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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/EquivDec.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/EquivDec.v')
-rw-r--r--theories/Classes/EquivDec.v24
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index 6ce34535e..4b9b26384 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -18,7 +18,7 @@
Require Export Coq.Classes.Equivalence.
-(** The [DecidableSetoid] class asserts decidability of a [Setoid]. It can be useful in proofs to reason more
+(** The [DecidableSetoid] class asserts decidability of a [Setoid]. It can be useful in proofs to reason more
classically. *)
Require Import Coq.Logic.Decidable.
@@ -43,8 +43,8 @@ Notation " x == y " := (equiv_dec (x :>) (y :>)) (no associativity, at level 70)
Definition swap_sumbool {A B} (x : { A } + { B }) : { B } + { A } :=
match x with
- | left H => @right _ _ H
- | right H => @left _ _ H
+ | left H => @right _ _ H
+ | right H => @left _ _ H
end.
Open Local Scope program_scope.
@@ -89,34 +89,34 @@ Obligation Tactic := unfold complement, equiv ; program_simpl.
Program Instance prod_eqdec `(EqDec A eq, EqDec B eq) :
! EqDec (prod A B) eq :=
{ equiv_dec x y :=
- let '(x1, x2) := x in
- let '(y1, y2) := y in
- if x1 == y1 then
+ let '(x1, x2) := x in
+ let '(y1, y2) := y in
+ if x1 == y1 then
if x2 == y2 then in_left
else in_right
else in_right }.
Program Instance sum_eqdec `(EqDec A eq, EqDec B eq) :
EqDec (sum A B) eq := {
- equiv_dec x y :=
+ equiv_dec x y :=
match x, y with
| inl a, inl b => if a == b then in_left else in_right
| inr a, inr b => if a == b then in_left else in_right
| inl _, inr _ | inr _, inl _ => in_right
end }.
-(** Objects of function spaces with countable domains like bool have decidable equality.
+(** Objects of function spaces with countable domains like bool have decidable equality.
Proving the reflection requires functional extensionality though. *)
Program Instance bool_function_eqdec `(EqDec A eq) : ! EqDec (bool -> A) eq :=
- { equiv_dec f g :=
+ { equiv_dec f g :=
if f true == g true then
if f false == g false then in_left
else in_right
else in_right }.
Next Obligation.
- Proof.
+ Proof.
extensionality x.
destruct x ; auto.
Qed.
@@ -124,11 +124,11 @@ Program Instance bool_function_eqdec `(EqDec A eq) : ! EqDec (bool -> A) eq :=
Require Import List.
Program Instance list_eqdec `(eqa : EqDec A eq) : ! EqDec (list A) eq :=
- { equiv_dec :=
+ { equiv_dec :=
fix aux (x : list A) y { struct x } :=
match x, y with
| nil, nil => in_left
- | cons hd tl, cons hd' tl' =>
+ | cons hd tl, cons hd' tl' =>
if hd == hd' then
if aux tl tl' then in_left else in_right
else in_right