(** ** Generalised Induction *)
Fixpoint size {b} (phi : form b) :=
match phi with
| Pr _ _ | Q | Fal => 1
| Impl phi1 phi2 => 1 + size phi1 + size phi2
| All n phi => 1 + size phi
end.

Lemma size_subst {b : logic} x t phi :
size (subst x t phi) = size phi.