subtype_comp_codRestrict — Mathlib

English

Restrict the codomain of a nonunital algebra homomorphism to a given subalgebra by enforcing the restriction on image values.

Русский

Ограничить кодомпозитор гомоморфизма до заданной подалгебры по значениям образа.

LaTeX

$$$\\text{codRestrict}(f,S,\\,hf) : A \\to B$ with $hf(x): f(x) \\in S$$$

Lean4

@[simp]
theorem subtype_comp_codRestrict (f : F) (S : NonUnitalSubalgebra R B) (hf : ∀ x : A, f x ∈ S) :
    (NonUnitalSubalgebraClass.subtype S).comp (NonUnitalAlgHom.codRestrict f S hf) = f :=
  rfl

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