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 m n d. m * m = n * n + d -> ((2 * (m * n)) * (2 * (m * n)) + (d) * (d) = (m * m + n * n) * (m * m + n * n))Constructive proof overview
Generated structural guide
Euclid's explicit constructor supplies either canonical ordering of its odd/difference and doubled-product legs.
The unchanged tactic script uses 2 declared prerequisites and contains 7 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 assumptionsL1–4
Original exact command ledger · 7 lines
- 0001
intro m - 0002
intro n - 0003
intro d - 0004
intro hgap - 0005
apply pythagorean_leg_swap - 0006
apply pythagorean_euclidean_identity - 0007
exact hgap