Ltac no_evars P := (has_evar P; fail 1) || idtac.Ltac putable x :=
 match x with
 | O => idtac
 | S ?x => putable x
 | Z.lt ?x ?y => putable x; putable y
 | Z.le ?x ?y => putable x; putable y
 | Z.gt ?x ?y => putable x; putable y
 | Z.ge ?x ?y => putable x; putable y
 | eq?x ?y => putable x; putable y
 | ?x <> ?y => putable x; putable y
 | Zpos ?x => putable x
 | Zneg ?x => putable x
 | Z0 => idtac
 | xH => idtac
 | xI ?x => putable x
 | xO ?x => putable x
 | Z.add ?x ?y => putable x; putable y
 | Z.sub ?x ?y => putable x; putable y
 | Z.mul ?x ?y => putable x; putable y
 | Z.div ?x ?y => putable x; putable y
 | Zmod ?x ?y => putable x; putable y
 | Z.max ?x ?y => putable x; putable y
 | Z.opp ?x => putable x
 | Ceq => idtac
 | Cne => idtac
 | Clt => idtac
 | Cle => idtac
 | Cgt => idtac
 | Cge => idtac
 | ?x /\ ?y => putable x; putable y
 | two_power_nat ?x => putable x
 | Int.eq ?x ?y => putable x; putable y
 | Int64.eq ?x ?y => putable x; putable y
 | Ptrofs.eq ?x ?y => putable x; putable y
 | Int.lt ?x ?y => putable x; putable y
 | Int64.lt ?x ?y => putable x; putable y
 | Ptrofs.lt ?x ?y => putable x; putable y
 | Int.ltu ?x ?y => putable x; putable y
 | Int64.ltu ?x ?y => putable x; putable y
 | Ptrofs.ltu ?x ?y => putable x; putable y
 | Int.add ?x ?y => putable x; putable y
 | Int64.add ?x ?y => putable x; putable y
 | Ptrofs.add ?x ?y => putable x; putable y
 | Int.sub ?x ?y => putable x; putable y
 | Int64.sub ?x ?y => putable x; putable y
 | Ptrofs.sub ?x ?y => putable x; putable y
 | Int.mul ?x ?y => putable x; putable y
 | Int64.mul ?x ?y => putable x; putable y
 | Ptrofs.mul ?x ?y => putable x; putable y
 | Int.neg ?x => putable x
 | Int64.neg ?x => putable x
 | Ptrofs.neg ?x => putable x
 | Ceq => idtac
 | Cne => idtac
 | Clt => idtac
 | Cle => idtac
 | Cgt => idtac
 | Cge => idtac
 | Int.cmp ?op ?x ?y => putable op; putable x; putable y
 | Int64.cmp ?op ?x ?y => putable op; putable x; putable y
 | Ptrofs.cmp ?op ?x ?y => putable op; putable x; putable y
 | Int.cmpu ?op ?x ?y => putable op; putable x; putable y
 | Int64.cmpu ?op ?x ?y => putable op; putable x; putable y
 | Ptrofs.cmpu ?op ?x ?y => putable op; putable x; putable y
 | Int.repr ?x => putable x
 | Int64.repr ?x => putable x
 | Ptrofs.repr ?x => putable x
 | Int.signed ?x => putable x
 | Int64.signed ?x => putable x
 | Ptrofs.signed ?x => putable x
 | Int.unsigned ?x => putable x
 | Int64.unsigned ?x => putable x
 | Ptrofs.unsigned ?x => putable x
 | two_power_nat ?x => putable x
 | Int.max_unsigned => idtac
 | Int64.max_unsigned => idtac
 | Ptrofs.max_unsigned => idtac
 | Int.min_signed => idtac
 | Int64.min_signed => idtac
 | Ptrofs.min_signed => idtac
 | Int.max_signed => idtac
 | Int64.max_signed => idtac
 | Ptrofs.max_signed => idtac
 | Int.modulus => idtac
 | Int64.modulus => idtac
 | Ptrofs.modulus => idtac
 | Int.zwordsize => idtac
 | Int64.zwordsize => idtac
 | Ptrofs.zwordsize => idtac
end.Ltac computable := match goal with |- ?x =>
 no_evars x;
 putable x;
 compute; clear; repeat split; auto; congruence;
  (match goal with |- context [Archi.ptr64] => idtac end;
    first [change Archi.ptr64 with false | change Archi.ptr64 with true];
    compute; repeat split; auto; congruence)
end.

(* Specifications: *)
Lemma sign_ext_range2: forall lo n i hi, 0 < n < Int.zwordsize -> lo = - two_p (n-1) -> hi = two_p (n-1) - 1 -> lo <= Int.signed (Int.sign_ext n i) <= hi.
Lemma zero_ext_range2: forall n i lo hi, 0 <= n < Int.zwordsize -> lo = 0 -> hi = two_p n - 1 -> lo <= Int.unsigned (Int.zero_ext n i) <= hi.