Theorems · Theorem · functional analysis

CFC.abs_intCast

∀ {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] (n : ℤ), CFC.abs ↑n = ↑|n|

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs
Cited by: 0 results in Mathlib
Foundations: Depth 218 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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Realstatement and proof · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
Algebrastatement and proof · cited by 11,388
Ringstatement and proof · cited by 7,463
PartialOrderstatement and proof · cited by 6,410
absstatement and proof · cited by 1,814
StarRingstatement and proof · cited by 1,686
T2Spacestatement and proof · cited by 1,351
StarOrderedRingstatement and proof · cited by 587
StarModulestatement and proof · cited by 570
IsSelfAdjointstatement and proof · cited by 545
IsTopologicalRingstatement and proof · cited by 402

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