diff options
Diffstat (limited to 'contrib/rtauto/Bintree.v')
| -rw-r--r-- | contrib/rtauto/Bintree.v | 15 |
1 files changed, 3 insertions, 12 deletions
diff --git a/contrib/rtauto/Bintree.v b/contrib/rtauto/Bintree.v index f4b24d4b..e90fea84 100644 --- a/contrib/rtauto/Bintree.v +++ b/contrib/rtauto/Bintree.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(* $Id: Bintree.v 8881 2006-05-31 18:16:34Z jforest $ *) +(* $Id: Bintree.v 10681 2008-03-16 13:40:45Z msozeau $ *) Require Export List. Require Export BinPos. @@ -20,15 +20,6 @@ Ltac caseq t := generalize (refl_equal t); pattern t at -1; case t. Functional Scheme Pcompare_ind := Induction for Pcompare Sort Prop. -Lemma Prect : forall P : positive -> Type, - P 1 -> - (forall n : positive, P n -> P (Psucc n)) -> forall p : positive, P p. -intros P H1 Hsucc n; induction n. -rewrite <- plus_iter_xI; apply Hsucc; apply iterate_add; assumption. -rewrite <- plus_iter_xO; apply iterate_add; assumption. -assumption. -Qed. - Lemma Gt_Eq_Gt : forall p q cmp, (p ?= q) Eq = Gt -> (p ?= q) cmp = Gt. apply (Pcompare_ind (fun p q cmp _ => (p ?= q) Eq = Gt -> (p ?= q) cmp = Gt)); @@ -116,7 +107,7 @@ intro ne;right;congruence. left;reflexivity. Defined. -Theorem pos_eq_dec_refl : forall m, pos_eq_dec m m = left (m<>m) (refl_equal m) . +Theorem pos_eq_dec_refl : forall m, pos_eq_dec m m = left _ (refl_equal m). fix 1;intros [mm|mm|]. simpl; rewrite pos_eq_dec_refl; reflexivity. simpl; rewrite pos_eq_dec_refl; reflexivity. @@ -125,7 +116,7 @@ Qed. Theorem pos_eq_dec_ex : forall m n, pos_eq m n =true -> exists h:m=n, - pos_eq_dec m n = left (m<>n) h. + pos_eq_dec m n = left _ h. fix 1;intros [mm|mm|] [nn|nn|];try (simpl;congruence). simpl;intro e. elim (pos_eq_dec_ex _ _ e). |