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+Require Setoid.
+Require ZArith.
+Import ZArith.
+
+Inductive Erasable(A : Set) : Prop :=
+  erasable: A -> Erasable A.
+
+Arguments erasable [A] _.
+
+Hint Constructors Erasable.
+
+Scheme Erasable_elim := Induction for Erasable Sort Prop.
+
+Notation "## T" := (Erasable T) (at level 1, format "## T") : Erasable_scope.
+Notation "# x" := (erasable x) (at level 1, format "# x") : Erasable_scope.
+Open Scope Erasable_scope.
+
+Axiom Erasable_inj : forall {A : Set}{a b : A}, #a=#b -> a=b.
+
+Lemma Erasable_rw : forall (A: Set)(a b : A), (#a=#b) <-> (a=b).
+Proof.
+  intros A a b.
+  split.
+  - apply Erasable_inj.
+  - congruence.
+Qed.
+
+Open Scope Z_scope.
+Opaque Z.mul.
+
+Infix "^" := Zpower_nat : Z_scope.
+
+Notation "f ; v <- x" := (let (v) := x in f)
+                            (at level 199, left associativity) : Erasable_scope.
+Notation "f ; < v" := (f ; v <- v)
+                         (at level 199, left associativity) : Erasable_scope.
+Notation "f |# v <- x" := (#f ; v <- x)
+                          (at level 199, left associativity) : Erasable_scope.
+Notation "f |# < v" := (#f ; < v)
+                          (at level 199, left associativity) : Erasable_scope.
+
+Ltac name_evars id := 
+  repeat match goal with |- context[?V] => 
+                         is_evar V; let H := fresh id in set (H:=V) in * end.
+
+Lemma Twoto0 : 2^0 = 1.
+Proof. compute. reflexivity. Qed.
+
+Ltac ring_simplify' := rewrite ?Twoto0; ring_simplify.
+
+Definition mp2a1s(x : Z)(n : nat) := x * 2^n + (2^n-1).
+
+Hint Unfold mp2a1s.
+
+Definition zotval(n1s : nat)(is2 : bool)(next_value : Z) : Z :=
+  2 * mp2a1s next_value n1s + if is2 then 2 else 0.
+
+Inductive zot'(eis2 : ##bool)(value : ##Z) : Set :=
+| Zot'(is2 : bool)
+      (iseq : eis2=#is2)
+      {next_is2 : ##bool}
+      (ok : is2=true -> next_is2=#false)
+      {next_value : ##Z}
+      (n1s : nat)
+      (veq : value = (zotval n1s is2 next_value |#<next_value))
+      (next : zot' next_is2 next_value)
+  : zot' eis2 value.
+
+Definition de2{eis2 value}(z : zot' eis2 value) : zot' #false value.
+Proof.
+  case z.
+  intros is2 iseq next_is2 ok next_value n1s veq next. 
+  subst.
+  destruct is2.
+  2:trivial.
+  clear z.
+  specialize (ok eq_refl). subst.
+  destruct n1s.
+  - refine (Zot' _ _ _ _ _ _ _ _).
+    all:shelve_unifiable.
+    reflexivity.
+    discriminate.
+    name_evars e.
+    case_eq next_value. intros next_valueU next_valueEU.
+    case_eq e. intros eU eEU.
+    f_equal.
+    unfold zotval.
+    unfold mp2a1s.
+    ring_simplify'.
+    replace 2 with (2*1) at 2 7 by omega.
+    rewrite <-?Z.mul_assoc.
+    rewrite <-?Z.mul_add_distr_l.
+    rewrite <-Z.mul_sub_distr_l.
+    rewrite Z.mul_cancel_l by omega.
+    replace 1 with (2-1) at 1 by omega.
+    rewrite Z.add_sub_assoc.
+    rewrite Z.sub_cancel_r.
+    Unshelve.
+    all:case_eq next.
+Abort.
+