diff options
author | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
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committer | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
commit | 61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch) | |
tree | 961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Lists/ListSet.v | |
parent | 6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff) |
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Lists/ListSet.v')
-rw-r--r-- | theories/Lists/ListSet.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Lists/ListSet.v b/theories/Lists/ListSet.v index 77caa9c22..d8a8183f3 100644 --- a/theories/Lists/ListSet.v +++ b/theories/Lists/ListSet.v @@ -47,7 +47,7 @@ Section first_definitions. | right _ => set_mem a x1 end end. - + (** If [a] belongs to [x], removes [a] from [x]. If not, does nothing *) Fixpoint set_remove (a:A) (x:set) {struct x} : set := match x with @@ -72,7 +72,7 @@ Section first_definitions. | nil => x | a1 :: y1 => set_add a1 (set_union x y1) end. - + (** returns the set of all els of [x] that does not belong to [y] *) Fixpoint set_diff (x y:set) {struct x} : set := match x with @@ -80,7 +80,7 @@ Section first_definitions. | a1 :: x1 => if set_mem a1 y then set_diff x1 y else set_add a1 (set_diff x1 y) end. - + Definition set_In : A -> set -> Prop := In (A:=A). @@ -123,7 +123,7 @@ Section first_definitions. case H3; auto. Qed. - + Lemma set_mem_correct1 : forall (a:A) (x:set), set_mem a x = true -> set_In a x. Proof. @@ -191,11 +191,11 @@ Section first_definitions. Lemma set_add_intro : forall (a b:A) (x:set), a = b \/ set_In a x -> set_In a (set_add b x). - + Proof. intros a b x [H1| H2]; auto with datatypes. Qed. - + Lemma set_add_elim : forall (a b:A) (x:set), set_In a (set_add b x) -> a = b \/ set_In a x. @@ -225,7 +225,7 @@ Section first_definitions. simple induction x; simpl in |- *. discriminate. intros; elim (Aeq_dec a a0); intros; discriminate. - Qed. + Qed. Lemma set_union_intro1 : @@ -289,7 +289,7 @@ Section first_definitions. elim (set_mem a y); simpl in |- *; intros. auto with datatypes. absurd (set_In a y); auto with datatypes. - elim (set_mem a0 y); [ right; auto with datatypes | auto with datatypes ]. + elim (set_mem a0 y); [ right; auto with datatypes | auto with datatypes ]. Qed. Lemma set_inter_elim1 : @@ -324,7 +324,7 @@ Section first_definitions. set_In a (set_inter x y) -> set_In a x /\ set_In a y. Proof. eauto with datatypes. - Qed. + Qed. Lemma set_diff_intro : forall (a:A) (x y:set), @@ -354,7 +354,7 @@ Section first_definitions. forall (a:A) (x y:set), set_In a (set_diff x y) -> ~ set_In a y. intros a x y; elim x; simpl in |- *. intros; contradiction. - intros a0 l Hrec. + intros a0 l Hrec. apply set_mem_ind2; auto. intros H1 H2; case (set_add_elim _ _ _ H2); intros; auto. rewrite H; trivial. @@ -387,10 +387,10 @@ Section other_definitions. Definition set_fold_left : (B -> A -> B) -> set A -> B -> B := fold_left (A:=B) (B:=A). - Definition set_fold_right (f:A -> B -> B) (x:set A) + Definition set_fold_right (f:A -> B -> B) (x:set A) (b:B) : B := fold_right f b x. - + End other_definitions. Unset Implicit Arguments. |