Lean verification record

Checked Artifact: Law of Cosines (mathlib)

Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.

Verification result

The recorded Lean checks passed

Build replaypassed with retained transcript
Unfinished stepsNone found
Source identityPinned commit and file recorded
Dependency profileAxiom closure recorded

Reproducibility details

What the checker recorded

Declaration checked: EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle
Module: Mathlib.Geometry.Euclidean.Triangle
Source file checked: Mathlib/Geometry/Euclidean/Triangle.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build transcript: passed · retained with this record
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Collection provenance: Clean source state recorded

ProofAtlas record

What has been checked

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed pageCurrent public presentation reviewed

Accepted Atlas resultNot recorded for the preferred artifact

Mathlib is the source of the theorem; the local Lean replay and page review are separate.

Evidence boundary

Exact formal statement only

This page indexes Mathlib's angle-at-point law of cosines for arbitrary points p₁, p₂, and p₃ in an affine metric space modeled on a real inner-product space. The selected identity places the angle at p₂ and the opposite distance between p₁ and p₃. It assumes neither distinctness nor non-collinearity, so degenerate triples are included. It is not restricted to the Euclidean plane and does not state the law of sines, recover an angle, or add a nondegenerate-triangle hypothesis.

This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.