kernImage_eq_compl — Mathlib

English

For any s ⊆ {x, y}, the set s is either empty, {x}, {y}, or {x, y}.

Русский

Для любого s ⊆ {x, y} множество s равно ∅, {x}, {y} или {x, y}.

LaTeX

$$$s \\subseteq \\{x, y\\} \\iff s = \\emptyset \\lor s = \\{x\\} \\lor s = \\{y\\} \\lor s = \\{x, y\\}$$$

Lean4

theorem kernImage_eq_compl {s : Set α} : kernImage f s = (f '' sᶜ)ᶜ :=
  Set.preimage_kernImage.u_unique (Set.image_preimage.compl) (fun t ↦ compl_compl (f ⁻¹' t) ▸ Set.preimage_compl)

Похожие утверждения