Theorems · Theorem · ring theory
StarAlgHom.ext_adjoin
∀ {F : Type u_1} {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : StarRing R]
[inst_2 : Semiring A] [inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : Semiring B] [inst_6 : Algebra R B]
[inst_7 : StarRing B] [inst_8 : StarModule R A] {s : Set A} [inst_9 : FunLike F (↥(StarAlgebra.adjoin R s)) B]
[AlgHomClass F R (↥(StarAlgebra.adjoin R s)) B] [StarHomClass F (↥(StarAlgebra.adjoin R s)) B] {f g : F},
(∀ (x : ↥(StarAlgebra.adjoin R s)), ↑x ∈ s → f x = g x) → f = g- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- FunLikestatement and proof · cited by 2,560
- StarRingstatement and proof · cited by 1,686
- map_mulproof · cited by 1,137
- Star.starproof · cited by 1,082
- map_addproof · cited by 964
- StarModulestatement and proof · cited by 570
Cited by1
Results whose statement or proof uses this declaration.
- StarAlgHom.ext_adjoin_singletonproof · cited by 0