diff options
author | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
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committer | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
commit | 61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch) | |
tree | 961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/ZArith/Zmin.v | |
parent | 6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (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.v | 10 |
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); |