diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-04-17 11:30:23 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-04-17 11:30:23 +0000 |
commit | cc1be0bf512b421336e81099aa6906ca47e4257a (patch) | |
tree | c25fa8ed965729d7a85efa3b3292fdf7f442963d /theories/Arith/Compare_dec.v | |
parent | ebf9aa9f97ef0d49ed1b799c9213f78efad4fec7 (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-x | theories/Arith/Compare_dec.v | 20 |
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. |