DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedaudited 2026-09-07

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Embedded smooth submanifolds with boundary

Definition

An embedded smooth submanifold with boundary of $M$ is a subset $S \subseteq M$ supplied with a manifold-with-boundary smooth structure for which $S ↪ M$ is a smooth embedding. In particular this definition does not assert $S \cap \partial M = \partial S$ .

Depends on

Immersions and embeddings for manifolds with boundary

Embedded smooth submanifolds with boundary

Definition

Depends on

Dependency tree · 2 levels

Sources