symm_range — Mathlib

English

For any Y, [TopologicalSpace Y], and g : Y → Path x y, Continuous ⁿ g is equivalent to Continuous g after uncurry.

Русский

Для любого Y и функции g: Y → Path x y акселерация непрерывности свернута обратно: Continuous(uncurry g) эквивалентно Continuous g.

LaTeX

$$$\\text{Continuous}(\\text{Path.instHasUncurryPath.uncurry } g) \\iff \\text{Continuous}(g)$$$

Lean4

@[simp]
theorem symm_range {a b : X} (γ : Path a b) : range γ.symm = range γ :=
  symm_involutive.surjective.range_comp γ

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