Theorems · Theorem · functional analysis
CFC.nnrpow_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 y : NNReal}, (a ^ x) ^ y = a ^ (x * y)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- CommSemiringproof · cited by 10,911
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialproof · cited by 2,416
- MulZeroClass.mul_zeroproof · cited by 2,091
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- MetricSpaceproof · cited by 1,684
Cited by5
Results whose statement or proof uses this declaration.
- CFC.sqrt_nnrpowproof · cited by 2
- CFC.nnrpow_inv_nnrpowproof · cited by 1
- CFC.nnrpow_nnrpow_invproof · cited by 1
- CFC.nnrpow_sqrtproof · cited by 1
- CFC.abs_nnrpow_two_mulproof · cited by 0