Theorems · Theorem · general topology
Path.range_subpath
∀ {X : Type u_1} [inst : TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ↑unitInterval),
Set.range ⇑(γ.subpath t₀ t₁) = ⇑γ '' Set.uIcc t₀ t₁The range of a subpath is the image of the original path on the relevant interval.
- Defined in
- Mathlib.Topology.Subpath
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 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.
Cites17
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 and proof · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- Set.Iccproof · cited by 1,702
- unitIntervalstatement and proof · cited by 607
- Set.uIccstatement · cited by 393
- Pathstatement and proof · cited by 318
- Set.range_compproof · cited by 223
Cited by2
Results whose statement or proof uses this declaration.
- Path.range_subpath_of_geproof · cited by 0
- Path.range_subpath_of_leproof · cited by 0