Theorems · Theorem · functional analysis

CFC.sqrt_algebraMap

∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : TopologicalSpace A]
  [inst_4 : StarOrderedRing A] [inst_5 : Algebra ℝ A] [inst_6 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
  [inst_7 : NonnegSpectrumClass ℝ A] [IsSemitopologicalRing A] [T2Space A] {r : NNReal},
  CFC.sqrt ((algebraMap NNReal A) r) = (algebraMap NNReal A) (NNReal.sqrt r)

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PartialOrder Ring StarRing TopologicalSpace StarOrderedRing Algebra ContinuousFunctionalCalculus NonnegSpectrumClass IsSemitopologicalRing 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.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Ringstatement and proof · cited by 7,463
PartialOrderstatement and proof · cited by 6,410
Algebra.algebraMapstatement and proof · cited by 4,706
NNRealstatement and proof · cited by 4,310
StarRingstatement and proof · cited by 1,686
T2Spacestatement and proof · cited by 1,351
OrderIsostatement · cited by 874

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.