intros k a b forces_ab.
unfold forces_t in |- *; unfold forces_t2 in |- *; simpl in |- *.
intros k' suc_k' suc_k''.
change (forces_t2 k k' a -> False \/ forces_t2 k k' b) in |- *.
intros forces_a; right.
apply (forces_ab k'); assumption.
Qed.

Lemma forces_a_imp_b__forces_a_imp_b_or_falsum :
forall (k : kripke_tree) (a b : form),
forces_t k (Imp a b) -> forces_t k (Imp a (OrF b Falsum)).