+lemma right_mk_tape :
+ ∀sig,ls,c,rs.(c = None ? → ls = [ ] ∨ rs = [ ]) → right ? (mk_tape sig ls c rs) = rs.
+#sig #ls #c #rs cases c // cases ls
+[ cases rs //
+| #l0 #ls0 #H normalize cases (H (refl ??)) #H1 [ destruct (H1) | >H1 % ] ]
+qed-.
+
+lemma left_mk_tape : ∀sig,ls,c,rs.left ? (mk_tape sig ls c rs) = ls.
+#sig #ls #c #rs cases c // cases ls // cases rs //
+qed.
+
+lemma current_mk_tape : ∀sig,ls,c,rs.current ? (mk_tape sig ls c rs) = c.
+#sig #ls #c #rs cases c // cases ls // cases rs //
+qed.
+