ext — Mathlib

English

There is a canonical algebra homomorphism from S to A over R, built from the tower.

Русский

Существует канонический алгебра-гомоморфизм из S в A над R, построенный из башни.

LaTeX

$$$\mathrm{toAlgHom} : S \to_{\mathbb{R}} A$$$

Lean4

@[ext]
theorem ext {S : Type u} {A : Type v} [CommSemiring S] [Semiring A] (h1 h2 : Algebra S A)
    (h : ∀ (r : S) (x : A), (by have I := h1; exact r • x) = r • x) : h1 = h2 :=
  Algebra.algebra_ext _ _ fun r => by
    simpa only [@Algebra.smul_def _ _ _ _ h1, @Algebra.smul_def _ _ _ _ h2, mul_one] using h r 1

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