Imported Upstream snapshot 8.3~beta0+13298

1 files changed, 24 insertions, 0 deletions

diff --git a/plugins/subtac/test/euclid.v b/plugins/subtac/test/euclid.v
new file mode 100644
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+++ b/plugins/subtac/test/euclid.v
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+Require Import Coq.Program.Program.
+Require Import Coq.Arith.Compare_dec.
+Notation "( x & y )" := (existS _ x y) : core_scope.
+
+Require Import Omega.
+
+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).
+
+Next Obligation.
+  assert(b * S q' = b * q' + b) by auto with arith ; omega.
+Defined.
+
+Program Definition test_euclid : (prod nat nat) := let (q, r) := euclid 4 2 in (q, q).
+
+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.