Theorems · Theorem · ring theory
IsSelfAdjoint.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} (hx : IsSelfAdjoint x), (selfAdjointPart R) x = ⟨x, hx⟩- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 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 · 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
- StarMulstatement and proof · cited by 195
Cited by1
Results whose statement or proof uses this declaration.
- selfAdjointPart_comp_subtype_selfAdjointproof · cited by 1