exists_disjoint_and_sup_eq — Mathlib

English

In a complemented modular lattice, for a ≤ b there exists b' disjoint from b with b ∨ b' = b.

Русский

В комплементной модульной решётке при a ≤ b существует b', несовmежный b, с b ∨ b' = b.

LaTeX

$$$\exists b'\; (Disjoint\ b\ b') \land (b\vee b')=b$$$

Lean4

theorem exists_disjoint_and_sup_eq (h : a ≤ b) : ∃ a', Disjoint a a' ∧ a ⊔ a' = b :=
  by
  simp_rw [disjoint_iff]
  apply exists_inf_eq_and_sup_eq (by simp) h

Похожие утверждения