Theorems · Theorem · functional analysis
CFC.posPart_nonneg
∀ {A : Type u_1} [inst : NonUnitalRing A] [inst_1 : Module ℝ A] [inst_2 : SMulCommClass ℝ A A]
[inst_3 : IsScalarTower ℝ A A] [inst_4 : StarRing A] [inst_5 : TopologicalSpace A]
[inst_6 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_7 : PartialOrder A] [StarOrderedRing A]
(a : A), 0 ≤ a⁺- Cited by
- 5 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalRingstatement and proof · cited by 422
- quasispectrumproof · cited by 292
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
Cited by5
Results whose statement or proof uses this declaration.
- CFC.posPart_eq_selfproof · cited by 2
- CStarAlgebra.exists_sum_four_nonnegproof · cited by 1
- CFC.negPart_eq_of_eq_PosPart_subproof · cited by 1
- CStarAlgebra.span_nonnegproof · cited by 1
- CFC.neg_negPart_leproof · cited by 0