diff options
author | filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-05-16 08:19:21 +0000 |
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committer | filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-05-16 08:19:21 +0000 |
commit | ce2b0190464e17b142695e6efe78ac8bdfe89a30 (patch) | |
tree | f32a794d3db5646fc9b9e84986cbdba31c5c51d2 /theories/ZArith/ZArith_dec.v | |
parent | 76ed85857b467d38200a75b3dc7cd02d2d48b063 (diff) |
suppression de inf_decidable dans ZArith_dec (pour SeachPattern)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2697 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/ZArith_dec.v')
-rw-r--r-- | theories/ZArith/ZArith_dec.v | 22 |
1 files changed, 9 insertions, 13 deletions
diff --git a/theories/ZArith/ZArith_dec.v b/theories/ZArith/ZArith_dec.v index 040a7414e..de9fb0aed 100644 --- a/theories/ZArith/ZArith_dec.v +++ b/theories/ZArith/ZArith_dec.v @@ -35,14 +35,10 @@ Qed. Section decidability. -Local inf_decidable := [P:Prop] {P}+{~P}. - Variables x,y : Z. - -Theorem Z_eq_dec : (inf_decidable (x=y)). +Theorem Z_eq_dec : {x=y}+{~x=y}. Proof. -Unfold inf_decidable. Apply Zcompare_rec with x:=x y:=y. Intro. Left. Elim (Zcompare_EGAL x y); Auto with arith. Intro H3. Right. Elim (Zcompare_EGAL x y). Intros H1 H2. Unfold not. Intro H4. @@ -51,36 +47,36 @@ Intro H3. Right. Elim (Zcompare_EGAL x y). Intros H1 H2. Unfold not. Intro H4. Rewrite (H2 H4) in H3. Discriminate H3. Qed. -Theorem Z_lt_dec : (inf_decidable (Zlt x y)). +Theorem Z_lt_dec : {(Zlt x y)}+{~(Zlt x y)}. Proof. -Unfold inf_decidable Zlt. +Unfold Zlt. Apply Zcompare_rec with x:=x y:=y; Intro H. Right. Rewrite H. Discriminate. Left; Assumption. Right. Rewrite H. Discriminate. Qed. -Theorem Z_le_dec : (inf_decidable (Zle x y)). +Theorem Z_le_dec : {(Zle x y)}+{~(Zle x y)}. Proof. -Unfold inf_decidable Zle. +Unfold Zle. Apply Zcompare_rec with x:=x y:=y; Intro H. Left. Rewrite H. Discriminate. Left. Rewrite H. Discriminate. Right. Tauto. Qed. -Theorem Z_gt_dec : (inf_decidable (Zgt x y)). +Theorem Z_gt_dec : {(Zgt x y)}+{~(Zgt x y)}. Proof. -Unfold inf_decidable Zgt. +Unfold Zgt. Apply Zcompare_rec with x:=x y:=y; Intro H. Right. Rewrite H. Discriminate. Right. Rewrite H. Discriminate. Left; Assumption. Qed. -Theorem Z_ge_dec : (inf_decidable (Zge x y)). +Theorem Z_ge_dec : {(Zge x y)}+{~(Zge x y)}. Proof. -Unfold inf_decidable Zge. +Unfold Zge. Apply Zcompare_rec with x:=x y:=y; Intro H. Left. Rewrite H. Discriminate. Right. Tauto. |