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authorGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
committerGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
commit61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch)
tree961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Classes/SetoidClass.v
parent6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (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/Classes/SetoidClass.v')
-rw-r--r--theories/Classes/SetoidClass.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Classes/SetoidClass.v b/theories/Classes/SetoidClass.v
index 055f02f8b..6af4b5ffe 100644
--- a/theories/Classes/SetoidClass.v
+++ b/theories/Classes/SetoidClass.v
@@ -7,7 +7,7 @@
(************************************************************************)
(* Typeclass-based setoids, tactics and standard instances.
-
+
Author: Matthieu Sozeau
Institution: LRI, CNRS UMR 8623 - UniversitĂcopyright Paris Sud
91405 Orsay, France *)
@@ -55,7 +55,7 @@ Existing Instance setoid_trans.
(* Program Instance eq_setoid : Setoid A := *)
(* equiv := eq ; setoid_equiv := eq_equivalence. *)
-Program Instance iff_setoid : Setoid Prop :=
+Program Instance iff_setoid : Setoid Prop :=
{ equiv := iff ; setoid_equiv := iff_equivalence }.
(** Overloaded notations for setoid equivalence and inequivalence. Not to be confused with [eq] and [=]. *)
@@ -69,7 +69,7 @@ Notation " x =/= y " := (complement equiv x y) (at level 70, no associativity) :
(** Use the [clsubstitute] command which substitutes an equality in every hypothesis. *)
-Ltac clsubst H :=
+Ltac clsubst H :=
match type of H with
?x == ?y => substitute H ; clear H x
end.
@@ -79,7 +79,7 @@ Ltac clsubst_nofail :=
| [ H : ?x == ?y |- _ ] => clsubst H ; clsubst_nofail
| _ => idtac
end.
-
+
(** [subst*] will try its best at substituting every equality in the goal. *)
Tactic Notation "clsubst" "*" := clsubst_nofail.
@@ -94,7 +94,7 @@ Qed.
Lemma equiv_nequiv_trans : forall `{Setoid A} (x y z : A), x == y -> y =/= z -> x =/= z.
Proof.
- intros; intro.
+ intros; intro.
assert(y == x) by (symmetry ; auto).
assert(y == z) by (transitivity x ; eauto).
contradiction.
@@ -127,7 +127,7 @@ Program Instance setoid_partial_app_morphism `(sa : Setoid A) (x : A) : Proper (
(** Partial setoids don't require reflexivity so we can build a partial setoid on the function space. *)
-Class PartialSetoid (A : Type) :=
+Class PartialSetoid (A : Type) :=
{ pequiv : relation A ; pequiv_prf :> PER pequiv }.
(** Overloaded notation for partial setoid equivalence. *)