Theorems · Theorem · ring theory
StarAlgHom.ext
∀ {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Star A] [inst_4 : Semiring B] [inst_5 : Algebra R B] [inst_6 : Star B] {f g : A →⋆ₐ[R] B},
(∀ (x : A), f x = g x) → f = g- Defined in
- Mathlib.Algebra.Star.StarAlgHom
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Starstatement and proof · cited by 496
- DFunLike.extproof · cited by 240
- StarAlgHomstatement and proof · cited by 215
Cited by14
Results whose statement or proof uses this declaration.
- StarAlgHomClass.ext_topologicalClosureproof · cited by 1
- StarAlgHom.fst_prodproof · cited by 0
- StarAlgHom.realContinuousMapOfNNReal_injectiveproof · cited by 0
- StarAlgHom.id_compproof · cited by 0
- StarAlgHom.restrictScalars_injectiveproof · cited by 0
- ContinuousMap.compStarAlgHom'_compproof · cited by 0
- ContinuousMap.compStarAlgHom'_idproof · cited by 0
- StarAlgHom.snd_prodproof · cited by 0
- StarAlgHom.subtype_comp_codRestrictproof · cited by 0
- StarAlgHom.mk_coeproof · cited by 0
- StarAlgHom.comp_idproof · cited by 0
- StarAlgEquiv.arrowCongr_compproof · cited by 0