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authorherbelin2000-07-01 10:20:11 +0000
committerherbelin2000-07-01 10:20:11 +0000
commit445171395557a2447e70d90bb793277639a9a01e (patch)
treed6a91489cac2e2c896e819f9c7dd11c3a6ac47a7
parent7da855f0e3ed56aa9ad9149f6ef95be11f7ec5d2 (diff)
Retrait des parenthèses inutiles autour des tactiques
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@543 85f007b7-540e-0410-9357-904b9bb8a0f7
-rw-r--r--theories/Lists/PolyList.v50
1 files changed, 25 insertions, 25 deletions
diff --git a/theories/Lists/PolyList.v b/theories/Lists/PolyList.v
index 1fe019af35..1129e9af02 100644
--- a/theories/Lists/PolyList.v
+++ b/theories/Lists/PolyList.v
@@ -77,15 +77,15 @@ Qed.
Lemma app_eq_nil: (x,y:list) (x^y)=nil -> x=nil /\ y=nil.
Proof.
- (Destruct x;Destruct y;Simpl;Auto).
- (Intros H;Discriminate H).
- (Intros a0 l0 H;Discriminate H).
+ Destruct x;Destruct y;Simpl;Auto.
+ Intros H;Discriminate H.
+ Intros a0 l0 H;Discriminate H.
Qed.
Lemma app_cons_not_nil: (x,y:list)(a:A)~nil=(x^(cons a y)).
Proof.
Unfold not .
- (Induction x;Simpl;Intros).
+ Induction x;Simpl;Intros.
Discriminate H.
Discriminate H0.
Qed.
@@ -94,17 +94,17 @@ Lemma app_eq_unit:(x,y:list)(a:A)
(x^y)=(cons a nil)-> (x=nil)/\ y=(cons a nil) \/ x=(cons a nil)/\ y=nil.
Proof.
- (Destruct x;Destruct y;Simpl).
- (Intros a H;Discriminate H).
- (Left;Split;Auto).
- (Right;Split;Auto).
+ Destruct x;Destruct y;Simpl.
+ Intros a H;Discriminate H.
+ Left;Split;Auto.
+ Right;Split;Auto.
Generalize H .
- (Generalize (app_nil_end l) ;Intros E).
- (Rewrite <- E;Auto).
+ Generalize (app_nil_end l) ;Intros E.
+ Rewrite <- E;Auto.
Intros.
Injection H.
Intro.
- (Cut nil=(l^(cons a0 l0));Auto).
+ Cut nil=(l^(cons a0 l0));Auto.
Intro.
Generalize (app_cons_not_nil H1); Intro.
Elim H2.
@@ -113,23 +113,23 @@ Qed.
Lemma app_inj_tail : (x,y:list)(a,b:A)
(x^(cons a nil))=(y^(cons b nil)) -> x=y /\ a=b.
Proof.
- (Induction x;Induction y;Simpl;Auto).
+ Induction x;Induction y;Simpl;Auto.
Intros.
Injection H.
Auto.
Intros.
- (Injection H0;Intros).
- (Generalize (app_cons_not_nil H1) ;Induction 1).
+ Injection H0;Intros.
+ Generalize (app_cons_not_nil H1) ;Induction 1.
Intros.
- (Injection H0;Intros).
- (Cut nil=(l^(cons a0 nil));Auto).
+ Injection H0;Intros.
+ Cut nil=(l^(cons a0 nil));Auto.
Intro.
- (Generalize (app_cons_not_nil H3) ;Induction 1).
+ Generalize (app_cons_not_nil H3) ;Induction 1.
Intros.
- (Injection H1;Intros).
+ Injection H1;Intros.
Generalize (H l0 a1 b H2) .
- (Induction 1;Split;Auto).
- (Rewrite <- H3;Rewrite <- H5;Auto).
+ Induction 1;Split;Auto.
+ Rewrite <- H3;Rewrite <- H5;Auto.
Qed.
(****************************************)
@@ -436,24 +436,24 @@ Proof.
Simpl.
Intros.
- (Apply app_nil_end;Auto).
+ Apply app_nil_end;Auto.
Intros.
Simpl.
- (Generalize (H y) ;Intros E;Rewrite -> E).
+ Generalize (H y) ;Intros E;Rewrite -> E.
Apply (app_ass (rev y) (rev l) (cons a nil)).
Qed.
Remark rev_unit : (l:list)(a:A) (rev l^(cons a nil))= (cons a (rev l)).
Proof.
Intros.
- (Apply (distr_rev l (cons a nil));Simpl;Auto).
+ Apply (distr_rev l (cons a nil));Simpl;Auto.
Qed.
Lemma idempot_rev : (l:list)(rev (rev l))=l.
Proof.
Induction l.
- (Simpl;Auto).
+ Simpl;Auto.
Intros.
Simpl.
@@ -480,7 +480,7 @@ Lemma rev_ind :
Proof.
Intros.
Generalize (idempot_rev l) .
- (Intros E;Rewrite <- E).
+ Intros E;Rewrite <- E.
Apply (rev_list_ind P).
Auto.