Theorems · Theorem · ring theory
LinearMap.intrinsicStar_mulLeft
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : InvolutiveStar R] {E : Type u_6} [inst_2 : NonUnitalNonAssocSemiring E]
[inst_3 : StarRing E] [inst_4 : Module R E] [inst_5 : StarModule R E] [inst_6 : SMulCommClass R E E]
[inst_7 : IsScalarTower R E E] (x : E),
star (WithConv.toConv (LinearMap.mulLeft R x)) = WithConv.toConv (LinearMap.mulRight R (star x))- Defined in
- Mathlib.Algebra.Star.LinearMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- LinearMap.extproof · cited by 844
- StarModulestatement and proof · cited by 570
- WithConvstatement · cited by 138
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.intrinsicStar_mulRightproof · cited by 0