Theorems · Theorem · functional analysis
coe_mem_spectrum_real_of_nonneg
∀ {A : Type u_1} [inst : Ring A] [inst_1 : PartialOrder A] [inst_2 : Algebra ℝ A] [NonnegSpectrumClass ℝ A] {a : A}
{x : NNReal}, autoParam (0 ≤ a) coe_mem_spectrum_real_of_nonneg._auto_1 → (↑x ∈ spectrum ℝ a ↔ x ∈ spectrum NNReal a)- Defined in
- Mathlib.Analysis.Real.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- spectrumstatement and proof · cited by 510
- NonnegSpectrumClassstatement and proof · cited by 292
- SpectrumRestricts.algebraMap_imageproof · cited by 12
- SpectrumRestricts.nnreal_of_nonnegproof · cited by 5
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