Theorems · Theorem · functional analysis
cfc_zpow
∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : Semifield R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
[inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : TopologicalSpace A] [inst_6 : Ring A]
[inst_7 : StarRing A] [inst_8 : Algebra R A] [inst_9 : ContinuousFunctionalCalculus R A p] [ContinuousInv₀ R] (a : Aˣ)
(n : ℤ), autoParam (p ↑a) cfc_zpow._auto_1 → cfc (fun x => x ^ n) ↑a = ↑(a ^ n)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousStarstatement and proof · cited by 543
- IsTopologicalSemiringstatement and proof · cited by 442
- Semifieldstatement and proof · cited by 439
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- zpow_natCastproof · cited by 271
Cited by2
Results whose statement or proof uses this declaration.
- cfc_comp_zpowproof · cited by 0
- CFC.rpow_intCastproof · cited by 0