Theorems · Theorem · ring theory
IsUnit.isSelfAdjoint_conjugate_iff
∀ {R : Type u_1} [inst : Monoid R] [inst_1 : StarMul R] {a u : R},
IsUnit u → (IsSelfAdjoint (u * a * star u) ↔ IsSelfAdjoint a)- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- Star.starstatement and proof · cited by 1,082
- IsSelfAdjointstatement · cited by 545
- StarMulstatement and proof · cited by 195
- star_starproof · cited by 135
- StarMul.star_mulproof · cited by 72
- IsUnit.mul_left_injproof · cited by 20
- IsUnit.mul_right_injproof · cited by 13
- IsUnit.starproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsUnit.isSelfAdjoint_conjugate_iff'proof · cited by 0