linearEquiv — Mathlib

English

The map domain restriction respects composition: lmapDomain M R (g ∘ f) = (lmapDomain M R g) ∘ (lmapDomain M R f).

Русский

Ограничение области определения respects композицию: lmapDomain M R (g ∘ f) = (lmapDomain M R g) ∘ (lmapDomain M R f).

LaTeX

$$$\\text{lmapDomain}\\ M\\ R\\ (g\\circ f) = (\\text{lmapDomain}\\ M\\ R\\ g) \\circ (\\text{lmapDomain}\\ M\\ R\\ f)$$$

Lean4

/-- `Finsupp.mapDomain` as a `LinearEquiv`. -/
def linearEquiv (f : α ≃ α') : (α →₀ M) ≃ₗ[R] (α' →₀ M)
    where
  __ := lmapDomain M R f.toFun
  invFun := mapDomain f.symm
  left_inv _ := by simp [← mapDomain_comp]
  right_inv _ := by simp [← mapDomain_comp]

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