Theorems · Theorem · functional analysis
CFC.rpow_inv_rpow
∀ {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) (x : ℝ),
x ≠ 0 → autoParam (IsStrictlyPositive a) CFC.rpow_inv_rpow._auto_1 → (a ^ x⁻¹) ^ x = a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- StarRingstatement and proof · cited by 1,686
- T2Spacestatement and proof · cited by 1,351
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- inv_invproof · cited by 494
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- NonnegSpectrumClassstatement and proof · cited by 292
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