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/FSets/FSetToFiniteSet.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/FSets/FSetToFiniteSet.v')
-rw-r--r-- | theories/FSets/FSetToFiniteSet.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/FSets/FSetToFiniteSet.v b/theories/FSets/FSetToFiniteSet.v index 7938beda7..23420109c 100644 --- a/theories/FSets/FSetToFiniteSet.v +++ b/theories/FSets/FSetToFiniteSet.v @@ -6,8 +6,8 @@ (* * GNU Lesser General Public License Version 2.1 *) (***********************************************************************) -(* Finite sets library. - * Authors: Pierre Letouzey and Jean-Christophe Filliâtre +(* Finite sets library. + * Authors: Pierre Letouzey and Jean-Christophe Filliâtre * Institution: LRI, CNRS UMR 8623 - Université Paris Sud * 91405 Orsay, France *) @@ -16,14 +16,14 @@ Require Import Ensembles Finite_sets. Require Import FSetInterface FSetProperties OrderedTypeEx DecidableTypeEx. -(** * Going from [FSets] with usual Leibniz equality +(** * Going from [FSets] with usual Leibniz equality to the good old [Ensembles] and [Finite_sets] theory. *) Module WS_to_Finite_set (U:UsualDecidableType)(M: WSfun U). Module MP:= WProperties_fun U M. Import M MP FM Ensembles Finite_sets. - Definition mkEns : M.t -> Ensemble M.elt := + Definition mkEns : M.t -> Ensemble M.elt := fun s x => M.In x s. Notation " !! " := mkEns. @@ -115,11 +115,11 @@ Module WS_to_Finite_set (U:UsualDecidableType)(M: WSfun U). Proof. intro s; pattern s; apply set_induction; clear s; intros. intros; replace (!!s) with (Empty_set elt); auto with sets. - symmetry; apply Extensionality_Ensembles. + symmetry; apply Extensionality_Ensembles. apply Empty_Empty_set; auto. replace (!!s') with (Add _ (!!s) x). constructor 2; auto. - symmetry; apply Extensionality_Ensembles. + symmetry; apply Extensionality_Ensembles. apply Add_Add; auto. Qed. @@ -128,18 +128,18 @@ Module WS_to_Finite_set (U:UsualDecidableType)(M: WSfun U). intro s; pattern s; apply set_induction; clear s; intros. intros; replace (!!s) with (Empty_set elt); auto with sets. rewrite cardinal_1; auto with sets. - symmetry; apply Extensionality_Ensembles. + symmetry; apply Extensionality_Ensembles. apply Empty_Empty_set; auto. replace (!!s') with (Add _ (!!s) x). - rewrite (cardinal_2 H0 H1); auto with sets. - symmetry; apply Extensionality_Ensembles. + rewrite (cardinal_2 H0 H1); auto with sets. + symmetry; apply Extensionality_Ensembles. apply Add_Add; auto. Qed. - (** we can even build a function from Finite Ensemble to FSet + (** we can even build a function from Finite Ensemble to FSet ... at least in Prop. *) - Lemma Ens_to_FSet : forall e : Ensemble M.elt, Finite _ e -> + Lemma Ens_to_FSet : forall e : Ensemble M.elt, Finite _ e -> exists s:M.t, !!s === e. Proof. induction 1. @@ -147,7 +147,7 @@ Module WS_to_Finite_set (U:UsualDecidableType)(M: WSfun U). apply empty_Empty_Set. destruct IHFinite as (s,Hs). exists (M.add x s). - apply Extensionality_Ensembles in Hs. + apply Extensionality_Ensembles in Hs. rewrite <- Hs. apply add_Add. Qed. |