Theorems · Theorem · functional analysis
range_cfc_nnreal
∀ {A : Type u_1} [inst : Ring A] [inst_1 : StarRing A] [inst_2 : Algebra ℝ A] [inst_3 : TopologicalSpace A]
[inst_4 : IsTopologicalRing A] [T2Space A] [inst_6 : PartialOrder A] [inst_7 : NonnegSpectrumClass ℝ A]
[inst_8 : StarOrderedRing A] [inst_9 : ContinuousStar A] [inst_10 : StarModule ℝ A]
[inst_11 : ClosedEmbeddingContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (a : A),
0 ≤ a → (Set.range fun x => cfc x a) = {x | x ∈ StarAlgebra.elemental ℝ a ∧ 0 ≤ x}- Cited by
- 0 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites42
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 and proof · cited by 53,352
- 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
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- NNRealstatement · cited by 4,310
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