Section logic2.
Context {L : Type}.
Context {ILO : ILogicOps L}.
Context {IL : ILogic L}.
Definition liff (A B : L) : L :=
(A -->> B) //\\ (B -->> A).
Local Notation "x <<-->> y" := (liff x y) (at level 78).

Lemma land_cancel : forall A B C,
A |-- B <<-->> C ->
A //\\ B -|- A //\\ C.