intros A World le forces0 kripke k w b forces_b.
intros a.
simpl in |- *.
intros k' w' le_k_k' forces_a.
apply forces_mon with (k := k); assumption.
Qed.

Lemma forces_a0_imp_a1_imp_b__forces_a0_and_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 a1 b : form,
forces A World le forces0 k (Imp a0 (Imp a1 b)) ->
forces A World le forces0 k (Imp (AndF a0 a1) b).