Theorems · Theorem · functional analysis
range_cfc_eq_range_cfcHom
∀ (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] [inst_9 : StarModule R A]
{a : A} (ha : p a), (Set.range fun x => cfc x a) = ↑(cfcHom ha).range- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- ContinuousMapstatement and proof · cited by 2,491
- Set.extproof · cited by 2,266
- StarRingstatement and proof · cited by 1,686
Cited by2
Results whose statement or proof uses this declaration.
- range_cfc_subsetproof · cited by 1
- range_cfcproof · cited by 1