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 lorexistsDL (f : T -> A) (P : A) {H : Inhabited T} : (Exists a, f a) \\// P |-- Exists a, (f a \\// P).