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authorglondu2009-09-17 15:58:14 +0000
committerglondu2009-09-17 15:58:14 +0000
commit61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch)
tree961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Numbers/Integer/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/Integer/SpecViaZ')
-rw-r--r--theories/Numbers/Integer/SpecViaZ/ZSig.v8
-rw-r--r--theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v6
2 files changed, 7 insertions, 7 deletions
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSig.v b/theories/Numbers/Integer/SpecViaZ/ZSig.v
index 4e45939831..00e292db0f 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSig.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSig.v
@@ -58,7 +58,7 @@ Module Type ZType.
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.
@@ -93,21 +93,21 @@ Module Type ZType.
Parameter sqrt : t -> t.
- Parameter spec_sqrt: forall x, 0 <= [x] ->
+ Parameter spec_sqrt: forall x, 0 <= [x] ->
[sqrt x] ^ 2 <= [x] < ([sqrt x] + 1) ^ 2.
Parameter div_eucl : t -> t -> t * t.
Parameter spec_div_eucl: forall x y, [y] <> 0 ->
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, [y] <> 0 -> [div x y] = [x] / [y].
Parameter modulo : t -> t -> t.
- Parameter spec_modulo: forall x y, [y] <> 0 ->
+ Parameter spec_modulo: forall x y, [y] <> 0 ->
[modulo x y] = [x] mod [y].
Parameter gcd : t -> t -> t.
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
index 4d1054553f..030c589ff9 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
@@ -27,7 +27,7 @@ Infix "-" := Z.sub : IntScope.
Infix "*" := Z.mul : IntScope.
Notation "- x" := (Z.opp x) : IntScope.
-Hint Rewrite
+Hint Rewrite
Z.spec_0 Z.spec_1 Z.spec_add Z.spec_sub Z.spec_pred Z.spec_succ
Z.spec_mul Z.spec_opp Z.spec_of_Z : Zspec.
@@ -91,7 +91,7 @@ Section Induction.
Variable A : Z.t -> Prop.
Hypothesis A_wd : predicate_wd Z.eq A.
Hypothesis A0 : A 0.
-Hypothesis AS : forall n, A n <-> A (Z.succ n).
+Hypothesis AS : forall n, A n <-> A (Z.succ n).
Add Morphism A with signature Z.eq ==> iff as A_morph.
Proof. apply A_wd. Qed.
@@ -214,7 +214,7 @@ Proof.
Qed.
Add Morphism Z.compare with signature Z.eq ==> Z.eq ==> (@eq comparison) as compare_wd.
-Proof.
+Proof.
intros x x' Hx y y' Hy.
rewrite 2 spec_compare_alt; unfold Z.eq in *; rewrite Hx, Hy; intuition.
Qed.