Lean verification record
Checked Artifact: Thales’ Theorem (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.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 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
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 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 does not establish novelty, transfer a historical acceptance decision, or authorize publication.