proposition: Theorem unionStateEq : forall S1 S2 S3 S4 : State, eqState S1 S3 -> eqState S2 S4 -> eqState (unionState S1 S2) (unionState S3 S4).
proof: Proof. intros S1 S2 S3 S4 H' H'0; red in |- *; split; auto with stalmarck. apply unionStateMin; auto with stalmarck. apply inclStateEqStateComp with (S1 := S3) (S3 := unionState S3 S4); auto with stalmarck. apply inclStateEqStateComp with (S1 := S4) (S3 := unionState S3 S4); auto with stalmarck. apply unionStateMin; auto with stalmarck. apply inclStateEqStateComp with (S1 := S1) (S3 := unionState S1 S2); auto with stalmarck. apply inclStateEqStateComp with (S1 := S2) (S3 := unionState S1 S2); auto with stalmarck. Qed.
imports: Coq(List)