disjoint_map — Mathlib

English

For an injective m, the disjointness of mapped filters is equivalent to the disjointness of the original filters.

Русский

При инъекции m дисjointность отображенных фильтров эквивалентна дисjointности исходных фильтров.

LaTeX

$$Disjoint (map f F) (map f G) ↔ Disjoint F G$$

Lean4

theorem disjoint_map {m : α → β} (hm : Injective m) {f₁ f₂ : Filter α} :
    Disjoint (map m f₁) (map m f₂) ↔ Disjoint f₁ f₂ := by simp only [disjoint_iff, ← map_inf hm, map_eq_bot_iff]

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