Theorems · Theorem · ring theory
IsSelfAdjoint.coe_selfAdjointPart_apply
∀ (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}, IsSelfAdjoint x → ↑((selfAdjointPart R) x) = x- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- StarModulestatement and proof · cited by 570
- Invertiblestatement and proof · cited by 549
- IsSelfAdjointstatement and proof · cited by 545
- StarAddMonoidstatement and proof · cited by 296
- Invertible.invOfproof · cited by 268
Cited by2
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.coe_realPartproof · cited by 6
- IsSelfAdjoint.selfAdjointPart_applyproof · cited by 1