1 files changed, 17 insertions, 56 deletions
diff --git a/contrib/subtac/test/euclid.v b/contrib/subtac/test/euclid.v
index ba5bdf23..a5a8b85f 100644
--- a/contrib/subtac/test/euclid.v
+++ b/contrib/subtac/test/euclid.v
@@ -1,66 +1,27 @@
-
-Notation "( x & y )" := (@existS _ _ x y) : core_scope.
-Unset Printing All.
-
-Definition t := fun (Evar46 : forall a : nat, (fun y : nat => @eq nat a y) a) (a : nat) =>
-@existS nat (fun x : nat => @sig nat (fun y : nat => @eq nat x y)) a
-  (@exist nat (fun y : nat => @eq nat a y) a (Evar46 a)).
-
-Program Definition testsig (a : nat) : { x : nat & { y : nat | x = y } } :=
-  (a & a).
-reflexivity.
-Defined.
-
-Extraction testsig.
-Extraction sig.
-Extract Inductive sig => "" [ "" ].
-Extraction testsig.
-
+Require Import Coq.subtac.Utils.
 Require Import Coq.Arith.Compare_dec.
-
-Require Import Omega.
-
-Lemma minus_eq_add : forall x y z w, y <= x -> x - y = y * z + w -> x = y * S z + w.
-intros.
-assert(y * S z = y * z + y).
-auto.
-rewrite H1.
-omega.
-Qed.
-
-Program Fixpoint euclid (a : nat) (b : { b : nat | b <> O }) {wf a lt}  :
+Notation "( x & y )" := (existS _ x y) : core_scope.
+  
+Program Fixpoint euclid (a : nat) (b : { b : nat | b <> O }) {wf lt a}  :
   { q : nat & { r : nat | a = b * q + r /\ r < b } } :=
   if le_lt_dec b a then let (q', r) := euclid (a - b) b in 
   (S q' & r)
   else (O & a).
-intro euclid.
-simpl ; intros.
-Print euclid_evars.
-eapply euclid_evars with euclid.
-refine (euclid_evars _ _ _ euclid a Acc_a b).
-; simpl ; intros.
-Show Existentials.
 
-induction b0 ; induction r.
-simpl in H.
-simpl.
-simpl in p0.
-destruct p0.
-split.
+Require Import Omega.
+
+Obligations.
+Solve Obligations using subtac_simpl ; omega.
+
+Next Obligation.
+  assert(x0 * S q' = x0 * q' + x0) by auto with arith ; omega.
+Defined.
 
-apply minus_eq_add.
-omega.
-auto with arith.
-auto.
-simpl.
-induction b0 ; simpl.
-split ; auto.
-omega.
-exact (euclid a0 Acc_a0 b0).
+Program Definition test_euclid : (prod nat nat) := let (q, r) := euclid 4 2 in (q, q).
 
-exact (Acc_a).
-auto.
-auto.
-Focus 1.
+Eval lazy beta zeta delta iota in test_euclid.
 
+Program Definition testsig (a : nat) : { x : nat & { y : nat | x < y } } :=
+  (a & S a).
 
+Check testsig.