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.
Exact expanded first-order arithmetic statement
forall a m n. ~(a = 0) -> m * m = n * n + a -> exists gap. gap + S n = mConstructive proof overview
Generated structural guide
The positive odd leg forces the two natural square roots into the required strict Euclidean order.
The unchanged tactic script uses 2 declared prerequisites and contains 13 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
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.
Named ingredients (2)
01Fix variables and assumptionsL1–5
02Establish hstrictL6–13
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply pythagorean positive add strict.
Original exact command ledger · 13 lines
- 0001
intro a - 0002
intro m - 0003
intro n - 0004
intro ha - 0005
intro hgap - 0006
have hstrict : exists gap. gap + S (n * n) = m * m - 0007
rewrite hgap - 0008
specialize pythagorean_positive_add_strict (n * n) - 0009
specialize pythagorean_positive_add_strict a - 0010
apply pythagorean_positive_add_strict - 0011
exact ha - 0012
apply square_lt_reflect - 0013
exact hstrict