Theorems · Theorem · ring theory

NonUnitalStarSubalgebra.coe_map

∀ {F : Type v'} {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : Module R A] [inst_3 : Star A] [inst_4 : NonUnitalNonAssocSemiring B] [inst_5 : Module R B] [inst_6 : Star B]
  [inst_7 : FunLike F A B] [inst_8 : NonUnitalAlgHomClass F R A B] [inst_9 : StarHomClass F A B]
  (S : NonUnitalStarSubalgebra R A) (f : F), ↑(NonUnitalStarSubalgebra.map f S) = ⇑f '' ↑S

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

2 results in Mathlib

Foundations

Depth 22 from the axioms · uses no axioms

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleStarNonUnitalNonAssocSemiringModuleStarFunLikeNonUnitalAlgHomClassStarHomClass