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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-04-17 11:30:23 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-04-17 11:30:23 +0000
commitcc1be0bf512b421336e81099aa6906ca47e4257a (patch)
treec25fa8ed965729d7a85efa3b3292fdf7f442963d /theories/Arith/Compare_dec.v
parentebf9aa9f97ef0d49ed1b799c9213f78efad4fec7 (diff)
Uniformisation (Qed/Save et Implicits Arguments)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2650 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Compare_dec.v')
-rwxr-xr-xtheories/Arith/Compare_dec.v20
1 files changed, 10 insertions, 10 deletions
diff --git a/theories/Arith/Compare_dec.v b/theories/Arith/Compare_dec.v
index f9e93b9bf..d729253b3 100755
--- a/theories/Arith/Compare_dec.v
+++ b/theories/Arith/Compare_dec.v
@@ -15,7 +15,7 @@ Require Decidable.
Theorem zerop : (n:nat){n=O}+{lt O n}.
NewDestruct n; Auto with arith.
-Save.
+Qed.
Theorem lt_eq_lt_dec : (n,m:nat){(lt n m)}+{n=m}+{(lt m n)}.
Proof.
@@ -61,42 +61,42 @@ Theorem dec_le:(x,y:nat)(decidable (le x y)).
Intros x y; Unfold decidable ; Elim (le_gt_dec x y); [
Auto with arith
| Intro; Right; Apply gt_not_le; Assumption].
-Save.
+Qed.
Theorem dec_lt:(x,y:nat)(decidable (lt x y)).
Intros x y; Unfold lt; Apply dec_le.
-Save.
+Qed.
Theorem dec_gt:(x,y:nat)(decidable (gt x y)).
Intros x y; Unfold gt; Apply dec_lt.
-Save.
+Qed.
Theorem dec_ge:(x,y:nat)(decidable (ge x y)).
Intros x y; Unfold ge; Apply dec_le.
-Save.
+Qed.
Theorem not_eq : (x,y:nat) ~ x=y -> (lt x y) \/ (lt y x).
Intros x y H; Elim (lt_eq_lt_dec x y); [
Intros H1; Elim H1; [ Auto with arith | Intros H2; Absurd x=y; Assumption]
| Auto with arith].
-Save.
+Qed.
Theorem not_le : (x,y:nat) ~(le x y) -> (gt x y).
Intros x y H; Elim (le_gt_dec x y);
[ Intros H1; Absurd (le x y); Assumption | Trivial with arith ].
-Save.
+Qed.
Theorem not_gt : (x,y:nat) ~(gt x y) -> (le x y).
Intros x y H; Elim (le_gt_dec x y);
[ Trivial with arith | Intros H1; Absurd (gt x y); Assumption].
-Save.
+Qed.
Theorem not_ge : (x,y:nat) ~(ge x y) -> (lt x y).
Intros x y H; Exact (not_le y x H).
-Save.
+Qed.
Theorem not_lt : (x,y:nat) ~(lt x y) -> (ge x y).
Intros x y H; Exact (not_gt y x H).
-Save.
+Qed.