From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Thu, 23 Nov 2006 13:45:53 +0000 (+0000)
Subject: Minor changes.
X-Git-Tag: 0.4.95@7852~795
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=544444b7fbb3882577f55b7dbd16046f39c52031;p=helm.git

Minor changes.
-This line, and those below, will be ignored--

M    library/nat/ord.ma
M    library/nat/gcd.ma
M    library/nat/factorization.ma
M    library/technicalities/setoids.ma
---

diff --git a/matita/library/nat/factorization.ma b/matita/library/nat/factorization.ma
index d0036e4a1..85351c06d 100644
--- a/matita/library/nat/factorization.ma
+++ b/matita/library/nat/factorization.ma
@@ -52,7 +52,7 @@ intros; apply divides_b_true_to_divides;
         apply (trans_lt ? (S O));
         [ unfold lt; apply le_n;
         | assumption; ] *) ] ]
-  | letin x \def prime. auto new.
+  | auto. 
     (* 
     apply prime_to_nth_prime;
     apply prime_smallest_factor_n;
@@ -70,8 +70,8 @@ apply divides_to_divides_b_true.
 cut (prime (nth_prime (max_prime_factor n))).
 apply lt_O_nth_prime_n.apply prime_nth_prime.
 cut (nth_prime (max_prime_factor n) \divides n).
-auto new.
-auto new.
+auto.
+auto.
 (*
   [ apply (transitive_divides ? n);
     [ apply divides_max_prime_factor_n.
diff --git a/matita/library/nat/gcd.ma b/matita/library/nat/gcd.ma
index fdb1e8d90..036167bd0 100644
--- a/matita/library/nat/gcd.ma
+++ b/matita/library/nat/gcd.ma
@@ -39,16 +39,18 @@ definition gcd : nat \to nat \to nat \def
 theorem divides_mod: \forall p,m,n:nat. O < n \to p \divides m \to p \divides n \to
 p \divides (m \mod n).
 intros.elim H1.elim H2.
-apply (witness ? ? (n2 - n1*(m / n))).
+(* apply (witness ? ? (n2 - n1*(m / n))). *)
+apply witness[|
 rewrite > distr_times_minus.
-rewrite < H3.
+rewrite < H3 in \vdash (? ? ? (? % ?)).
 rewrite < assoc_times.
-rewrite < H4.
-apply sym_eq.
-apply plus_to_minus.
+rewrite < H4 in \vdash (? ? ? (? ? (? % ?))).
+apply sym_eq.apply plus_to_minus.
 rewrite > sym_times.
-apply div_mod.
-assumption.
+letin x \def div.
+rewrite < (div_mod ? ? H).
+reflexivity.
+]
 qed.
 
 theorem divides_mod_to_divides: \forall p,m,n:nat. O < n \to
diff --git a/matita/library/nat/ord.ma b/matita/library/nat/ord.ma
index ba08a0dcf..b7d02f87f 100644
--- a/matita/library/nat/ord.ma
+++ b/matita/library/nat/ord.ma
@@ -215,7 +215,7 @@ apply (absurd ? ? H10 H5).
 apply (absurd ? ? H10 H7).
 (* rewrite > H6.
 rewrite > H8. *)
-auto paramodulation library=yes.
+auto paramodulation.
 unfold prime in H. elim H. assumption.
 qed.
 
diff --git a/matita/library/technicalities/setoids.ma b/matita/library/technicalities/setoids.ma
index c440795ff..4d23d7725 100644
--- a/matita/library/technicalities/setoids.ma
+++ b/matita/library/technicalities/setoids.ma
@@ -228,7 +228,7 @@ definition equality_morphism_of_symmetric_areflexive_transitive_relation:
     unfold transitive in H;
     unfold symmetric in sym;
     intro;
-    auto
+    auto new
   ].
 qed.