Theorems · Theorem · ring theory
selfAdjointPart_apply_coe
∀ (R : Type u_1) {A : Type u_2} [inst : Semiring R] [inst_1 : StarMul R] [inst_2 : TrivialStar R]
[inst_3 : AddCommGroup A] [inst_4 : Module R A] [inst_5 : StarAddMonoid A] [inst_6 : StarModule R A]
[inst_7 : Invertible 2] (x : A), ↑((selfAdjointPart R) x) = ⅟2 • (x + star x)- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- AddSubgroupstatement · cited by 3,232
- Star.starstatement · cited by 1,082
- StarModulestatement and proof · cited by 570
- Invertiblestatement and proof · cited by 549
- StarAddMonoidstatement and proof · cited by 296
- Invertible.invOfstatement · cited by 268
Cited by5
Results whose statement or proof uses this declaration.
- realPart_add_I_smul_imaginaryPartproof · cited by 10
- realPart_apply_coeproof · cited by 9
- IsSelfAdjoint.coe_selfAdjointPart_applyproof · cited by 2
- selfAdjointPart_comp_subtype_skewAdjointproof · cited by 0
- StarModule.selfAdjointPart_add_skewAdjointPartproof · cited by 0