Theorems · Theorem · functional analysis
range_cfc_subset
∀ (𝕜 : Type u_1) {A : Type u_2} {p : A → Prop} [inst : RCLike 𝕜] [inst_1 : Ring A] [inst_2 : StarRing A]
[inst_3 : Algebra 𝕜 A] [inst_4 : TopologicalSpace A] [inst_5 : StarModule 𝕜 A]
[inst_6 : ContinuousFunctionalCalculus 𝕜 A p] [inst_7 : IsTopologicalRing A] [inst_8 : ContinuousStar A] {a : A},
p a → (Set.range fun x => cfc x a) ⊆ ↑(StarAlgebra.elemental 𝕜 a)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Set.rangestatement · cited by 4,705
- RCLikestatement and proof · cited by 2,829
- le_reflproof · cited by 2,061
- StarRingstatement and proof · cited by 1,686
- le_imp_le_of_le_of_leproof · cited by 576
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
Cited by1
Results whose statement or proof uses this declaration.
- range_cfc_nnreal_subsetproof · cited by 1