rearranged sessions to save approx. 1min elapsed time, 5min CPU time;

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Multivariate_Analysis/ex/Approximations.thy	Fri Apr 03 21:25:55 2015 +0200
@@ -0,0 +1,38 @@
+section {* Binary Approximations to Constants *}
+
+theory Approximations
+imports "~~/src/HOL/Multivariate_Analysis/Complex_Transcendental"
+begin
+
+declare of_real_numeral [simp]
+
+subsection{*Approximation to pi*}
+
+lemma sin_pi6_straddle:
+  assumes "0 \<le> a" "a \<le> b" "b \<le> 4" "sin(a/6) \<le> 1/2" "1/2 \<le> sin(b/6)"
+    shows "a \<le> pi \<and> pi \<le> b"
+proof -
+  have *: "\<And>x::real. 0 < x & x < 7/5 \<Longrightarrow> 0 < sin x"
+    using pi_ge_two
+    by (auto intro: sin_gt_zero)
+  have ab: "(b \<le> pi * 3 \<Longrightarrow> pi \<le> b)" "(a \<le> pi * 3 \<Longrightarrow> a \<le> pi)"
+    using sin_mono_le_eq [of "pi/6" "b/6"] sin_mono_le_eq [of "a/6" "pi/6"] assms
+    by (simp_all add: sin_30 power.power_Suc norm_divide)
+  show ?thesis
+    using assms Taylor_sin [of "a/6" 0] pi_ge_two
+    by (auto simp: sin_30 power.power_Suc norm_divide intro: ab)
+qed
+
+(*32-bit approximation. SLOW simplification steps: big calculations with the rewriting engine*)
+lemma pi_approx_32: "abs(pi - 13493037705/4294967296) \<le> inverse(2 ^ 32)"
+  apply (simp only: abs_diff_le_iff)
+  apply (rule sin_pi6_straddle, simp_all)
+  using Taylor_sin [of "1686629713/3221225472" 11]
+  apply (simp add: in_Reals_norm sin_coeff_def Re_sin atMost_nat_numeral fact_numeral)
+  apply (simp only: pos_le_divide_eq [symmetric])
+  using Taylor_sin [of "6746518853/12884901888" 11]
+  apply (simp add: in_Reals_norm sin_coeff_def Re_sin atMost_nat_numeral fact_numeral)
+  apply (simp only: pos_le_divide_eq [symmetric] pos_divide_le_eq [symmetric])
+  done
+
+end

--- a/src/HOL/ROOT	Fri Apr 03 21:04:56 2015 +0200
+++ b/src/HOL/ROOT	Fri Apr 03 21:25:55 2015 +0200
@@ -527,7 +527,6 @@
     "~~/src/HOL/Library/Transitive_Closure_Table"
     Cartouche_Examples
   theories
-    Approximations
     Commands
     Adhoc_Overloading_Examples
     Iff_Oracle
@@ -693,6 +692,10 @@
   document_files
     "root.tex"
 
+session "HOL-Multivariate_Analysis-ex" in "Multivariate_Analysis/ex" = "HOL-Multivariate_Analysis" +
+  theories
+    Approximations
+
 session "HOL-Probability" in "Probability" = "HOL-Multivariate_Analysis" +
   theories [document = false]
     "~~/src/HOL/Library/Countable"

--- a/src/HOL/ex/Approximations.thy	Fri Apr 03 21:04:56 2015 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,39 +0,0 @@
-section {* Binary Approximations to Constants *}
-
-theory Approximations
-imports "~~/src/HOL/Multivariate_Analysis/Complex_Transcendental"
-
-begin
-
-declare of_real_numeral [simp]
-
-subsection{*Approximation to pi*}
-
-lemma sin_pi6_straddle:
-  assumes "0 \<le> a" "a \<le> b" "b \<le> 4" "sin(a/6) \<le> 1/2" "1/2 \<le> sin(b/6)"
-    shows "a \<le> pi \<and> pi \<le> b"
-proof -
-  have *: "\<And>x::real. 0 < x & x < 7/5 \<Longrightarrow> 0 < sin x"
-    using pi_ge_two
-    by (auto intro: sin_gt_zero)
-  have ab: "(b \<le> pi * 3 \<Longrightarrow> pi \<le> b)" "(a \<le> pi * 3 \<Longrightarrow> a \<le> pi)"
-    using sin_mono_le_eq [of "pi/6" "b/6"] sin_mono_le_eq [of "a/6" "pi/6"] assms
-    by (simp_all add: sin_30 power.power_Suc norm_divide)
-  show ?thesis
-    using assms Taylor_sin [of "a/6" 0] pi_ge_two
-    by (auto simp: sin_30 power.power_Suc norm_divide intro: ab)
-qed
-
-(*32-bit approximation. SLOW simplification steps: big calculations with the rewriting engine*)
-lemma pi_approx_32: "abs(pi - 13493037705/4294967296) \<le> inverse(2 ^ 32)"
-  apply (simp only: abs_diff_le_iff)
-  apply (rule sin_pi6_straddle, simp_all)
-  using Taylor_sin [of "1686629713/3221225472" 11]
-  apply (simp add: in_Reals_norm sin_coeff_def Re_sin atMost_nat_numeral fact_numeral)
-  apply (simp only: pos_le_divide_eq [symmetric])
-  using Taylor_sin [of "6746518853/12884901888" 11]
-  apply (simp add: in_Reals_norm sin_coeff_def Re_sin atMost_nat_numeral fact_numeral)
-  apply (simp only: pos_le_divide_eq [symmetric] pos_divide_le_eq [symmetric])
-  done
-
-end