map_comp — Mathlib

English

For uniformly continuous f: α → β and g: β → γ, the induced map satisfies map g ∘ map f = map (g ∘ f).

Русский

Для равномерно непрерывных f: α → β и g: β → γ выполняется map g ∘ map f = map (g ∘ f).

LaTeX

$$$\text{map } g \circ \text{map } f = \text{map } (g \circ f)$$$

Lean4

theorem map_comp {f : α → β} {g : β → γ} (hf : UniformContinuous f) (hg : UniformContinuous g) :
    map g ∘ map f = map (g ∘ f) :=
  (map_unique (hg.comp hf) <| by simp only [Function.comp_def, map_mk, hf, hg]).symm

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