Theorems · Theorem · functional analysis

CFC.abs_algebraMap_nnreal

∀ {A : Type u_2} [inst : Ring A] [inst_1 : StarRing A] [inst_2 : TopologicalSpace A] [inst_3 : Algebra ℝ A]
  [inst_4 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_5 : PartialOrder A] [inst_6 : StarOrderedRing A]
  [inst_7 : NonnegSpectrumClass ℝ A] [IsTopologicalRing A] [T2Space A] [StarModule ℝ A] (x : NNReal),
  CFC.abs ((algebraMap NNReal A) x) = (algebraMap NNReal A) x

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs
Cited by: 1 results in Mathlib
Foundations: Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring StarRing TopologicalSpace Algebra ContinuousFunctionalCalculus PartialOrder StarOrderedRing NonnegSpectrumClass IsTopologicalRing T2Space StarModule

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Cites23

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
StarOrderedRingstatement and proof · cited by 587

Cited by1

Results whose statement or proof uses this declaration.

CFC.abs_natCastproof · cited by 2