intros A World le forces0 k a0 a1 b forces_a0_b forces_a1_b.
simpl in |- *.
intros k' u0 u1 forces_a0_or_a1.
elim forces_a0_or_a1; clear forces_a0_or_a1.
intro forces_a0.
apply (forces_a0_b k' u0 u1 forces_a0).
intro forces_a1.
apply (forces_a1_b k' u0 u1 forces_a1).
Qed.

Lemma forces_a1_imp_b__forces_a0_imp_a1_imp_b :
forall (A : Set) (World : A -> Type) (le : A -> A -> Type)
(forces0 : A -> Int -> Prop),
Kripke_Model A World le forces0 ->
forall k : A,
World k ->
forall a0 : form,
forces A World le forces0 k a0 ->
forall a1 b : form,
forces A World le forces0 k (Imp a1 b) ->
forces A World le forces0 k (Imp (Imp a0 a1) b).