intros A World le forces0 k a0 a1 c b forces_a0_c forces_a1_c forces_c_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_c_b k' u0 u1).
apply (forces_a0_c k' u0 u1 forces_a0).
intro forces_a1.
apply (forces_c_b k' u0 u1).
apply (forces_a1_c k' u0 u1 forces_a1).
Qed.

Lemma forces_a0_imp_b_and_a1_imp_b__forces_a0_or_a1_imp_b :
forall (A : Set) (World : A -> Type) (le : A -> A -> Type)
(forces0 : A -> Int -> Prop) (k : A) (a0 a1 b : form),
forces A World le forces0 k (Imp a0 b) ->
forces A World le forces0 k (Imp a1 b) ->
forces A World le forces0 k (Imp (OrF a0 a1) b).