closure_left — Mathlib

English

If s and t are disjoint and t is open, then closure(s) is disjoint from t.

Русский

Если s и t дистинкты и t открыто, то closure(s) дистинктивно относительно t.

LaTeX

$$Disjoint(s,t) \land IsOpen(t) \Rightarrow Disjoint(\overline{s}, t)$$

Lean4

theorem closure_left (hd : Disjoint s t) (ht : IsOpen t) : Disjoint (closure s) t :=
  disjoint_compl_left.mono_left <| closure_minimal hd.subset_compl_right ht.isClosed_compl

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