isCompl_sup_right_of_isCompl_sup_left

English

Another symmetric formulation of disjointness with supremum on left.

Русский

Ещё одна симметричная формулировка дисjointности с объединением слева.

LaTeX

$$$\forall a,b,c: \text{Disjoint } a (b\vee c) \Leftarrow \text{Disjoint } a b \land \text{Disjoint } a c.$$$

Lean4

theorem isCompl_sup_right_of_isCompl_sup_left [Lattice α] [BoundedOrder α] [IsModularLattice α] (h : Disjoint a b)
    (hcomp : IsCompl (a ⊔ b) c) : IsCompl a (b ⊔ c) :=
  ⟨h.disjoint_sup_right_of_disjoint_sup_left hcomp.disjoint, codisjoint_assoc.mp hcomp.codisjoint⟩

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