Technical Lean evidence record
Checked Artifact: Tietze Extension Theorem — Bounded Real-Valued Form (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
BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding- Module
Mathlib.Topology.TietzeExtension- Source file checked
Mathlib/Topology/TietzeExtension.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 target indexes Mathlib's bounded real-valued Tietze extension theorem in closed-embedding form. For topological spaces X and Y with Y normal, a bounded continuous f : X →ᵇ ℝ and a closed embedding e : X → Y admit a bounded continuous g : Y →ᵇ ℝ with ‖g‖ = ‖f‖ and g ∘ e = f. It is not the unbounded-function theorem, an arbitrary-codomain theorem, a uniqueness statement, or a canonical or constructive extension algorithm.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.