Theorems · Theorem · functional analysis
CFC.sqrt_nnrpow
∀ {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]
[IsSemitopologicalRing A] [T2Space A] {a : A} {x : NNReal}, CFC.sqrt (a ^ x) = a ^ (x / 2)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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 and proof · cited by 4,310
- IsScalarTowerstatement and proof · cited by 3,896
- one_mulproof · cited by 2,841
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- T2Spacestatement and proof · cited by 1,351
- div_eq_mul_invproof · cited by 715
- StarOrderedRingstatement and proof · cited by 587
Cited by2
Results whose statement or proof uses this declaration.
- CFC.sqrt_nnrpow_twoproof · cited by 1
- CFC.sqrt_rpow_nnrealproof · cited by 0