Theorems · Theorem · functional analysis
CFC.posPart_add_negPart
∀ {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] [IsTopologicalRing A] [T2Space A] (a : A),
autoParam (IsSelfAdjoint a) CFC.posPart_add_negPart._auto_1 → a⁺ + a⁻ = CFC.abs a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- T2Spacestatement and proof · cited by 1,351
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- neg_zeroproof · cited by 542
- NonUnitalRingstatement and proof · cited by 422
Cited by2
Results whose statement or proof uses this declaration.
- CFC.abs_add_selfproof · cited by 0
- CFC.abs_sub_selfproof · cited by 0