Theorems · Theorem · functional analysis
spectrum.singleton_add_eq
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] (a : A) (r : R),
{r} + spectrum R a = spectrum R ((algebraMap R A) r + a)- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- Set.extproof · cited by 2,266
- add_commproof · cited by 1,535
- neg_negproof · cited by 960
- spectrumstatement and proof · cited by 510
- map_negproof · cited by 378
Cited by4
Results whose statement or proof uses this declaration.
- spectrum.scalar_eqproof · cited by 2
- spectrum.singleton_sub_eqproof · cited by 2
- spectrum.add_singleton_eqproof · cited by 0
- spectrum.vadd_eqproof · cited by 0