Theorems · Theorem · functional analysis
CFC.abs_neg
∀ {A : Type u_2} [inst : NonUnitalRing A] [inst_1 : StarRing A] [inst_2 : TopologicalSpace A] [inst_3 : Module ℝ A]
[inst_4 : SMulCommClass ℝ A A] [inst_5 : IsScalarTower ℝ A A]
[inst_6 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_7 : PartialOrder A]
[inst_8 : StarOrderedRing A] [inst_9 : NonnegSpectrumClass ℝ A] (a : A), CFC.abs (-a) = CFC.abs a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, 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.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- PartialOrderstatement and proof · cited by 6,410
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- StarOrderedRingstatement and proof · cited by 587
Cited by2
Results whose statement or proof uses this declaration.
- CFC.abs_of_nonposproof · cited by 0
- CFC.abs_intCastproof · cited by 0