setPreimage_comp — Mathlib

English

For f: α→β and g: β→γ, the preimage of g∘f equals the composition of the preimages: (g∘f)^{-1} = f^{-1} ∘ g^{-1}.

Русский

Для функций f: α→β и g: β→γ верно: (g∘f)^{-1} = f^{-1} ∘ g^{-1}.

LaTeX

$$$$ \operatorname{setPreimage}(g \circ f) = (\operatorname{setPreimage} f) \circ (\operatorname{setPreimage} g). $$$$

Lean4

theorem setPreimage_comp (g : β → γ) (f : α → β) : setPreimage (g ∘ f) = (setPreimage f).comp (setPreimage g) :=
  rfl

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