Theorems · Theorem · general topology
JoinedIn.mono
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {U V : Set X}, JoinedIn U x y → U ⊆ V → JoinedIn V x y- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- unitIntervalproof · cited by 607
- JoinedInstatement and proof · cited by 40
- JoinedIn.somePathproof · cited by 12
- JoinedIn.somePath_memproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- IsPathConnected.subset_pathComponentInproof · cited by 2
- IsPathConnected.unionproof · cited by 0