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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 t₁

The 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

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