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/ZArith/ZArith_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/ZArith/ZArith_dec.v')
-rw-r--r-- | theories/ZArith/ZArith_dec.v | 20 |
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. |