disjoint_sup_left_of_disjoint_sup_right

English

Symmetric version: if b ⊥ c and a ⊔ b ⊥ c then a ⊔ b ⊥ c.

Русский

Симметричная версия: если b ⊥ c и a ⊔ b ⊥ c, то a ⊔ b ⊥ c.

LaTeX

$$$\text{Disjoint } b c \rightarrow \text{Disjoint } (a\vee b) c \rightarrow \text{Disjoint } (a\vee b) c.$$$

Lean4

theorem disjoint_sup_left_of_disjoint_sup_right [Lattice α] [OrderBot α] [IsModularLattice α] (h : Disjoint b c)
    (hsup : Disjoint a (b ⊔ c)) : Disjoint (a ⊔ b) c :=
  by
  rw [disjoint_comm, sup_comm]
  apply Disjoint.disjoint_sup_right_of_disjoint_sup_left h.symm
  rwa [sup_comm, disjoint_comm] at hsup

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