proposition: Lemma commutativity_map_S_fst_snd (Lambda:T_over_B_distributive) (BS: BT_coalgebroid) (x:BS.(bs_states)) : fst (Str.(transition) (Lam_coiterator Lambda BS x)) = fst( lift_B_ _ _ (Beta Lambda) (lift_B_ _ _ (lift_T_ _ _ (Lam_coiterator Lambda BS)) (bs_transition BS x))) /\ snd (Str.(transition) (Lam_coiterator Lambda BS x)) (=) snd( lift_B_ _ _ (Beta Lambda) (lift_B_ _ _ (lift_T_ _ _ (Lam_coiterator Lambda BS)) (bs_transition BS x))).
proof: Proof. apply -> rel_image_lift_F_Str_bisimilar_spelled. apply commutativity_Lam_coiterator_rel_image_lifting. Qed.
imports: IntensionalLambdaBisimulation ZStreamCoalgebra ZArith