# HG changeset patch
# User huffman
# Date 1332868865 -7200
# Node ID 9344891b504b8ea0499d820827aeb01e7fed63e7
# Parent  6a4c479ba94f03195678df906a3dbb4ffc1894e1
remove redundant lemmas

diff -r 6a4c479ba94f -r 9344891b504b NEWS
--- a/NEWS	Tue Mar 27 16:04:51 2012 +0200
+++ b/NEWS	Tue Mar 27 19:21:05 2012 +0200
@@ -144,6 +144,8 @@
   zmod_self ~> mod_self
   zdiv_zero ~> div_0
   zmod_zero ~> mod_0
+  zdiv_zmod_equality ~> div_mod_equality2
+  zdiv_zmod_equality2 ~> div_mod_equality
   zmod_zdiv_trivial ~> mod_div_trivial
   zdiv_zminus_zminus ~> div_minus_minus
   zmod_zminus_zminus ~> mod_minus_minus
diff -r 6a4c479ba94f -r 9344891b504b src/HOL/Divides.thy
--- a/src/HOL/Divides.thy	Tue Mar 27 16:04:51 2012 +0200
+++ b/src/HOL/Divides.thy	Tue Mar 27 19:21:05 2012 +0200
@@ -1436,12 +1436,6 @@
 lemma zmod_zdiv_equality: "(a::int) = b * (a div b) + (a mod b)"
   by (fact mod_div_equality2 [symmetric])
 
-lemma zdiv_zmod_equality: "(b * (a div b) + (a mod b)) + k = (a::int)+k"
-  by (fact div_mod_equality2)
-
-lemma zdiv_zmod_equality2: "((a div b) * b + (a mod b)) + k = (a::int)+k"
-  by (fact div_mod_equality)
-
 text {* Tool setup *}
 
 (* FIXME: Theorem list add_0s doesn't exist, because Numeral0 has gone. *)
@@ -1456,7 +1450,7 @@
   val mk_sum = Arith_Data.mk_sum HOLogic.intT;
   val dest_sum = Arith_Data.dest_sum;
 
-  val div_mod_eqs = map mk_meta_eq [@{thm zdiv_zmod_equality}, @{thm zdiv_zmod_equality2}];
+  val div_mod_eqs = map mk_meta_eq [@{thm div_mod_equality}, @{thm div_mod_equality2}];
 
   val prove_eq_sums = Arith_Data.prove_conv2 all_tac (Arith_Data.simp_all_tac 
     (@{thm diff_minus} :: @{thms add_0s} @ @{thms add_ac}))
diff -r 6a4c479ba94f -r 9344891b504b src/HOL/Groebner_Basis.thy
--- a/src/HOL/Groebner_Basis.thy	Tue Mar 27 16:04:51 2012 +0200
+++ b/src/HOL/Groebner_Basis.thy	Tue Mar 27 19:21:05 2012 +0200
@@ -53,7 +53,7 @@
 declare div_by_0[algebra]
 declare mod_by_0[algebra]
 declare zmod_zdiv_equality[symmetric,algebra]
-declare zdiv_zmod_equality[symmetric, algebra]
+declare div_mod_equality2[symmetric, algebra]
 declare div_minus_minus[algebra]
 declare mod_minus_minus[algebra]
 declare div_minus_right[algebra]
diff -r 6a4c479ba94f -r 9344891b504b src/HOL/Library/Float.thy
--- a/src/HOL/Library/Float.thy	Tue Mar 27 16:04:51 2012 +0200
+++ b/src/HOL/Library/Float.thy	Tue Mar 27 19:21:05 2012 +0200
@@ -488,7 +488,7 @@
         hence "x < x - x mod 2 +  2" unfolding algebra_simps by auto
         thus ?thesis by auto
       qed
-      also have "x - x mod 2 + 2 = (x div 2 + 1) * 2" unfolding algebra_simps using `0 < x` zdiv_zmod_equality2[of x 2 0] by auto
+      also have "x - x mod 2 + 2 = (x div 2 + 1) * 2" unfolding algebra_simps using `0 < x` div_mod_equality[of x 2 0] by auto
       also have "\<dots> \<le> 2^nat (bitlen (x div 2)) * 2" using hyp[OF `0 < x div 2`, THEN conjunct2] by (rule mult_right_mono, auto)
       also have "\<dots> = 2^(1 + nat (bitlen (x div 2)))" unfolding power_Suc2[symmetric] by auto
       finally have "x + 1 \<le> 2^(1 + nat (bitlen (x div 2)))" .
@@ -1122,7 +1122,7 @@
     show ?thesis
     proof (cases "m mod ?p = 0")
       case True
-      have m: "m = m div ?p * ?p + 0" unfolding True[symmetric] using zdiv_zmod_equality2[where k=0, unfolded monoid_add_class.add_0_right, symmetric] .
+      have m: "m = m div ?p * ?p + 0" unfolding True[symmetric] using mod_div_equality [symmetric] .
       have "real (Float m e) = real (Float (m div ?p) (e + ?d))" unfolding real_of_float_simp arg_cong[OF m, of real]
         by (auto simp add: pow2_add `0 < ?d` pow_d)
       thus ?thesis
@@ -1130,7 +1130,7 @@
         by auto
     next
       case False
-      have "m = m div ?p * ?p + m mod ?p" unfolding zdiv_zmod_equality2[where k=0, unfolded monoid_add_class.add_0_right] ..
+      have "m = m div ?p * ?p + m mod ?p" unfolding mod_div_equality ..
       also have "\<dots> \<le> (m div ?p + 1) * ?p" unfolding left_distrib mult_1 by (rule add_left_mono, rule pos_mod_bound[OF `0 < ?p`, THEN less_imp_le])
       finally have "real (Float m e) \<le> real (Float (m div ?p + 1) (e + ?d))" unfolding real_of_float_simp add_commute[of e]
         unfolding pow2_add mult_assoc[symmetric] real_of_int_le_iff[of m, symmetric]
@@ -1156,7 +1156,7 @@
     case True
     hence pow_d: "pow2 ?d = real ?p" using pow2_int[symmetric] by simp
     have "m div ?p * ?p \<le> m div ?p * ?p + m mod ?p" by (auto simp add: pos_mod_bound[OF `0 < ?p`, THEN less_imp_le])
-    also have "\<dots> \<le> m" unfolding zdiv_zmod_equality2[where k=0, unfolded monoid_add_class.add_0_right] ..
+    also have "\<dots> \<le> m" unfolding mod_div_equality ..
     finally have "real (Float (m div ?p) (e + ?d)) \<le> real (Float m e)" unfolding real_of_float_simp add_commute[of e]
       unfolding pow2_add mult_assoc[symmetric] real_of_int_le_iff[of _ m, symmetric]
       by (auto intro!: mult_mono simp add: pow2_add `0 < ?d` pow_d)
diff -r 6a4c479ba94f -r 9344891b504b src/HOL/Presburger.thy
--- a/src/HOL/Presburger.thy	Tue Mar 27 16:04:51 2012 +0200
+++ b/src/HOL/Presburger.thy	Tue Mar 27 19:21:05 2012 +0200
@@ -405,8 +405,8 @@
 declare mod_div_equality[presburger]
 declare mod_mult_self1[presburger]
 declare mod_mult_self2[presburger]
-declare zdiv_zmod_equality2[presburger]
-declare zdiv_zmod_equality[presburger]
+declare div_mod_equality[presburger]
+declare div_mod_equality2[presburger]
 declare mod2_Suc_Suc[presburger]
 lemma [presburger]: "(a::int) div 0 = 0" and [presburger]: "a mod 0 = a"
 by simp_all