Theorems · Theorem · algebraic topology
Path.Homotopic.hpath_hext
∀ {X : Type u} [inst : TopologicalSpace X] {x₀ x₁ x₂ x₃ : X} {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃},
(∀ (t : ↑unitInterval), p₁ t = p₂ t) → ⟦p₁⟧ ≍ ⟦p₂⟧- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 132 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
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
- Path.Homotopic.Quotientstatement · cited by 55
- Path.extproof · cited by 30
- Path.sourceproof · cited by 26
- Path.targetproof · cited by 24
- Path.Homotopic.setoidstatement and proof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMap.Homotopy.heq_path_of_eq_imageproof · cited by 1
- ContinuousMap.Homotopy.evalAt_eqproof · cited by 1