English
Same composition principle as above, expressed with the explicit composite map and the two hypotheses.
Русский
Та же идея композиции ограничений, выраженная через явную композицию и две гипотезы.
LaTeX
$$$g \\circ f = e \\land \\mathrm{QuasispectrumRestricts}(a,f) \\land \\mathrm{QuasispectrumRestricts}(a,g) \\Rightarrow \\mathrm{QuasispectrumRestricts}(a,e)$$$
Lean4
/-- A (reducible) alias of `QuasispectrumRestricts` which enforces stronger type class assumptions
on the types involved, as it's really intended for the `spectrum`. The separate definition also
allows for dot notation. -/
@[reducible]
def SpectrumRestricts {R S A : Type*} [Semifield R] [Semifield S] [Ring A] [Algebra R A] [Algebra S A] [Algebra R S]
(a : A) (f : S → R) : Prop :=
QuasispectrumRestricts a f
