Theorems · Theorem · algebraic topology
Path.Homotopy.refl_apply
∀ {X : Type u} [inst : TopologicalSpace X] {x₀ x₁ : X} (p : Path x₀ x₁) (x : ↑unitInterval × ↑unitInterval),
(Path.Homotopy.refl p) x = p x.2- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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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
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- ContinuousMapstatement · cited by 2,491
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
- ContinuousMap.HomotopyWithstatement · cited by 33
- Path.toContinuousMapstatement · cited by 27
- Path.Homotopy.reflstatement and proof · cited by 2
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