Technical Lean evidence record
Checked Artifact: Law of Cosines (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
ProofAtlas record
What has been checked
These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.
Mechanical evidence
- 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
- passed · transcript retained
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Clean collection provenance
- Recorded
Evidence boundary
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 is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.