Theorems · Theorem · functional analysis
cfc_pow_id
∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : CommSemiring 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] [instCFC : ContinuousFunctionalCalculus R A p] (a : A) (n : ℕ),
autoParam (p a) cfc_pow_id._auto_1 → cfc (fun x => x ^ n) a = a ^ n- Cited by
- 7 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousStarstatement and proof · cited by 543
- spectrumproof · cited by 510
- IsTopologicalSemiringstatement and proof · cited by 442
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- cfcstatement · cited by 228
- continuousOn_id'proof · cited by 109
Cited by7
Results whose statement or proof uses this declaration.
- cfc_zpowproof · cited by 2
- CStarAlgebra.pow_antitoneproof · cited by 1
- CStarAlgebra.pow_nonnegproof · cited by 1
- cfc_comp_powproof · cited by 0
- CStarAlgebra.pow_monotoneproof · cited by 0
- CFC.log_powproof · cited by 0
- CFC.rpow_natCastproof · cited by 0