pow_const — Mathlib

English

If f =^l g, then f⁻¹ =^l g⁻¹ when β has an inverse operation.

Русский

Если f =^l g, то f⁻¹ =^l g⁻¹ при наличии операции обращения в β.

LaTeX

$$$\\\\forall f,g : \\\\alpha \\\\to \\\\beta \\\\forall l \\\\ (l : Filter \\\\alpha), \\\\ (f =^l g) \\\\Rightarrow \\\\ (f^{-1} =^l g^{-1})$$$

Lean4

@[to_additive (attr := gcongr, to_additive) const_smul]
theorem pow_const {γ} [Pow β γ] {f g : α → β} {l : Filter α} (h : f =ᶠ[l] g) (c : γ) : f ^ c =ᶠ[l] g ^ c :=
  h.fun_comp (· ^ c)

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