∀ j. ∀ k. ∀ l. a · (f + i) + b · (e + j) + (c · (g + l) + d · (h + k)) = a · f + b · e + (c · g + d · h) + (a · i + b · j + (c · l + d · k))Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 13 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 assumptionsL1–10
02Fix variables and assumptionsL11–12
03Calculate and transport equalitiesL13–13
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L13
simp [mul_add, add_assoc, add_comm, four_square_add_swap_right_tail]