Ltac solveLiftGenX :=
intros; split; intros;
repeat
match goal with
| [ H : exists _, _ |- _ ] => destruct H as [? [? ?]]
| [ H : semGenSize _ _ _ |- _ ] =>
try (apply semBindSize in H; destruct H as [? [? ?]]);
try (apply semReturnSize in H; subst)
end;
[ by repeat (eexists; split; [eassumption |])
| repeat (apply semBindSize; eexists; split; try eassumption);
by apply semReturnSize ].

(* Specifications: *)
Lemma semLiftGenSize {A B} (f: A -> B) (g: G A) size :
semGenSize (liftGen f g) size <--> f @: (semGenSize g size).