| N ⇒ null
].
+lemma injective_low_char: injective … low_char.
+#c1 #c2 cases c1 cases c2 normalize //
+ [#b1 #H destruct
+ |#b1 #H destruct
+ |#b1 #b2 #H destruct //
+ ]
+qed.
+
+lemma injective_low_mv: injective … low_mv.
+#m1 #m2 cases m1 cases m2 // normalize #H destruct
+qed.
+
(******************************** tuple encoding ******************************)
definition tuple_type ≝ λn.
(Nat_to n × (option FinBool)) × (Nat_to n × (option FinBool) × move).