Theorems · Theorem · functional analysis

CFC.nnrpow_one_eqOn

∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : NonUnitalRing A] [inst_2 : TopologicalSpace A] [inst_3 : StarRing A]
  [inst_4 : Module ℝ A] [inst_5 : SMulCommClass ℝ A A] [inst_6 : IsScalarTower ℝ A A] [inst_7 : StarOrderedRing A]
  [inst_8 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_9 : NonnegSpectrumClass ℝ A],
  Set.EqOn (fun a => a ^ 1) id (Set.Ici 0)

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PartialOrder NonUnitalRing TopologicalSpace StarRing Module SMulCommClass IsScalarTower StarOrderedRing NonUnitalContinuousFunctionalCalculus NonnegSpectrumClass

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites16

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
Modulestatement and proof · cited by 20,661
PartialOrderstatement and proof · cited by 6,410
NNRealstatement · cited by 4,310
IsScalarTowerstatement and proof · cited by 3,896
SMulCommClassstatement and proof · cited by 1,927
StarRingstatement and proof · cited by 1,686
Set.Icistatement and proof · cited by 1,070
Set.EqOnstatement · cited by 603
StarOrderedRingstatement and proof · cited by 587
IsSelfAdjointstatement and proof · cited by 545

Cited by1

Results whose statement or proof uses this declaration.

CFC.concaveOn_nnrpowproof · cited by 2