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