# HG changeset patch
# User nipkow
# Date 1235905317 -3600
# Node ID 05629f28f0f78438ef37e072187a7ff82692c9cb
# Parent  6d29a873141f4c99c3c119283705a4e1f57ef2ba
removed redundant lemmas

diff -r 6d29a873141f -r 05629f28f0f7 NEWS
--- a/NEWS	Sun Mar 01 10:24:57 2009 +0100
+++ b/NEWS	Sun Mar 01 12:01:57 2009 +0100
@@ -385,6 +385,7 @@
 nat_mod_mod_trivial    -> mod_mod_trivial
 zdiv_zadd_self1        -> div_add_self1
 zdiv_zadd_self2        -> div_add_self2
+zdiv_zmult_self1       -> div_mult_self2_is_id
 zdiv_zmult_self2       -> div_mult_self1_is_id
 zdvd_triv_left         -> dvd_triv_left
 zdvd_triv_right        -> dvd_triv_right
diff -r 6d29a873141f -r 05629f28f0f7 src/HOL/IntDiv.thy
--- a/src/HOL/IntDiv.thy	Sun Mar 01 10:24:57 2009 +0100
+++ b/src/HOL/IntDiv.thy	Sun Mar 01 12:01:57 2009 +0100
@@ -689,9 +689,6 @@
 apply (blast intro: divmod_rel_div_mod [THEN zmult1_lemma, THEN divmod_rel_mod])
 done
 
-lemma zdiv_zmult_self1 [simp]: "b \<noteq> (0::int) ==> (a*b) div b = a"
-by (simp add: zdiv_zmult1_eq)
-
 lemma zmod_zdiv_trivial: "(a mod b) div b = (0::int)"
 apply (case_tac "b = 0", simp)
 apply (auto simp add: linorder_neq_iff div_pos_pos_trivial div_neg_neg_trivial)
@@ -717,7 +714,7 @@
   assume not0: "b \<noteq> 0"
   show "(a + c * b) div b = c + a div b"
     unfolding zdiv_zadd1_eq [of a "c * b"] using not0 
-      by (simp add: zmod_zmult1_eq zmod_zdiv_trivial)
+      by (simp add: zmod_zmult1_eq zmod_zdiv_trivial zdiv_zmult1_eq)
 qed auto
 
 lemma posDivAlg_div_mod:
diff -r 6d29a873141f -r 05629f28f0f7 src/HOL/Library/Float.thy
--- a/src/HOL/Library/Float.thy	Sun Mar 01 10:24:57 2009 +0100
+++ b/src/HOL/Library/Float.thy	Sun Mar 01 12:01:57 2009 +0100
@@ -1093,7 +1093,7 @@
   { have "2^(prec - 1) * m \<le> 2^(prec - 1) * 2^?b" using `m < 2^?b`[THEN less_imp_le] by (rule mult_left_mono, auto)
     also have "\<dots> = 2 ^ nat (int prec + bitlen m - 1)" unfolding pow_split zpower_zadd_distrib by auto
     finally have "2^(prec - 1) * m div m \<le> 2 ^ nat (int prec + bitlen m - 1) div m" using `0 < m` by (rule zdiv_mono1)
-    hence "2^(prec - 1) \<le> 2 ^ nat (int prec + bitlen m - 1) div m" unfolding zdiv_zmult_self1[OF `m \<noteq> 0`] .
+    hence "2^(prec - 1) \<le> 2 ^ nat (int prec + bitlen m - 1) div m" unfolding div_mult_self2_is_id[OF `m \<noteq> 0`] .
     hence "2^(prec - 1) * inverse (2 ^ nat (int prec + bitlen m - 1)) \<le> ?d"
       unfolding real_of_int_le_iff[of "2^(prec - 1)", symmetric] by auto }
   from mult_left_mono[OF this[unfolded pow_split power_add inverse_mult_distrib real_mult_assoc[symmetric] right_inverse[OF pow_not0] real_mult_1], of "2^?e"]