ringInverse_eq_inverse — Mathlib

English

For invertible g, (g ∘ f).inverse = f.inverse ∘ g.inverse.

Русский

Для обратимого $g$ выполнено $(g \circ f)^{-1} = f^{-1} \circ g^{-1}$.

LaTeX

$$inverse_comp_of_left {g : M_2 →L[R] M_3} {f : M →L[R] M_2} (hg : g.IsInvertible) : (g ∘L f).inverse = f.inverse ∘L g.inverse$$

Lean4

theorem ringInverse_eq_inverse : Ring.inverse = inverse (R := R) (M := M) :=
  by
  ext
  simp [inverse_eq_ringInverse (ContinuousLinearEquiv.refl R M)]

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