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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/Numbers/Natural/SpecViaZ
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/Numbers/Natural/SpecViaZ')
-rw-r--r--theories/Numbers/Natural/SpecViaZ/NSig.v4
-rw-r--r--theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v4
2 files changed, 4 insertions, 4 deletions
diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v
index e53e627ec..5295aaec2 100644
--- a/theories/Numbers/Natural/SpecViaZ/NSig.v
+++ b/theories/Numbers/Natural/SpecViaZ/NSig.v
@@ -58,7 +58,7 @@ Module Type NType.
Parameter spec_eq_bool: forall x y,
if eq_bool x y then [x] = [y] else [x] <> [y].
-
+
Parameter succ : t -> t.
Parameter spec_succ: forall n, [succ n] = [n] + 1.
@@ -98,7 +98,7 @@ Module Type NType.
Parameter spec_div_eucl: forall x y,
0 < [y] ->
let (q,r) := div_eucl x y in ([q], [r]) = Zdiv_eucl [x] [y].
-
+
Parameter div : t -> t -> t.
Parameter spec_div: forall x y, 0 < [y] -> [div x y] = [x] / [y].
diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
index 773807120..578cb6256 100644
--- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
+++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
@@ -97,7 +97,7 @@ Section Induction.
Variable A : N.t -> Prop.
Hypothesis A_wd : predicate_wd N.eq A.
Hypothesis A0 : A 0.
-Hypothesis AS : forall n, A n <-> A (N.succ n).
+Hypothesis AS : forall n, A n <-> A (N.succ n).
Add Morphism A with signature N.eq ==> iff as A_morph.
Proof. apply A_wd. Qed.
@@ -221,7 +221,7 @@ Proof.
Qed.
Add Morphism N.compare with signature N.eq ==> N.eq ==> (@eq comparison) as compare_wd.
-Proof.
+Proof.
intros x x' Hx y y' Hy.
rewrite 2 spec_compare_alt. unfold N.eq in *. rewrite Hx, Hy; intuition.
Qed.