Theorems · Theorem · functional analysis

CFC.rpow_nonneg

∀ {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] {a : A} {y : ℝ}, 0 ≤ a ^ y

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PartialOrder Ring StarRing TopologicalSpace StarOrderedRing Algebra ContinuousFunctionalCalculus NonnegSpectrumClass

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Cites12

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

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
NNRealproof · cited by 4,310
StarRingstatement and proof · cited by 1,686
StarOrderedRingstatement and proof · cited by 587
IsSelfAdjointstatement and proof · cited by 545
ContinuousFunctionalCalculusstatement and proof · cited by 331
NonnegSpectrumClassstatement and proof · cited by 292
cfc_predicateproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

le_iff_norm_sqrt_mul_rpowproof · cited by 1