# HG changeset patch
# User haftmann
# Date 1408624868 -7200
# Node ID 464c1815fde9623ba343510d4257320066c0188e
# Parent  6594e73ec1a4fac1fc1ea28aa0e1837c3d71b5ab
integrated appendix theory into main theory;
tuned ML

diff -r 6594e73ec1a4 -r 464c1815fde9 src/ZF/Bin.thy
--- a/src/ZF/Bin.thy	Thu Aug 21 14:41:05 2014 +0200
+++ b/src/ZF/Bin.thy	Thu Aug 21 14:41:08 2014 +0200
@@ -594,4 +594,92 @@
      "(integ_of(w) = x $* y) \<longleftrightarrow> (x $* y = integ_of(w))"
 by auto
 
+(** To simplify inequalities involving integer negation and literals,
+    such as -x = #3
+**)
+
+lemmas [simp] =
+  zminus_equation [where y = "integ_of(w)"]
+  equation_zminus [where x = "integ_of(w)"]
+  for w
+
+lemmas [iff] =
+  zminus_zless [where y = "integ_of(w)"]
+  zless_zminus [where x = "integ_of(w)"]
+  for w
+
+lemmas [iff] =
+  zminus_zle [where y = "integ_of(w)"]
+  zle_zminus [where x = "integ_of(w)"]
+  for w
+
+lemmas [simp] =
+  Let_def [where s = "integ_of(w)"] for w
+
+
+(*** Simprocs for numeric literals ***)
+
+(** Combining of literal coefficients in sums of products **)
+
+lemma zless_iff_zdiff_zless_0: "(x $< y) \<longleftrightarrow> (x$-y $< #0)"
+  by (simp add: zcompare_rls)
+
+lemma eq_iff_zdiff_eq_0: "[| x \<in> int; y \<in> int |] ==> (x = y) \<longleftrightarrow> (x$-y = #0)"
+  by (simp add: zcompare_rls)
+
+lemma zle_iff_zdiff_zle_0: "(x $<= y) \<longleftrightarrow> (x$-y $<= #0)"
+  by (simp add: zcompare_rls)
+
+
+(** For combine_numerals **)
+
+lemma left_zadd_zmult_distrib: "i$*u $+ (j$*u $+ k) = (i$+j)$*u $+ k"
+  by (simp add: zadd_zmult_distrib zadd_ac)
+
+
+(** For cancel_numerals **)
+
+lemmas rel_iff_rel_0_rls =
+  zless_iff_zdiff_zless_0 [where y = "u $+ v"]
+  eq_iff_zdiff_eq_0 [where y = "u $+ v"]
+  zle_iff_zdiff_zle_0 [where y = "u $+ v"]
+  zless_iff_zdiff_zless_0 [where y = n]
+  eq_iff_zdiff_eq_0 [where y = n]
+  zle_iff_zdiff_zle_0 [where y = n]
+  for u v (* FIXME n (!?) *)
+
+lemma eq_add_iff1: "(i$*u $+ m = j$*u $+ n) \<longleftrightarrow> ((i$-j)$*u $+ m = intify(n))"
+  apply (simp add: zdiff_def zadd_zmult_distrib)
+  apply (simp add: zcompare_rls)
+  apply (simp add: zadd_ac)
+  done
+
+lemma eq_add_iff2: "(i$*u $+ m = j$*u $+ n) \<longleftrightarrow> (intify(m) = (j$-i)$*u $+ n)"
+  apply (simp add: zdiff_def zadd_zmult_distrib)
+  apply (simp add: zcompare_rls)
+  apply (simp add: zadd_ac)
+  done
+
+lemma less_add_iff1: "(i$*u $+ m $< j$*u $+ n) \<longleftrightarrow> ((i$-j)$*u $+ m $< n)"
+  apply (simp add: zdiff_def zadd_zmult_distrib zadd_ac rel_iff_rel_0_rls)
+  done
+
+lemma less_add_iff2: "(i$*u $+ m $< j$*u $+ n) \<longleftrightarrow> (m $< (j$-i)$*u $+ n)"
+  apply (simp add: zdiff_def zadd_zmult_distrib zadd_ac rel_iff_rel_0_rls)
+  done
+
+lemma le_add_iff1: "(i$*u $+ m $<= j$*u $+ n) \<longleftrightarrow> ((i$-j)$*u $+ m $<= n)"
+  apply (simp add: zdiff_def zadd_zmult_distrib)
+  apply (simp add: zcompare_rls)
+  apply (simp add: zadd_ac)
+  done
+
+lemma le_add_iff2: "(i$*u $+ m $<= j$*u $+ n) \<longleftrightarrow> (m $<= (j$-i)$*u $+ n)"
+  apply (simp add: zdiff_def zadd_zmult_distrib)
+  apply (simp add: zcompare_rls)
+  apply (simp add: zadd_ac)
+  done
+
+ML_file "int_arith.ML"
+
 end
diff -r 6594e73ec1a4 -r 464c1815fde9 src/ZF/IntArith.thy
--- a/src/ZF/IntArith.thy	Thu Aug 21 14:41:05 2014 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,94 +0,0 @@
-
-theory IntArith imports Bin
-begin
-
-
-(** To simplify inequalities involving integer negation and literals,
-    such as -x = #3
-**)
-
-lemmas [simp] =
-  zminus_equation [where y = "integ_of(w)"]
-  equation_zminus [where x = "integ_of(w)"]
-  for w
-
-lemmas [iff] =
-  zminus_zless [where y = "integ_of(w)"]
-  zless_zminus [where x = "integ_of(w)"]
-  for w
-
-lemmas [iff] =
-  zminus_zle [where y = "integ_of(w)"]
-  zle_zminus [where x = "integ_of(w)"]
-  for w
-
-lemmas [simp] =
-  Let_def [where s = "integ_of(w)"] for w
-
-
-(*** Simprocs for numeric literals ***)
-
-(** Combining of literal coefficients in sums of products **)
-
-lemma zless_iff_zdiff_zless_0: "(x $< y) \<longleftrightarrow> (x$-y $< #0)"
-  by (simp add: zcompare_rls)
-
-lemma eq_iff_zdiff_eq_0: "[| x \<in> int; y \<in> int |] ==> (x = y) \<longleftrightarrow> (x$-y = #0)"
-  by (simp add: zcompare_rls)
-
-lemma zle_iff_zdiff_zle_0: "(x $<= y) \<longleftrightarrow> (x$-y $<= #0)"
-  by (simp add: zcompare_rls)
-
-
-(** For combine_numerals **)
-
-lemma left_zadd_zmult_distrib: "i$*u $+ (j$*u $+ k) = (i$+j)$*u $+ k"
-  by (simp add: zadd_zmult_distrib zadd_ac)
-
-
-(** For cancel_numerals **)
-
-lemmas rel_iff_rel_0_rls =
-  zless_iff_zdiff_zless_0 [where y = "u $+ v"]
-  eq_iff_zdiff_eq_0 [where y = "u $+ v"]
-  zle_iff_zdiff_zle_0 [where y = "u $+ v"]
-  zless_iff_zdiff_zless_0 [where y = n]
-  eq_iff_zdiff_eq_0 [where y = n]
-  zle_iff_zdiff_zle_0 [where y = n]
-  for u v (* FIXME n (!?) *)
-
-lemma eq_add_iff1: "(i$*u $+ m = j$*u $+ n) \<longleftrightarrow> ((i$-j)$*u $+ m = intify(n))"
-  apply (simp add: zdiff_def zadd_zmult_distrib)
-  apply (simp add: zcompare_rls)
-  apply (simp add: zadd_ac)
-  done
-
-lemma eq_add_iff2: "(i$*u $+ m = j$*u $+ n) \<longleftrightarrow> (intify(m) = (j$-i)$*u $+ n)"
-  apply (simp add: zdiff_def zadd_zmult_distrib)
-  apply (simp add: zcompare_rls)
-  apply (simp add: zadd_ac)
-  done
-
-lemma less_add_iff1: "(i$*u $+ m $< j$*u $+ n) \<longleftrightarrow> ((i$-j)$*u $+ m $< n)"
-  apply (simp add: zdiff_def zadd_zmult_distrib zadd_ac rel_iff_rel_0_rls)
-  done
-
-lemma less_add_iff2: "(i$*u $+ m $< j$*u $+ n) \<longleftrightarrow> (m $< (j$-i)$*u $+ n)"
-  apply (simp add: zdiff_def zadd_zmult_distrib zadd_ac rel_iff_rel_0_rls)
-  done
-
-lemma le_add_iff1: "(i$*u $+ m $<= j$*u $+ n) \<longleftrightarrow> ((i$-j)$*u $+ m $<= n)"
-  apply (simp add: zdiff_def zadd_zmult_distrib)
-  apply (simp add: zcompare_rls)
-  apply (simp add: zadd_ac)
-  done
-
-lemma le_add_iff2: "(i$*u $+ m $<= j$*u $+ n) \<longleftrightarrow> (m $<= (j$-i)$*u $+ n)"
-  apply (simp add: zdiff_def zadd_zmult_distrib)
-  apply (simp add: zcompare_rls)
-  apply (simp add: zadd_ac)
-  done
-
-ML_file "int_arith.ML"
-
-end
diff -r 6594e73ec1a4 -r 464c1815fde9 src/ZF/IntDiv_ZF.thy
--- a/src/ZF/IntDiv_ZF.thy	Thu Aug 21 14:41:05 2014 +0200
+++ b/src/ZF/IntDiv_ZF.thy	Thu Aug 21 14:41:08 2014 +0200
@@ -29,7 +29,9 @@
 
 header{*The Division Operators Div and Mod*}
 
-theory IntDiv_ZF imports IntArith OrderArith begin
+theory IntDiv_ZF
+imports Bin OrderArith
+begin
 
 definition
   quorem :: "[i,i] => o"  where
diff -r 6594e73ec1a4 -r 464c1815fde9 src/ZF/int_arith.ML
--- a/src/ZF/int_arith.ML	Thu Aug 21 14:41:05 2014 +0200
+++ b/src/ZF/int_arith.ML	Thu Aug 21 14:41:08 2014 +0200
@@ -151,7 +151,7 @@
 
 structure CancelNumeralsCommon =
   struct
-  val mk_sum            = (fn T:typ => mk_sum)
+  val mk_sum            = (fn _ : typ => mk_sum)
   val dest_sum          = dest_sum
   val mk_coeff          = mk_coeff
   val dest_coeff        = dest_coeff 1
@@ -236,7 +236,7 @@
   type coeff            = int
   val iszero            = (fn x => x = 0)
   val add               = op + 
-  val mk_sum            = (fn T:typ => long_mk_sum) (*to work for #2*x $+ #3*x *)
+  val mk_sum            = (fn _ : typ => long_mk_sum) (*to work for #2*x $+ #3*x *)
   val dest_sum          = dest_sum
   val mk_coeff          = mk_coeff
   val dest_coeff        = dest_coeff 1
@@ -284,7 +284,7 @@
   type coeff            = int
   val iszero            = (fn x => x = 0)
   val add               = op *
-  val mk_sum            = (fn T:typ => mk_prod)
+  val mk_sum            = (fn _ : typ => mk_prod)
   val dest_sum          = dest_prod
   fun mk_coeff(k,t) = if t=one then mk_numeral k
                       else raise TERM("mk_coeff", [])