# HG changeset patch
# User nipkow
# Date 1116839201 -7200
# Node ID 5a8736668cedf3d67bcb4aa47993debbfd7add1e
# Parent  6e7616eba0b8be4e032ff20966df5e9bce76a09e
simplifier trace info; Suc-intervals

diff -r 6e7616eba0b8 -r 5a8736668ced src/HOL/Matrix/SparseMatrix.thy
--- a/src/HOL/Matrix/SparseMatrix.thy	Mon May 23 10:49:25 2005 +0200
+++ b/src/HOL/Matrix/SparseMatrix.thy	Mon May 23 11:06:41 2005 +0200
@@ -595,7 +595,7 @@
   disj_matrices :: "('a::zero) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool"
   "disj_matrices A B == (! j i. (Rep_matrix A j i \<noteq> 0) \<longrightarrow> (Rep_matrix B j i = 0)) & (! j i. (Rep_matrix B j i \<noteq> 0) \<longrightarrow> (Rep_matrix A j i = 0))"  
 
-ML {* simp_depth_limit := 2 *}
+ML {* simp_depth_limit := 6 *}
 
 lemma disj_matrices_contr1: "disj_matrices A B \<Longrightarrow> Rep_matrix A j i \<noteq> 0 \<Longrightarrow> Rep_matrix B j i = 0"
    by (simp add: disj_matrices_def)
diff -r 6e7616eba0b8 -r 5a8736668ced src/HOL/SetInterval.thy
--- a/src/HOL/SetInterval.thy	Mon May 23 10:49:25 2005 +0200
+++ b/src/HOL/SetInterval.thy	Mon May 23 11:06:41 2005 +0200
@@ -266,10 +266,10 @@
   of @{term atLeastLessThan}*}
 lemma atLeast0LessThan: "{0::nat..<n} = {..<n}"
 by(simp add:lessThan_def atLeastLessThan_def)
-
+(*
 lemma atLeastLessThan0 [simp]: "{m..<0::nat} = {}"
 by (simp add: atLeastLessThan_def)
-
+*)
 subsubsection {* Intervals of nats with @{term Suc} *}
 
 text{*Not a simprule because the RHS is too messy.*}
@@ -279,13 +279,13 @@
 
 lemma atLeastLessThan_singleton [simp]: "{m..<Suc m} = {m}"
 by (auto simp add: atLeastLessThan_def)
-
+(*
 lemma atLeast_sum_LessThan [simp]: "{m + k..<k::nat} = {}"
 by (induct k, simp_all add: atLeastLessThanSuc)
 
 lemma atLeastSucLessThan [simp]: "{Suc n..<n} = {}"
 by (auto simp add: atLeastLessThan_def)
-
+*)
 lemma atLeastLessThanSuc_atLeastAtMost: "{l..<Suc u} = {l..u}"
   by (simp add: lessThan_Suc_atMost atLeastAtMost_def atLeastLessThan_def)
 
@@ -612,10 +612,11 @@
  setsum f {a..<b} = setsum g {c..<d}"
 by(rule setsum_cong, simp_all)
 
-(* FIXME delete
-lemma Summation_Suc[simp]: "(\<Sum>i < Suc n. b i) = b n + (\<Sum>i < n. b i)"
-by (simp add:lessThan_Suc)
-*)
+(* FIXME why are the following simp rules but the corresponding eqns
+on intervals are not? *)
+
+lemma setsum_lessThan_Suc[simp]: "(\<Sum>i < Suc n. f i) = (\<Sum>i < n. f i) + f n"
+by (simp add:lessThan_Suc add_ac)
 
 lemma setsum_cl_ivl_Suc[simp]:
   "setsum f {m..Suc n} = (if Suc n < m then 0 else setsum f {m..n} + f(Suc n))"
@@ -624,11 +625,11 @@
 lemma setsum_op_ivl_Suc[simp]:
   "setsum f {m..<Suc n} = (if n < m then 0 else setsum f {m..<n} + f(n))"
 by (auto simp:add_ac atLeastLessThanSuc)
-
+(*
 lemma setsum_cl_ivl_add_one_nat: "(n::nat) <= m + 1 ==>
     (\<Sum>i=n..m+1. f i) = (\<Sum>i=n..m. f i) + f(m + 1)"
 by (auto simp:add_ac atLeastAtMostSuc_conv)
-
+*)
 lemma setsum_add_nat_ivl: "\<lbrakk> m \<le> n; n \<le> p \<rbrakk> \<Longrightarrow>
   setsum f {m..<n} + setsum f {n..<p} = setsum f {m..<p::nat}"
 by (simp add:setsum_Un_disjoint[symmetric] ivl_disj_int ivl_disj_un)