English
The coborder of any set is dense in the ambient space.
Русский
Граница coborder любого множества плотна в рамках пространства.
LaTeX
$$$\operatorname{Dense}(\operatorname{coborder}(s))$$$
Lean4
/-- The coborder of any set is dense -/
theorem dense_coborder {s : Set X} : Dense (coborder s) :=
by
rw [dense_iff_closure_eq, coborder_eq_union_closure_compl, closure_union, ← univ_subset_iff]
refine _root_.subset_trans ?_ (union_subset_union_right _ (subset_closure))
simp