Theorems · Theorem · functional analysis

Commute.cfcAbs_left

∀ {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 b : A},
  Commute a b → Commute a (star b) → Commute (CFC.abs a) b

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs
Cited by: 2 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NonUnitalRing StarRing TopologicalSpace Module SMulCommClass IsScalarTower NonUnitalContinuousFunctionalCalculus PartialOrder StarOrderedRing NonnegSpectrumClass IsTopologicalRing T2Space

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites21

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
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
Star.starstatement and proof · cited by 1,082
Commutestatement and proof · cited by 639
StarOrderedRingstatement and proof · cited by 587

Cited by2

Results whose statement or proof uses this declaration.

Commute.cfcAbs_rightproof · cited by 0
CFC.commute_abs_selfproof · cited by 0