Theorems · Theorem · general topology
JoinedIn.somePath_mem
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {F : Set X} (h : JoinedIn F x y) (t : ↑unitInterval),
h.somePath t ∈ F- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 121 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- unitIntervalstatement and proof · cited by 607
- Pathstatement · cited by 318
- JoinedInstatement and proof · cited by 40
- JoinedIn.somePathstatement · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- IsPathConnected.image'proof · cited by 3
- JoinedIn.monoproof · cited by 2
- JoinedIn.addproof · cited by 1
- JoinedIn.joined_subtypeproof · cited by 1
- JoinedIn.mulproof · cited by 1
- JoinedIn.invproof · cited by 0
- JoinedIn.negproof · cited by 0