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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/Zmax.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/Zmax.v')
-rw-r--r--theories/ZArith/Zmax.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/ZArith/Zmax.v b/theories/ZArith/Zmax.v
index 59fcfa494..413b685a2 100644
--- a/theories/ZArith/Zmax.v
+++ b/theories/ZArith/Zmax.v
@@ -30,15 +30,15 @@ Proof.
intros n m P H1 H2; unfold Zmax in |- *; case (n ?= m); auto with arith.
Qed.
-Lemma Zmax_case_strong : forall (n m:Z) (P:Z -> Type),
+Lemma Zmax_case_strong : forall (n m:Z) (P:Z -> Type),
(m<=n -> P n) -> (n<=m -> P m) -> P (Zmax n m).
Proof.
intros n m P H1 H2; unfold Zmax, Zle, Zge in *.
rewrite <- (Zcompare_antisym n m) in H1.
- destruct (n ?= m); (apply H1|| apply H2); discriminate.
+ destruct (n ?= m); (apply H1|| apply H2); discriminate.
Qed.
-Lemma Zmax_spec : forall x y:Z,
+Lemma Zmax_spec : forall x y:Z,
x >= y /\ Zmax x y = x \/
x < y /\ Zmax x y = y.
Proof.
@@ -90,13 +90,13 @@ Qed.
Lemma Zmax_comm : forall n m:Z, Zmax n m = Zmax m n.
Proof.
- intros; do 2 apply Zmax_case_strong; intros;
+ intros; do 2 apply Zmax_case_strong; intros;
apply Zle_antisym; auto with zarith.
Qed.
Lemma Zmax_assoc : forall n m p:Z, Zmax n (Zmax m p) = Zmax (Zmax n m) p.
Proof.
- intros n m p; repeat apply Zmax_case_strong; intros;
+ intros n m p; repeat apply Zmax_case_strong; intros;
reflexivity || (try apply Zle_antisym); eauto with zarith.
Qed.
@@ -114,7 +114,7 @@ Qed.
(** * Operations preserving max *)
-Lemma Zsucc_max_distr :
+Lemma Zsucc_max_distr :
forall n m:Z, Zsucc (Zmax n m) = Zmax (Zsucc n) (Zsucc m).
Proof.
intros n m; unfold Zmax in |- *; rewrite (Zcompare_succ_compat n m);