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_limpl_specializeL_ap : forall P Q R G,
R |-- P ->
Q //\\ R |-- G ->
R //\\ (P -->> Q) |-- G.