injective — Mathlib

English

The evaluation map on GoodProducts is injective.

Русский

Отображение оценки на GoodProducts инъективно.

LaTeX

$$$$ \\operatorname{Injective}(\\mathrm{eval}\\ C). $$$$

Lean4

theorem injective : Function.Injective (eval C) :=
  by
  intro ⟨a, ha⟩ ⟨b, hb⟩ h
  dsimp [eval] at h
  by_contra! hne
  cases hne.lt_or_gt with
  | inl h' => apply hb; rw [← h]; exact Submodule.subset_span ⟨a, h', rfl⟩
  | inr h' => apply ha; rw [h]; exact Submodule.subset_span ⟨b, h', rfl⟩

Похожие утверждения