English
Let ha be a QuasispectrumRestricts a ContinuousMap.realToNNReal. Then for every r ∈ ℝ≥0, the strict inequality relations between quasispectrum in NNReal and in Real coincide.
Русский
Пусть ha — QuasispectrumRestricts a ContinuousMap.realToNNReal. Тогда для каждого r ∈ ℝ≥0 строгие неравенства между квази-спектром NNReal и спектра Real совпадают.
LaTeX
$$$\forall r \in \mathbb{R}_{\ge 0},\; (\forall x \in quasispectrum_{\mathbb{R}_{\ge 0}} a, x < r) \iff (\forall x \in quasispectrum_{\mathbb{R}} a, x < r)$$$
Lean4
instance instSeminormClass : SeminormClass (Seminorm 𝕜 E) 𝕜 E
where
map_zero f := f.map_zero'
map_add_le_add f := f.add_le'
map_neg_eq_map f := f.neg'
map_smul_eq_mul f := f.smul'
