Technical Lean evidence record
Checked Artifact: Holomorphic Open Mapping 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
AnalyticOnNhd.is_constant_or_isOpen- Module
Mathlib.Analysis.Complex.OpenMapping- Source file checked
Mathlib/Analysis/Complex/OpenMapping.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 global holomorphic open-mapping declaration for a map g from a complex normed space E to ℂ that is analytic on a neighborhood of every point of a preconnected set U. It proves a disjunction: either g is constant on U, or the image of every ambient-open subset s contained in U is open in ℂ. It does not require U to be open, assert that g(U) is open when U is not open, state a global IsOpenMap result, or allow an arbitrary vector-valued codomain.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.