Theorems · Theorem · functional analysis
SpectrumRestricts.of_spectrum_eq
∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : Semifield R] [inst_1 : Semifield S] [inst_2 : Ring A]
[inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] {a b : A} {f : S → R},
SpectrumRestricts a f → spectrum S a = spectrum S b → SpectrumRestricts b f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- spectrumstatement and proof · cited by 510
- Semifieldstatement and proof · cited by 439
- SpectrumRestrictsstatement and proof · cited by 51
- Set.RightInvOnproof · cited by 47
- QuasispectrumRestricts.left_invproof · cited by 13
- quasispectrum_eq_spectrum_union_zeroproof · cited by 8
- QuasispectrumRestricts.rightInvOnproof · cited by 6
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