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 -> forces_t2 k k' b \/ False) in |- *.
intros forces_a; left.
apply (forces_ab k'); assumption.
Qed.

(* Specifications: *)
Lemma forces_a_imp_falsum_imp_b1_t :
forall (k : kripke_tree) (a b1 : form), forces_t k (Imp a (Imp Falsum b1)).