restrict_id_hom — Mathlib

English

If s is contained in t as subsets of a graded module, then the vanishing ideals satisfy the reverse inclusion: vanishingIdeal(t) ⊆ vanishingIdeal(s).

Русский

Если s ⊆ t, то соответствующие vanishingIdeals удовлетворяют обратному включению: vanishingIdeal(t) ⊆ vanishingIdeal(s).

LaTeX

$$$s \subseteq t \Rightarrow \mathrm{vanishingIdeal}(t) \subseteq \mathrm{vanishingIdeal}(s)$$$

Lean4

theorem restrict_id_hom (f : X.PartialMap Y) : (f.restrict f.domain f.dense_domain le_rfl).hom = f.hom := by simp

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