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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/ZArith/Zmin.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/ZArith/Zmin.v')
-rw-r--r--theories/ZArith/Zmin.v10
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/ZArith/Zmin.v b/theories/ZArith/Zmin.v
index beb91a738..fa454fa96 100644
--- a/theories/ZArith/Zmin.v
+++ b/theories/ZArith/Zmin.v
@@ -30,12 +30,12 @@ Unboxed Definition Zmin (n m:Z) :=
(** * Characterization of the minimum on binary integer numbers *)
-Lemma Zmin_case_strong : forall (n m:Z) (P:Z -> Type),
+Lemma Zmin_case_strong : forall (n m:Z) (P:Z -> Type),
(n<=m -> P n) -> (m<=n -> P m) -> P (Zmin n m).
Proof.
intros n m P H1 H2; unfold Zmin, Zle, Zge in *.
rewrite <- (Zcompare_antisym n m) in H2.
- destruct (n ?= m); (apply H1|| apply H2); discriminate.
+ destruct (n ?= m); (apply H1|| apply H2); discriminate.
Qed.
Lemma Zmin_case : forall (n m:Z) (P:Z -> Type), P n -> P m -> P (Zmin n m).
@@ -43,7 +43,7 @@ Proof.
intros n m P H1 H2; unfold Zmin in |- *; case (n ?= m); auto with arith.
Qed.
-Lemma Zmin_spec : forall x y:Z,
+Lemma Zmin_spec : forall x y:Z,
x <= y /\ Zmin x y = x \/
x > y /\ Zmin x y = y.
Proof.
@@ -93,7 +93,7 @@ Qed.
Lemma Zmin_assoc : forall n m p:Z, Zmin n (Zmin m p) = Zmin (Zmin n m) p.
Proof.
- intros n m p; repeat apply Zmin_case_strong; intros;
+ intros n m p; repeat apply Zmin_case_strong; intros;
reflexivity || (try apply Zle_antisym); eauto with zarith.
Qed.
@@ -118,7 +118,7 @@ Qed.
(** * Operations preserving min *)
-Lemma Zsucc_min_distr :
+Lemma Zsucc_min_distr :
forall n m:Z, Zsucc (Zmin n m) = Zmin (Zsucc n) (Zsucc m).
Proof.
intros n m; unfold Zmin in |- *; rewrite (Zcompare_succ_compat n m);