antisymmetry not a default intro rule any longer
authorhaftmann
Fri Oct 19 19:45:29 2007 +0200 (2007-10-19)
changeset 25102db3e412c4cb1
parent 25101 cae0f68b693b
child 25103 1ee419a5a30f
antisymmetry not a default intro rule any longer
src/HOL/Lattices.thy
src/HOL/OrderedGroup.thy
     1.1 --- a/src/HOL/Lattices.thy	Fri Oct 19 16:20:27 2007 +0200
     1.2 +++ b/src/HOL/Lattices.thy	Fri Oct 19 19:45:29 2007 +0200
     1.3 @@ -30,9 +30,6 @@
     1.4  context lower_semilattice
     1.5  begin
     1.6  
     1.7 -lemmas antisym_intro [intro!] = antisym
     1.8 -lemmas (in -) [rule del] = antisym_intro
     1.9 -
    1.10  lemma le_infI1[intro]:
    1.11    assumes "a \<sqsubseteq> x"
    1.12    shows "a \<sqinter> b \<sqsubseteq> x"
    1.13 @@ -58,11 +55,11 @@
    1.14  lemmas (in -) [rule del] = le_infE
    1.15  
    1.16  lemma le_inf_iff [simp]:
    1.17 - "x \<sqsubseteq> y \<sqinter> z = (x \<sqsubseteq> y \<and> x \<sqsubseteq> z)"
    1.18 +  "x \<sqsubseteq> y \<sqinter> z = (x \<sqsubseteq> y \<and> x \<sqsubseteq> z)"
    1.19  by blast
    1.20  
    1.21  lemma le_iff_inf: "(x \<sqsubseteq> y) = (x \<sqinter> y = x)"
    1.22 -by(blast dest:eq_iff[THEN iffD1])
    1.23 +  by (blast intro: antisym dest: eq_iff [THEN iffD1])
    1.24  
    1.25  end
    1.26  
    1.27 @@ -73,9 +70,6 @@
    1.28  context upper_semilattice
    1.29  begin
    1.30  
    1.31 -lemmas antisym_intro [intro!] = antisym
    1.32 -lemmas (in -) [rule del] = antisym_intro
    1.33 -
    1.34  lemma le_supI1[intro]: "x \<sqsubseteq> a \<Longrightarrow> x \<sqsubseteq> a \<squnion> b"
    1.35    by (rule order_trans) auto
    1.36  lemmas (in -) [rule del] = le_supI1
    1.37 @@ -92,13 +86,12 @@
    1.38    by (blast intro: order_trans)
    1.39  lemmas (in -) [rule del] = le_supE
    1.40  
    1.41 -
    1.42  lemma ge_sup_conv[simp]:
    1.43 - "x \<squnion> y \<sqsubseteq> z = (x \<sqsubseteq> z \<and> y \<sqsubseteq> z)"
    1.44 +  "x \<squnion> y \<sqsubseteq> z = (x \<sqsubseteq> z \<and> y \<sqsubseteq> z)"
    1.45  by blast
    1.46  
    1.47  lemma le_iff_sup: "(x \<sqsubseteq> y) = (x \<squnion> y = y)"
    1.48 -by(blast dest:eq_iff[THEN iffD1])
    1.49 +  by (blast intro: antisym dest: eq_iff [THEN iffD1])
    1.50  
    1.51  end
    1.52  
    1.53 @@ -113,25 +106,25 @@
    1.54  begin
    1.55  
    1.56  lemma inf_commute: "(x \<sqinter> y) = (y \<sqinter> x)"
    1.57 -by blast
    1.58 +  by (blast intro: antisym)
    1.59  
    1.60  lemma inf_assoc: "(x \<sqinter> y) \<sqinter> z = x \<sqinter> (y \<sqinter> z)"
    1.61 -by blast
    1.62 +  by (blast intro: antisym)
    1.63  
    1.64  lemma inf_idem[simp]: "x \<sqinter> x = x"
    1.65 -by blast
    1.66 +  by (blast intro: antisym)
    1.67  
    1.68  lemma inf_left_idem[simp]: "x \<sqinter> (x \<sqinter> y) = x \<sqinter> y"
    1.69 -by blast
    1.70 +  by (blast intro: antisym)
    1.71  
    1.72  lemma inf_absorb1: "x \<sqsubseteq> y \<Longrightarrow> x \<sqinter> y = x"
    1.73 -by blast
    1.74 +  by (blast intro: antisym)
    1.75  
    1.76  lemma inf_absorb2: "y \<sqsubseteq> x \<Longrightarrow> x \<sqinter> y = y"
    1.77 -by blast
    1.78 +  by (blast intro: antisym)
    1.79  
    1.80  lemma inf_left_commute: "x \<sqinter> (y \<sqinter> z) = y \<sqinter> (x \<sqinter> z)"
    1.81 -by blast
    1.82 +  by (blast intro: antisym)
    1.83  
    1.84  lemmas inf_ACI = inf_commute inf_assoc inf_left_commute inf_left_idem
    1.85  
    1.86 @@ -142,25 +135,25 @@
    1.87  begin
    1.88  
    1.89  lemma sup_commute: "(x \<squnion> y) = (y \<squnion> x)"
    1.90 -by blast
    1.91 +  by (blast intro: antisym)
    1.92  
    1.93  lemma sup_assoc: "(x \<squnion> y) \<squnion> z = x \<squnion> (y \<squnion> z)"
    1.94 -by blast
    1.95 +  by (blast intro: antisym)
    1.96  
    1.97  lemma sup_idem[simp]: "x \<squnion> x = x"
    1.98 -by blast
    1.99 +  by (blast intro: antisym)
   1.100  
   1.101  lemma sup_left_idem[simp]: "x \<squnion> (x \<squnion> y) = x \<squnion> y"
   1.102 -by blast
   1.103 +  by (blast intro: antisym)
   1.104  
   1.105  lemma sup_absorb1: "y \<sqsubseteq> x \<Longrightarrow> x \<squnion> y = x"
   1.106 -by blast
   1.107 +  by (blast intro: antisym)
   1.108  
   1.109  lemma sup_absorb2: "x \<sqsubseteq> y \<Longrightarrow> x \<squnion> y = y"
   1.110 -by blast
   1.111 +  by (blast intro: antisym)
   1.112  
   1.113  lemma sup_left_commute: "x \<squnion> (y \<squnion> z) = y \<squnion> (x \<squnion> z)"
   1.114 -by blast
   1.115 +  by (blast intro: antisym)
   1.116  
   1.117  lemmas sup_ACI = sup_commute sup_assoc sup_left_commute sup_left_idem
   1.118  
   1.119 @@ -170,10 +163,10 @@
   1.120  begin
   1.121  
   1.122  lemma inf_sup_absorb: "x \<sqinter> (x \<squnion> y) = x"
   1.123 -by(blast intro: antisym inf_le1 inf_greatest sup_ge1)
   1.124 +  by (blast intro: antisym inf_le1 inf_greatest sup_ge1)
   1.125  
   1.126  lemma sup_inf_absorb: "x \<squnion> (x \<sqinter> y) = x"
   1.127 -by(blast intro: antisym sup_ge1 sup_least inf_le1)
   1.128 +  by (blast intro: antisym sup_ge1 sup_least inf_le1)
   1.129  
   1.130  lemmas ACI = inf_ACI sup_ACI
   1.131  
   1.132 @@ -182,10 +175,10 @@
   1.133  text{* Towards distributivity *}
   1.134  
   1.135  lemma distrib_sup_le: "x \<squnion> (y \<sqinter> z) \<sqsubseteq> (x \<squnion> y) \<sqinter> (x \<squnion> z)"
   1.136 -by blast
   1.137 +  by blast
   1.138  
   1.139  lemma distrib_inf_le: "(x \<sqinter> y) \<squnion> (x \<sqinter> z) \<sqsubseteq> x \<sqinter> (y \<squnion> z)"
   1.140 -by blast
   1.141 +  by blast
   1.142  
   1.143  
   1.144  text{* If you have one of them, you have them all. *}
   1.145 @@ -293,10 +286,10 @@
   1.146    by (rule distrib_lattice_min_max)
   1.147  
   1.148  lemma inf_min: "inf = (min \<Colon> 'a\<Colon>{lower_semilattice, linorder} \<Rightarrow> 'a \<Rightarrow> 'a)"
   1.149 -  by (rule ext)+ auto
   1.150 +  by (rule ext)+ (auto intro: antisym)
   1.151  
   1.152  lemma sup_max: "sup = (max \<Colon> 'a\<Colon>{upper_semilattice, linorder} \<Rightarrow> 'a \<Rightarrow> 'a)"
   1.153 -  by (rule ext)+ auto
   1.154 +  by (rule ext)+ (auto intro: antisym)
   1.155  
   1.156  lemmas le_maxI1 = min_max.sup_ge1
   1.157  lemmas le_maxI2 = min_max.sup_ge2
   1.158 @@ -313,7 +306,7 @@
   1.159    undesirable.
   1.160  *}
   1.161  
   1.162 -lemmas [rule del] = min_max.antisym_intro min_max.le_infI min_max.le_supI
   1.163 +lemmas [rule del] = min_max.le_infI min_max.le_supI
   1.164    min_max.le_supE min_max.le_infE min_max.le_supI1 min_max.le_supI2
   1.165    min_max.le_infI1 min_max.le_infI2
   1.166  
   1.167 @@ -330,10 +323,10 @@
   1.168  begin
   1.169  
   1.170  lemma Inf_Sup: "\<Sqinter>A = \<Squnion>{b. \<forall>a \<in> A. b \<le> a}"
   1.171 -  by (auto intro: Inf_lower Inf_greatest Sup_upper Sup_least)
   1.172 +  by (auto intro: antisym Inf_lower Inf_greatest Sup_upper Sup_least)
   1.173  
   1.174  lemma Sup_Inf:  "\<Squnion>A = \<Sqinter>{b. \<forall>a \<in> A. a \<le> b}"
   1.175 -  by (auto intro: Inf_lower Inf_greatest Sup_upper Sup_least)
   1.176 +  by (auto intro: antisym Inf_lower Inf_greatest Sup_upper Sup_least)
   1.177  
   1.178  lemma Inf_Univ: "\<Sqinter>UNIV = \<Squnion>{}"
   1.179    unfolding Sup_Inf by auto
   1.180 @@ -453,6 +446,9 @@
   1.181  end
   1.182  *}
   1.183  
   1.184 +context complete_lattice
   1.185 +begin
   1.186 +
   1.187  lemma le_SUPI: "i : A \<Longrightarrow> M i \<le> (SUP i:A. M i)"
   1.188    by (auto simp add: SUPR_def intro: Sup_upper)
   1.189  
   1.190 @@ -466,10 +462,12 @@
   1.191    by (auto simp add: INFI_def intro: Inf_greatest)
   1.192  
   1.193  lemma SUP_const[simp]: "A \<noteq> {} \<Longrightarrow> (SUP i:A. M) = M"
   1.194 -  by (auto intro: order_antisym SUP_leI le_SUPI)
   1.195 +  by (auto intro: antisym SUP_leI le_SUPI)
   1.196  
   1.197  lemma INF_const[simp]: "A \<noteq> {} \<Longrightarrow> (INF i:A. M) = M"
   1.198 -  by (auto intro: order_antisym INF_leI le_INFI)
   1.199 +  by (auto intro: antisym INF_leI le_INFI)
   1.200 +
   1.201 +end
   1.202  
   1.203  
   1.204  subsection {* Bool as lattice *}
     2.1 --- a/src/HOL/OrderedGroup.thy	Fri Oct 19 16:20:27 2007 +0200
     2.2 +++ b/src/HOL/OrderedGroup.thy	Fri Oct 19 19:45:29 2007 +0200
     2.3 @@ -879,7 +879,7 @@
     2.4    then have "a + a + - a = - a" by simp
     2.5    then have "a + (a + - a) = - a" by (simp only: add_assoc)
     2.6    then have a: "- a = a" by simp (*FIXME tune proof*)
     2.7 -  show "a = 0" apply rule
     2.8 +  show "a = 0" apply (rule antisym)
     2.9    apply (unfold neg_le_iff_le [symmetric, of a])
    2.10    unfolding a apply simp
    2.11    unfolding zero_le_double_add_iff_zero_le_single_add [symmetric, of a]