Theorems · Theorem · ring theory
IsSelfAdjoint.sub
∀ {R : Type u_1} [inst : AddGroup R] [inst_1 : StarAddMonoid R] {x y : R},
IsSelfAdjoint x → IsSelfAdjoint y → IsSelfAdjoint (x - y)- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupStarAddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- IsSelfAdjointstatement and proof · cited by 545
- StarAddMonoidstatement and proof · cited by 296
- IsSelfAdjoint.star_eqproof · cited by 58
- star_subproof · cited by 11
Cited by13
Results whose statement or proof uses this declaration.
- Unitization.inr_le_iffproof · cited by 8
- IsStarProjection.le_tfaeproof · cited by 4
- IsStarProjection.sub_of_mul_eq_leftproof · cited by 3
- Matrix.IsHermitian.subproof · cited by 3
- ContinuousLinearMap.isStarNormal_iff_norm_eq_adjointproof · cited by 2
- IsStarProjection.one_subproof · cited by 2
- SpectrumRestricts.nnreal_iff_nnnormproof · cited by 2
- CFC.negPart_eq_of_eq_PosPart_subproof · cited by 1
- IsSelfAdjoint.map'proof · cited by 1
- IsStarProjection.sub_iff_mul_eq_leftproof · cited by 1
- CFC.posPart_eq_of_eq_sub_negPartproof · cited by 0
- CFC.posPart_negPart_uniqueproof · cited by 0