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_lexists_ap : forall T (P : T -> L) Q R S,
(forall x, S //\\ P x //\\ Q |-- R) ->
S //\\ (lexists P) //\\ Q |-- R.