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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/Wf_Z.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/Wf_Z.v')
-rw-r--r--theories/ZArith/Wf_Z.v20
1 files changed, 10 insertions, 10 deletions
diff --git a/theories/ZArith/Wf_Z.v b/theories/ZArith/Wf_Z.v
index 5f1d6ba47..be8820481 100644
--- a/theories/ZArith/Wf_Z.v
+++ b/theories/ZArith/Wf_Z.v
@@ -45,7 +45,7 @@ NewDestruct x; Intros;
[ Unfold Zle; Simpl; Do 2 (Unfold not); Auto with arith
| Assumption]
].
-Save.
+Qed.
Lemma ZL4_inf: (y:positive) { h:nat | (convert y)=(S h) }.
Induction y; [
@@ -55,7 +55,7 @@ Induction y; [
| Intros p H1;Elim H1;Intros x H2; Exists (plus x (S x)); Unfold convert;
Simpl; Rewrite ZL0; Rewrite ZL2;Unfold convert in H2; Rewrite H2; Auto with arith
| Exists O ;Auto with arith].
-Save.
+Qed.
Lemma inject_nat_complete_inf :
(x:Z)`0 <= x` -> { n:nat | (x=(inject_nat n)) }.
@@ -71,7 +71,7 @@ NewDestruct x; Intros;
[ Unfold Zle; Simpl; Do 2 (Unfold not); Auto with arith
| Assumption]
].
-Save.
+Qed.
Lemma inject_nat_prop :
(P:Z->Prop)((n:nat)(P (inject_nat n))) ->
@@ -80,7 +80,7 @@ Intros.
Specialize (inject_nat_complete x H0).
Intros Hn; Elim Hn; Intros.
Rewrite -> H1; Apply H.
-Save.
+Qed.
Lemma inject_nat_set :
(P:Z->Set)((n:nat)(P (inject_nat n))) ->
@@ -89,14 +89,14 @@ Intros.
Specialize (inject_nat_complete_inf x H0).
Intros Hn; Elim Hn; Intros.
Rewrite -> p; Apply H.
-Save.
+Qed.
Lemma ZERO_le_inj :
(n:nat) `0 <= (inject_nat n)`.
Induction n; Simpl; Intros;
[ Apply Zle_n
| Unfold Zle; Simpl; Discriminate].
-Save.
+Qed.
Lemma natlike_ind : (P:Z->Prop) (P `0`) ->
((x:Z)(`0 <= x` -> (P x) -> (P (Zs x)))) ->
@@ -107,7 +107,7 @@ Intros; Apply inject_nat_prop;
| Intros; Rewrite -> (inj_S n0);
Exact (H0 (inject_nat n0) (ZERO_le_inj n0) H2) ]
| Assumption].
-Save.
+Qed.
Lemma natlike_rec : (P:Z->Set) (P `0`) ->
((x:Z)(`0 <= x` -> (P x) -> (P (Zs x)))) ->
@@ -118,7 +118,7 @@ Intros; Apply inject_nat_set;
| Intros; Rewrite -> (inj_S n0);
Exact (H0 (inject_nat n0) (ZERO_le_inj n0) H2) ]
| Assumption].
-Save.
+Qed.
Lemma Z_lt_induction :
(P:Z->Prop)
@@ -148,7 +148,7 @@ Apply Zlt_le_trans with y. Intuition.
Apply Zgt_S_le. Apply Zlt_gt. Intuition.
Assumption.
-Save.
+Qed.
Lemma Z_lt_rec :
(P:Z->Set)
@@ -178,4 +178,4 @@ Apply Zlt_le_trans with y. Intuition.
Apply Zgt_S_le. Apply Zlt_gt. Intuition.
Assumption.
-Save.
+Qed.