proposition: Lemma ntrans_vee_nt_R : forall a u1 v1 u2 v2 r s t (x:obsy vee_data), ntrans (vee_nt a u1 v1 u2 v2 r s t) (R x) = match x with o1 => r | o2 => s | o3 => t end.
proof: Proof. ir. uf vee_nt. rw ntrans_nttyd. rw X_rewrite. tv. rw ob_catyd. sh x; tv. ap vee_data_property. Qed.
imports: Arith cat_examples cardinal fc_limits