Artifact · open
Mathlib v4.30 source proposition Nat.euler_four_squares
This page records one proposition and the evidence attached to it. Text from the source ledger is shown as record data.
- Identifier
- F:ml430-nat-euler-four-squares-21d8c900
- Proof route
- Not assigned
- External status
- proved
- Axiom footprint
- Empty
Recorded description
The proposition declared as `Nat.euler_four_squares` in the pinned Mathlib v4.30 source.
∀ (a b c d x y z w : ℕ),
(↑a * ↑x - ↑b * ↑y - ↑c * ↑z - ↑d * ↑w).natAbs ^ 2 + (↑a * ↑y + ↑b * ↑x + ↑c * ↑w - ↑d * ↑z).natAbs ^ 2 +
(↑a * ↑z - ↑b * ↑w + ↑c * ↑x + ↑d * ↑y).natAbs ^ 2 +
(↑a * ↑w + ↑b * ↑z - ↑c * ↑y + ↑d * ↑x).natAbs ^ 2 =
(a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) * (x ^ 2 + y ^ 2 + z ^ 2 + w ^ 2)Dependencies
The graph shows direct ledger edges. Follow a node to open its artifact page.
0 direct dependencies 0 direct dependents
Evidence
Provenance
{
"date": "2026-08-29",
"established_by": "not established in this ledger",
"source": "statement-only extraction of `Nat.euler_four_squares` from Mathlib v4.30.0; no proof value was exposed",
"prior_art": [
{
"who": "the Mathlib contributors",
"what": "the theorem declaration `Nat.euler_four_squares`",
"where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
"year": 2026,
"attribution": "the proposition was read from the pinned statement-only inventory; the proof term and tactic trace were not consulted"
}
]
}