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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/ZArith/ZArith_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/ZArith/ZArith_dec.v')
-rw-r--r--theories/ZArith/ZArith_dec.v20
1 files changed, 10 insertions, 10 deletions
diff --git a/theories/ZArith/ZArith_dec.v b/theories/ZArith/ZArith_dec.v
index ee7ee48b7..040a7414e 100644
--- a/theories/ZArith/ZArith_dec.v
+++ b/theories/ZArith/ZArith_dec.v
@@ -18,7 +18,7 @@ Require Zsyntax.
Lemma Dcompare_inf : (r:relation) {r=EGAL} + {r=INFERIEUR} + {r=SUPERIEUR}.
Proof.
Induction r; Auto with arith.
-Save.
+Qed.
Lemma Zcompare_rec :
(P:Set)(x,y:Z)
@@ -30,7 +30,7 @@ Proof.
Intros P x y H1 H2 H3.
Elim (Dcompare_inf (Zcompare x y)).
Intro H. Elim H; Auto with arith. Auto with arith.
-Save.
+Qed.
Section decidability.
@@ -49,7 +49,7 @@ Intro H3. Right. Elim (Zcompare_EGAL x y). Intros H1 H2. Unfold not. Intro H4.
Rewrite (H2 H4) in H3. Discriminate H3.
Intro H3. Right. Elim (Zcompare_EGAL x y). Intros H1 H2. Unfold not. Intro H4.
Rewrite (H2 H4) in H3. Discriminate H3.
-Save.
+Qed.
Theorem Z_lt_dec : (inf_decidable (Zlt x y)).
Proof.
@@ -58,7 +58,7 @@ Apply Zcompare_rec with x:=x y:=y; Intro H.
Right. Rewrite H. Discriminate.
Left; Assumption.
Right. Rewrite H. Discriminate.
-Save.
+Qed.
Theorem Z_le_dec : (inf_decidable (Zle x y)).
Proof.
@@ -67,7 +67,7 @@ Apply Zcompare_rec with x:=x y:=y; Intro H.
Left. Rewrite H. Discriminate.
Left. Rewrite H. Discriminate.
Right. Tauto.
-Save.
+Qed.
Theorem Z_gt_dec : (inf_decidable (Zgt x y)).
Proof.
@@ -76,7 +76,7 @@ Apply Zcompare_rec with x:=x y:=y; Intro H.
Right. Rewrite H. Discriminate.
Right. Rewrite H. Discriminate.
Left; Assumption.
-Save.
+Qed.
Theorem Z_ge_dec : (inf_decidable (Zge x y)).
Proof.
@@ -85,7 +85,7 @@ Apply Zcompare_rec with x:=x y:=y; Intro H.
Left. Rewrite H. Discriminate.
Right. Tauto.
Left. Rewrite H. Discriminate.
-Save.
+Qed.
Theorem Z_lt_ge_dec : {`x < y`}+{`x >= y`}.
Proof Z_lt_dec.
@@ -94,7 +94,7 @@ Theorem Z_le_gt_dec : {`x <= y`}+{`x > y`}.
Proof.
Elim Z_le_dec; Auto with arith.
Intro. Right. Apply not_Zle; Auto with arith.
-Save.
+Qed.
Theorem Z_gt_le_dec : {`x > y`}+{`x <= y`}.
Proof Z_gt_dec.
@@ -103,7 +103,7 @@ Theorem Z_ge_lt_dec : {`x >= y`}+{`x < y`}.
Proof.
Elim Z_ge_dec; Auto with arith.
Intro. Right. Apply not_Zge; Auto with arith.
-Save.
+Qed.
Theorem Z_le_lt_eq_dec : `x <= y` -> {`x < y`}+{x=y}.
@@ -113,7 +113,7 @@ Apply Zcompare_rec with x:=x y:=y.
Intro. Right. Elim (Zcompare_EGAL x y); Auto with arith.
Intro. Left. Elim (Zcompare_EGAL x y); Auto with arith.
Intro H1. Absurd `x > y`; Auto with arith.
-Save.
+Qed.
End decidability.