Theorems · Theorem · general topology
JoinedIn.mem
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {F : Set X}, JoinedIn F x y → x ∈ F ∧ y ∈ F- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 5 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.
Cites9
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
- Pathproof · cited by 318
- JoinedInstatement and proof · cited by 40
- Path.sourceproof · cited by 26
- Path.targetproof · cited by 24
Cited by5
Results whose statement or proof uses this declaration.
- JoinedIn.transproof · cited by 4
- JoinedIn.symmproof · cited by 3
- JoinedIn.target_memproof · cited by 2
- JoinedIn.source_memproof · cited by 1
- isPathConnected_iff_eqproof · cited by 0