Technical Lean evidence record
Checked Artifact: Thales’ Theorem (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.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter- Module
Mathlib.Geometry.Euclidean.Angle.Sphere- Source file checked
Mathlib/Geometry/Euclidean/Angle/Sphere.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 theorem for a metric affine space P modeled on a real inner-product space V. Once s.IsDiameter p₁ p₃ is given, the declaration proves ∠p₁p₂p₃ = π/2 if and only if p₂ ∈ s. It has no dimension-two, pairwise-distinctness, or positive-radius hypothesis. A planar great-circle picture is an illustrative cross-section, not the theorem’s full scope. The selected declaration does not prove the nearby two-dimensional result that recovers a diameter from three points already lying on an arbitrary sphere.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.