+lemma nth_current_chars : ∀sig,n,tapes,i.
+ nth i ? (current_chars sig n tapes) (None ?)
+ = current sig (nth i ? tapes (niltape sig)).
+#sig #n #tapes #i >(nth_vec_map … (current sig) i (S n)) %
+qed.
+
+definition tape_move_multi ≝
+ λsig,n,ts,mvs.
+ pmap_vec ??? (tape_move_mono sig) n ts mvs.
+
+lemma tape_move_multi_def : ∀sig,n,ts,mvs.
+ tape_move_multi sig n ts mvs = pmap_vec ??? (tape_move_mono sig) n ts mvs.
+// qed.
+