proposition: Lemma rel_image_maximal_bisimulation_sym: forall (S1 S2 : F_coalgebra) fs1 fs2, rel_image_lift_F_ _ _ (maximal_bisimulation S2 S2) fs1 fs2 -> rel_image_lift_F_ _ _ (maximal_bisimulation S2 S2) fs2 fs1.
proof: Proof. intros S1 S2 fs1 fs2 (x1 & y1 & hyp11 & hyp12 & hyp13); exists y1; exists x1; repeat split; trivial; apply sym_bisimilar; assumption. Qed.
imports: ExtensionalFunctor Setoid