Theorems · Theorem · general topology
Path.ext
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {γ₁ γ₂ : Path x y}, ⇑γ₁ = ⇑γ₂ → γ₁ = γ₂- Defined in
- Mathlib.Topology.Path
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 119 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Continuousproof · cited by 2,592
- ContinuousMapproof · cited by 2,491
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
- ContinuousMap.toFunproof · cited by 72
- ContinuousMap.casesOnproof · cited by 18
- Path.casesOnproof · cited by 1
Cited by30
Results whose statement or proof uses this declaration.
- Path.trans_symmproof · cited by 3
- Path.truncate_selfproof · cited by 2
- Path.segment_sameproof · cited by 2
- IsCoveringMap.map_liftPathQuotientproof · cited by 2
- Path.Homotopic.hpath_hextproof · cited by 2
- Circle.path_selfproof · cited by 2
- Path.trans_pi_eq_pi_transproof · cited by 1
- Path.delayReflRight_oneproof · cited by 1
- Path.delayReflRight_zeroproof · cited by 1
- Path.refl_trans_reflproof · cited by 1
- Path.map_transproof · cited by 1
- Path.ofLine_extendproof · cited by 0