unitsLift_symm_apply_apply_inv' — Mathlib

English

For f ∈ Units(C(X, M)), the symmetric inverse under unitsLift gives (unitsLift.symm f)(x)⁻¹ = f(x)⁻¹.

Русский

Для f ∈ Units(C(X, M)) симметрично обратное gives (unitsLift.symm f)(x)⁻¹ = f(x)⁻¹.

LaTeX

$$$(\mathrm{unitsLift})^{-1} (f)(x)^{-1} = f(x)^{-1}.$$$

Lean4

@[to_additive (attr := simp)]
theorem unitsLift_symm_apply_apply_inv' (f : C(X, M)ˣ) (x : X) :
    (ContinuousMap.unitsLift.symm f x)⁻¹ = (↑f⁻¹ : C(X, M)) x := by rfl

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