Theorems · Definition · general topology
JoinedIn.somePath
{X : Type u_1} → [inst : TopologicalSpace X] → {x y : X} → {F : Set X} → JoinedIn F x y → Path x yWhen x and y are joined in F, choose a path from x to y inside F
- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Pathstatement · cited by 318
- JoinedInstatement and proof · cited by 40
Cited by12
Results whose statement or proof uses this declaration.
- JoinedIn.somePath_memstatement · cited by 7
- IsPathConnected.image'proof · cited by 3
- JoinedIn.joinedproof · cited by 2
- JoinedIn.monoproof · cited by 2
- JoinedIn.addproof · cited by 1
- JoinedIn.joined_subtypeproof · cited by 1
- JoinedIn.mulproof · cited by 1
- JoinedIn.piproof · cited by 1
- JoinedIn.prodproof · cited by 1
- JoinedIn.somePath.congr_simpstatement and proof · cited by 0
- JoinedIn.invproof · cited by 0
- JoinedIn.negproof · cited by 0