Ltac landL :=
    repeat match goal with
    | |- ?L1 //\\ ?L2 |-- ?R =>
        match L1 with
        | context [R] => apply landL1
        | _ =>
          match L2 with
          | context [R] => apply landL2
          end
        end
    end.

Lemma limplexistsE (P : T -> A) (Q : A) : (Exists x, P x) -->> Q -|- Forall x, (P x -->> Q).