src/HOL/Presburger.thy
 changeset 23477 f4b83f03cac9 parent 23472 02099ea56555 child 23685 1b0f4071946c
```     1.1 --- a/src/HOL/Presburger.thy	Fri Jun 22 22:41:17 2007 +0200
1.2 +++ b/src/HOL/Presburger.thy	Sat Jun 23 19:33:22 2007 +0200
1.3 @@ -60,7 +60,7 @@
1.4    "\<forall>x k. F = F"
1.5  by simp_all
1.6    (clarsimp simp add: dvd_def, rule iffI, clarsimp,rule_tac x = "kb - ka*k" in exI,
1.7 -    simp add: ring_eq_simps, clarsimp,rule_tac x = "kb + ka*k" in exI,simp add: ring_eq_simps)+
1.8 +    simp add: ring_simps, clarsimp,rule_tac x = "kb + ka*k" in exI,simp add: ring_simps)+
1.9
1.10  subsection{* The A and B sets *}
1.11  lemma bset:
1.12 @@ -98,7 +98,7 @@
1.13    {fix x assume nob: "\<forall>j\<in>{1 .. D}. \<forall>b\<in>B. x \<noteq> b + j" and g: "x > t" and ng: "\<not> (x - D) > t"
1.14      hence "x -t \<le> D" and "1 \<le> x - t" by simp+
1.15        hence "\<exists>j \<in> {1 .. D}. x - t = j" by auto
1.16 -      hence "\<exists>j \<in> {1 .. D}. x = t + j" by (simp add: ring_eq_simps)
1.17 +      hence "\<exists>j \<in> {1 .. D}. x = t + j" by (simp add: ring_simps)
1.18        with nob tB have "False" by simp}
1.19    thus "\<forall>x.(\<forall>j\<in>{1 .. D}. \<forall>b\<in>B. x \<noteq> b + j)\<longrightarrow> (x > t) \<longrightarrow> (x - D > t)" by blast
1.20  next
1.21 @@ -106,18 +106,18 @@
1.22    {fix x assume nob: "\<forall>j\<in>{1 .. D}. \<forall>b\<in>B. x \<noteq> b + j" and g: "x \<ge> t" and ng: "\<not> (x - D) \<ge> t"
1.23      hence "x - (t - 1) \<le> D" and "1 \<le> x - (t - 1)" by simp+
1.24        hence "\<exists>j \<in> {1 .. D}. x - (t - 1) = j" by auto
1.25 -      hence "\<exists>j \<in> {1 .. D}. x = (t - 1) + j" by (simp add: ring_eq_simps)
1.26 +      hence "\<exists>j \<in> {1 .. D}. x = (t - 1) + j" by (simp add: ring_simps)
1.27        with nob tB have "False" by simp}
1.28    thus "\<forall>x.(\<forall>j\<in>{1 .. D}. \<forall>b\<in>B. x \<noteq> b + j)\<longrightarrow> (x \<ge> t) \<longrightarrow> (x - D \<ge> t)" by blast
1.29  next
1.30    assume d: "d dvd D"
1.31    {fix x assume H: "d dvd x + t" with d have "d dvd (x - D) + t"
1.32 -      by (clarsimp simp add: dvd_def,rule_tac x= "ka - k" in exI,simp add: ring_eq_simps)}
1.33 +      by (clarsimp simp add: dvd_def,rule_tac x= "ka - k" in exI,simp add: ring_simps)}
1.34    thus "\<forall>(x::int).(\<forall>j\<in>{1 .. D}. \<forall>b\<in>B. x \<noteq> b + j)\<longrightarrow> (d dvd x+t) \<longrightarrow> (d dvd (x - D) + t)" by simp
1.35  next
1.36    assume d: "d dvd D"
1.37    {fix x assume H: "\<not>(d dvd x + t)" with d have "\<not>d dvd (x - D) + t"
1.38 -      by (clarsimp simp add: dvd_def,erule_tac x= "ka + k" in allE,simp add: ring_eq_simps)}
1.39 +      by (clarsimp simp add: dvd_def,erule_tac x= "ka + k" in allE,simp add: ring_simps)}
1.40    thus "\<forall>(x::int).(\<forall>j\<in>{1 .. D}. \<forall>b\<in>B. x \<noteq> b + j)\<longrightarrow> (\<not>d dvd x+t) \<longrightarrow> (\<not>d dvd (x - D) + t)" by auto
1.41  qed blast
1.42
1.43 @@ -156,26 +156,26 @@
1.44    {fix x assume nob: "\<forall>j\<in>{1 .. D}. \<forall>b\<in>A. x \<noteq> b - j" and g: "x < t" and ng: "\<not> (x + D) < t"
1.45      hence "t - x \<le> D" and "1 \<le> t - x" by simp+
1.46        hence "\<exists>j \<in> {1 .. D}. t - x = j" by auto
1.47 -      hence "\<exists>j \<in> {1 .. D}. x = t - j" by (auto simp add: ring_eq_simps)
1.48 +      hence "\<exists>j \<in> {1 .. D}. x = t - j" by (auto simp add: ring_simps)
1.49        with nob tA have "False" by simp}
1.50    thus "\<forall>x.(\<forall>j\<in>{1 .. D}. \<forall>b\<in>A. x \<noteq> b - j)\<longrightarrow> (x < t) \<longrightarrow> (x + D < t)" by blast
1.51  next
1.52    assume dp: "D > 0" and tA:"t + 1\<in> A"
1.53    {fix x assume nob: "\<forall>j\<in>{1 .. D}. \<forall>b\<in>A. x \<noteq> b - j" and g: "x \<le> t" and ng: "\<not> (x + D) \<le> t"
1.54 -    hence "(t + 1) - x \<le> D" and "1 \<le> (t + 1) - x" by (simp_all add: ring_eq_simps)
1.55 +    hence "(t + 1) - x \<le> D" and "1 \<le> (t + 1) - x" by (simp_all add: ring_simps)
1.56        hence "\<exists>j \<in> {1 .. D}. (t + 1) - x = j" by auto
1.57 -      hence "\<exists>j \<in> {1 .. D}. x = (t + 1) - j" by (auto simp add: ring_eq_simps)
1.58 +      hence "\<exists>j \<in> {1 .. D}. x = (t + 1) - j" by (auto simp add: ring_simps)
1.59        with nob tA have "False" by simp}
1.60    thus "\<forall>x.(\<forall>j\<in>{1 .. D}. \<forall>b\<in>A. x \<noteq> b - j)\<longrightarrow> (x \<le> t) \<longrightarrow> (x + D \<le> t)" by blast
1.61  next
1.62    assume d: "d dvd D"
1.63    {fix x assume H: "d dvd x + t" with d have "d dvd (x + D) + t"
1.64 -      by (clarsimp simp add: dvd_def,rule_tac x= "ka + k" in exI,simp add: ring_eq_simps)}
1.65 +      by (clarsimp simp add: dvd_def,rule_tac x= "ka + k" in exI,simp add: ring_simps)}
1.66    thus "\<forall>(x::int).(\<forall>j\<in>{1 .. D}. \<forall>b\<in>A. x \<noteq> b - j)\<longrightarrow> (d dvd x+t) \<longrightarrow> (d dvd (x + D) + t)" by simp
1.67  next
1.68    assume d: "d dvd D"
1.69    {fix x assume H: "\<not>(d dvd x + t)" with d have "\<not>d dvd (x + D) + t"
1.70 -      by (clarsimp simp add: dvd_def,erule_tac x= "ka - k" in allE,simp add: ring_eq_simps)}
1.71 +      by (clarsimp simp add: dvd_def,erule_tac x= "ka - k" in allE,simp add: ring_simps)}
1.72    thus "\<forall>(x::int).(\<forall>j\<in>{1 .. D}. \<forall>b\<in>A. x \<noteq> b - j)\<longrightarrow> (\<not>d dvd x+t) \<longrightarrow> (\<not>d dvd (x + D) + t)" by auto
1.73  qed blast
1.74
1.75 @@ -302,7 +302,7 @@
1.76    from ePeqP1 obtain z where P1eqP: "\<forall>x>z. P x = P' x" ..
1.77    let ?w' = "x + (abs(x-z)+1) * d"
1.78    let ?w = "x - (-(abs(x-z) + 1))*d"
1.79 -  have ww'[simp]: "?w = ?w'" by (simp add: ring_eq_simps)
1.80 +  have ww'[simp]: "?w = ?w'" by (simp add: ring_simps)
1.81    from dpos have w: "?w > z" by(simp only: ww' incr_lemma)
1.82    hence "P' x = P' ?w" using P1eqP1 by blast
1.83    also have "\<dots> = P(?w)" using w P1eqP by blast
```