diff options
Diffstat (limited to 'contrib/subtac/test/euclid.v')
-rw-r--r-- | contrib/subtac/test/euclid.v | 11 |
1 files changed, 4 insertions, 7 deletions
diff --git a/contrib/subtac/test/euclid.v b/contrib/subtac/test/euclid.v index a5a8b85f..501aa798 100644 --- a/contrib/subtac/test/euclid.v +++ b/contrib/subtac/test/euclid.v @@ -1,20 +1,17 @@ -Require Import Coq.subtac.Utils. +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). -Require Import Omega. - -Obligations. -Solve Obligations using subtac_simpl ; omega. - Next Obligation. - assert(x0 * S q' = x0 * q' + x0) by auto with arith ; omega. + 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). |