domCongr_comp_lsingle — Mathlib

English

The composition with lsingle commutes with domCongr: (domCongr k A e).toLinearMap ∘ lsingle g = lsingle (e g).

Русский

Сослагательнe с lsingle и domCongr: (domCongr k A e).toLinearMap ∘ lsingle g = lsingle (e g).

LaTeX

$$$\\big(\\mathrm{domCongr}\\ k\\;A\\;e\\big).toLinearMap \\circ \\mathrm{lsingle}\\ g = \\mathrm{lsingle}(e g)$$$

Lean4

@[to_additive (attr := simp)]
theorem domCongr_comp_lsingle (e : G ≃* H) (g : G) : (domCongr k A e).toLinearMap ∘ₗ lsingle g = lsingle (e g) := by
  ext; simp

Похожие утверждения