Theorems · Theorem · functional analysis

IsUnit.cfcNNRpow

∀ {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] (a : A) (y : NNReal),
  IsUnit a → y ≠ 0 → autoParam (0 ≤ a) IsUnit.cfcNNRpow._auto_1 → IsUnit (a ^ y)

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PartialOrder Ring StarRing TopologicalSpace StarOrderedRing Algebra ContinuousFunctionalCalculus NonnegSpectrumClass IsSemitopologicalRing T2Space

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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
NNRealstatement and proof · cited by 4,310
StarRingstatement and proof · cited by 1,686
IsUnitstatement and proof · cited by 1,602
T2Spacestatement and proof · cited by 1,351
StarOrderedRingstatement and proof · cited by 587
IsSelfAdjointstatement and proof · cited by 545
ContinuousFunctionalCalculusstatement and proof · cited by 331

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