intros k l.
elim l; clear l.
intros b forces_ab.
apply forces_ab with (k' := k); try assumption.
unfold Suc in |- *; apply successor_refl.
simpl in |- *; intros i l ih b forces_ab.
apply ih.
intros k' suc1.
unfold forces_t in |- *; unfold forces_t2 in |- *; simpl in |- *.
intros k'' suc2 suc3 forces_i.
change (forces_t2 k k'' b) in |- *.
apply forces_ab.
assumption.
Qed.

Lemma forces_a_imp_b_imp_c__forces_a_imp_falsum_imp_c_t2 :
forall (k k' : kripke_tree) (a b c : form),
Suc k' k ->
forces_t2 k k' (Imp (Imp a b) c) -> forces_t2 k k' (Imp (Imp a Falsum) c).