Theorems · Theorem · general topology
Joined.symm
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X}, Joined x y → Joined y x- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 3 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Path.symmproof · cited by 35
- Joinedstatement and proof · cited by 29
- Joined.somePathproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- JoinedIn.symmproof · cited by 3
- mem_pathComponent_of_memproof · cited by 1
- pathComponent_congrproof · cited by 0