src/HOL/Bali/Basis.thy
author wenzelm
Mon, 25 Feb 2002 20:48:14 +0100
changeset 12937 0c4fd7529467
parent 12925 99131847fb93
child 13462 56610e2ba220
permissions -rw-r--r--
clarified syntax of ``long'' statements: fixes/assumes/shows;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
12857
a4386cc9b1c3 tuned header;
wenzelm
parents: 12854
diff changeset
     1
(*  Title:      HOL/Bali/Basis.thy
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     2
    ID:         $Id$
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     3
    Author:     David von Oheimb
12858
wenzelm
parents: 12857
diff changeset
     4
    License:    GPL (GNU GENERAL PUBLIC LICENSE)
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     5
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     6
*)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     7
header {* Definitions extending HOL as logical basis of Bali *}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     8
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
     9
theory Basis = Main:
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    10
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    11
ML_setup {*
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    12
Unify.search_bound := 40;
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    13
Unify.trace_bound  := 40;
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    14
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    15
(*print_depth 100;*)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    16
(*Syntax.ambiguity_level := 1;*)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    17
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    18
section "misc"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    19
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    20
declare same_fstI [intro!] (*### TO HOL/Wellfounded_Relations *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    21
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    22
(* ###TO HOL/???.ML?? *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    23
ML {*
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    24
fun make_simproc name pat pred thm = Simplifier.mk_simproc name
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    25
   [Thm.read_cterm (Thm.sign_of_thm thm) (pat, HOLogic.typeT)] 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    26
   (K (K (fn s => if pred s then None else Some (standard (mk_meta_eq thm)))))
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    27
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    28
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    29
declare split_if_asm  [split] option.split [split] option.split_asm [split]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    30
ML {*
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    31
simpset_ref() := simpset() addloop ("split_all_tac", split_all_tac)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    32
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    33
declare if_weak_cong [cong del] option.weak_case_cong [cong del]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    34
declare length_Suc_conv [iff];
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    35
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    36
(*###to be phased out *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    37
ML {*
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    38
bind_thm ("make_imp", rearrange_prems [1,0] mp)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    39
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    40
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    41
lemma Collect_split_eq: "{p. P (split f p)} = {(a,b). P (f a b)}"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    42
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    43
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    44
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    45
lemma subset_insertD: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    46
  "A <= insert x B ==> A <= B & x ~: A | (EX B'. A = insert x B' & B' <= B)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    47
apply (case_tac "x:A")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    48
apply (rule disjI2)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    49
apply (rule_tac x = "A-{x}" in exI)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    50
apply fast+
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    51
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    52
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    53
syntax
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
    54
  "3" :: nat   ("3") 
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    55
  "4" :: nat   ("4")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    56
translations
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    57
 "3" == "Suc 2"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    58
 "4" == "Suc 3"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    59
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    60
(*unused*)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    61
lemma range_bool_domain: "range f = {f True, f False}"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    62
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    63
apply (case_tac "xa")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    64
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    65
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    66
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    67
(* context (theory "Transitive_Closure") *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    68
lemma irrefl_tranclI': "r^-1 Int r^+ = {} ==> !x. (x, x) ~: r^+"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    69
apply (rule allI)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    70
apply (erule irrefl_tranclI)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    71
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    72
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    73
lemma trancl_rtrancl_trancl:
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    74
"\<lbrakk>(x,y)\<in>r^+; (y,z)\<in>r^*\<rbrakk> \<Longrightarrow> (x,z)\<in>r^+"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    75
by (auto dest: tranclD rtrancl_trans rtrancl_into_trancl2)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    76
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    77
lemma rtrancl_into_trancl3:
12925
99131847fb93 Added check for field/method access to operational semantics and proved the acesses valid.
schirmer
parents: 12919
diff changeset
    78
"\<lbrakk>(a,b)\<in>r^*; a\<noteq>b\<rbrakk> \<Longrightarrow> (a,b)\<in>r^+" 
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    79
apply (drule rtranclD)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    80
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    81
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    82
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    83
lemma rtrancl_into_rtrancl2: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    84
  "\<lbrakk> (a, b) \<in>  r; (b, c) \<in> r^* \<rbrakk> \<Longrightarrow> (a, c) \<in>  r^*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    85
by (auto intro: r_into_rtrancl rtrancl_trans)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    86
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    87
lemma triangle_lemma:
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    88
 "\<lbrakk> \<And> a b c. \<lbrakk>(a,b)\<in>r; (a,c)\<in>r\<rbrakk> \<Longrightarrow> b=c; (a,x)\<in>r\<^sup>*; (a,y)\<in>r\<^sup>*\<rbrakk> 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    89
 \<Longrightarrow> (x,y)\<in>r\<^sup>* \<or> (y,x)\<in>r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    90
proof -
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    91
  note converse_rtrancl_induct = converse_rtrancl_induct [consumes 1]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    92
  note converse_rtranclE = converse_rtranclE [consumes 1] 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    93
  assume unique: "\<And> a b c. \<lbrakk>(a,b)\<in>r; (a,c)\<in>r\<rbrakk> \<Longrightarrow> b=c"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    94
  assume "(a,x)\<in>r\<^sup>*" 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    95
  then show "(a,y)\<in>r\<^sup>* \<Longrightarrow> (x,y)\<in>r\<^sup>* \<or> (y,x)\<in>r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    96
  proof (induct rule: converse_rtrancl_induct)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    97
    assume "(x,y)\<in>r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    98
    then show ?thesis 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
    99
      by blast
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   100
  next
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   101
    fix a v
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   102
    assume a_v_r: "(a, v) \<in> r" and
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   103
          v_x_rt: "(v, x) \<in> r\<^sup>*" and
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   104
          a_y_rt: "(a, y) \<in> r\<^sup>*"  and
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   105
             hyp: "(v, y) \<in> r\<^sup>* \<Longrightarrow> (x, y) \<in> r\<^sup>* \<or> (y, x) \<in> r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   106
    from a_y_rt 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   107
    show "(x, y) \<in> r\<^sup>* \<or> (y, x) \<in> r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   108
    proof (cases rule: converse_rtranclE)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   109
      assume "a=y"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   110
      with a_v_r v_x_rt have "(y,x) \<in> r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   111
	by (auto intro: r_into_rtrancl rtrancl_trans)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   112
      then show ?thesis 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   113
	by blast
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   114
    next
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   115
      fix w 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   116
      assume a_w_r: "(a, w) \<in> r" and
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   117
            w_y_rt: "(w, y) \<in> r\<^sup>*"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   118
      from a_v_r a_w_r unique 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   119
      have "v=w" 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   120
	by auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   121
      with w_y_rt hyp 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   122
      show ?thesis
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   123
	by blast
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   124
    qed
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   125
  qed
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   126
qed
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   127
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   128
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   129
lemma rtrancl_cases [consumes 1, case_names Refl Trancl]:
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   130
 "\<lbrakk>(a,b)\<in>r\<^sup>*;  a = b \<Longrightarrow> P; (a,b)\<in>r\<^sup>+ \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   131
apply (erule rtranclE)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   132
apply (auto dest: rtrancl_into_trancl1)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   133
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   134
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   135
(* ### To Transitive_Closure *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   136
theorems converse_rtrancl_induct 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   137
 = converse_rtrancl_induct [consumes 1,case_names Id Step]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   138
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   139
theorems converse_trancl_induct 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   140
         = converse_trancl_induct [consumes 1,case_names Single Step]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   141
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   142
(* context (theory "Set") *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   143
lemma Ball_weaken:"\<lbrakk>Ball s P;\<And> x. P x\<longrightarrow>Q x\<rbrakk>\<Longrightarrow>Ball s Q"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   144
by auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   145
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   146
(* context (theory "Finite") *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   147
lemma finite_SetCompr2: "[| finite (Collect P); !y. P y --> finite (range (f y)) |] ==>  
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   148
  finite {f y x |x y. P y}"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   149
apply (subgoal_tac "{f y x |x y. P y} = UNION (Collect P) (%y. range (f y))")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   150
prefer 2 apply  fast
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   151
apply (erule ssubst)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   152
apply (erule finite_UN_I)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   153
apply fast
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   154
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   155
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   156
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   157
(* ### TO theory "List" *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   158
lemma list_all2_trans: "\<forall> a b c. P1 a b \<longrightarrow> P2 b c \<longrightarrow> P3 a c \<Longrightarrow>
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   159
 \<forall>xs2 xs3. list_all2 P1 xs1 xs2 \<longrightarrow> list_all2 P2 xs2 xs3 \<longrightarrow> list_all2 P3 xs1 xs3"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   160
apply (induct_tac "xs1")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   161
apply simp
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   162
apply (rule allI)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   163
apply (induct_tac "xs2")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   164
apply simp
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   165
apply (rule allI)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   166
apply (induct_tac "xs3")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   167
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   168
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   169
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   170
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   171
section "pairs"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   172
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   173
lemma surjective_pairing5: "p = (fst p, fst (snd p), fst (snd (snd p)), fst (snd (snd (snd p))), 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   174
  snd (snd (snd (snd p))))"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   175
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   176
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   177
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   178
lemma fst_splitE [elim!]: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   179
"[| fst s' = x';  !!x s. [| s' = (x,s);  x = x' |] ==> Q |] ==> Q"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   180
apply (cut_tac p = "s'" in surjective_pairing)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   181
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   182
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   183
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   184
lemma fst_in_set_lemma [rule_format (no_asm)]: "(x, y) : set l --> x : fst ` set l"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   185
apply (induct_tac "l")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   186
apply  auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   187
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   188
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   189
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   190
section "quantifiers"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   191
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   192
(*###to be phased out *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   193
ML {* 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   194
fun noAll_simpset () = simpset() setmksimps 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   195
	mksimps (filter (fn (x,_) => x<>"All") mksimps_pairs)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   196
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   197
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   198
lemma All_Ex_refl_eq2 [simp]: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   199
 "(!x. (? b. x = f b & Q b) \<longrightarrow> P x) = (!b. Q b --> P (f b))"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   200
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   201
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   202
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   203
lemma ex_ex_miniscope1 [simp]:
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   204
  "(EX w v. P w v & Q v) = (EX v. (EX w. P w v) & Q v)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   205
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   206
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   207
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   208
lemma ex_miniscope2 [simp]:
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   209
  "(EX v. P v & Q & R v) = (Q & (EX v. P v & R v))" 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   210
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   211
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   212
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   213
lemma ex_reorder31: "(\<exists>z x y. P x y z) = (\<exists>x y z. P x y z)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   214
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   215
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   216
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   217
lemma All_Ex_refl_eq1 [simp]: "(!x. (? b. x = f b) --> P x) = (!b. P (f b))"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   218
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   219
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   220
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   221
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   222
section "sums"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   223
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   224
hide const In0 In1
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   225
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   226
syntax
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   227
  fun_sum :: "('a => 'c) => ('b => 'c) => (('a+'b) => 'c)" (infixr "'(+')"80)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   228
translations
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   229
 "fun_sum" == "sum_case"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   230
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   231
consts    the_Inl  :: "'a + 'b \<Rightarrow> 'a"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   232
          the_Inr  :: "'a + 'b \<Rightarrow> 'b"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   233
primrec  "the_Inl (Inl a) = a"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   234
primrec  "the_Inr (Inr b) = b"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   235
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   236
datatype ('a, 'b, 'c) sum3 = In1 'a | In2 'b | In3 'c
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   237
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   238
consts    the_In1  :: "('a, 'b, 'c) sum3 \<Rightarrow> 'a"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   239
          the_In2  :: "('a, 'b, 'c) sum3 \<Rightarrow> 'b"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   240
          the_In3  :: "('a, 'b, 'c) sum3 \<Rightarrow> 'c"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   241
primrec  "the_In1 (In1 a) = a"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   242
primrec  "the_In2 (In2 b) = b"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   243
primrec  "the_In3 (In3 c) = c"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   244
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   245
syntax
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   246
	 In1l	:: "'al \<Rightarrow> ('al + 'ar, 'b, 'c) sum3"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   247
	 In1r	:: "'ar \<Rightarrow> ('al + 'ar, 'b, 'c) sum3"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   248
translations
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   249
	"In1l e" == "In1 (Inl e)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   250
	"In1r c" == "In1 (Inr c)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   251
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   252
ML {*
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   253
fun sum3_instantiate thm = map (fn s => simplify(simpset()delsimps[not_None_eq])
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   254
 (read_instantiate [("t","In"^s^" ?x")] thm)) ["1l","2","3","1r"]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   255
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   256
(* e.g. lemmas is_stmt_rews = is_stmt_def [of "In1l x", simplified] *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   257
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   258
translations
12919
d6a0d168291e removed theory Option;
wenzelm
parents: 12893
diff changeset
   259
  "option"<= (type) "Datatype.option"
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   260
  "list"  <= (type) "List.list"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   261
  "sum3"  <= (type) "Basis.sum3"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   262
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   263
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   264
section "quantifiers for option type"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   265
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   266
syntax
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   267
  Oall :: "[pttrn, 'a option, bool] => bool"   ("(3! _:_:/ _)" [0,0,10] 10)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   268
  Oex  :: "[pttrn, 'a option, bool] => bool"   ("(3? _:_:/ _)" [0,0,10] 10)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   269
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   270
syntax (symbols)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   271
  Oall :: "[pttrn, 'a option, bool] => bool"   ("(3\<forall>_\<in>_:/ _)"  [0,0,10] 10)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   272
  Oex  :: "[pttrn, 'a option, bool] => bool"   ("(3\<exists>_\<in>_:/ _)"  [0,0,10] 10)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   273
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   274
translations
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   275
  "! x:A: P"    == "! x:o2s A. P"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   276
  "? x:A: P"    == "? x:o2s A. P"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   277
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   278
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   279
section "unique association lists"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   280
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   281
constdefs
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   282
  unique   :: "('a \<times> 'b) list \<Rightarrow> bool"
12893
cbb4dc5e6478 replaced nodups by distinct;
wenzelm
parents: 12859
diff changeset
   283
 "unique \<equiv> distinct \<circ> map fst"
12854
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   284
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   285
lemma uniqueD [rule_format (no_asm)]: 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   286
"unique l--> (!x y. (x,y):set l --> (!x' y'. (x',y'):set l --> x=x'-->  y=y'))"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   287
apply (unfold unique_def o_def)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   288
apply (induct_tac "l")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   289
apply  (auto dest: fst_in_set_lemma)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   290
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   291
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   292
lemma unique_Nil [simp]: "unique []"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   293
apply (unfold unique_def)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   294
apply (simp (no_asm))
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   295
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   296
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   297
lemma unique_Cons [simp]: "unique ((x,y)#l) = (unique l & (!y. (x,y) ~: set l))"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   298
apply (unfold unique_def)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   299
apply  (auto dest: fst_in_set_lemma)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   300
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   301
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   302
lemmas unique_ConsI = conjI [THEN unique_Cons [THEN iffD2], standard]
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   303
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   304
lemma unique_single [simp]: "!!p. unique [p]"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   305
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   306
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   307
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   308
lemma unique_ConsD: "unique (x#xs) ==> unique xs"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   309
apply (simp add: unique_def)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   310
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   311
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   312
lemma unique_append [rule_format (no_asm)]: "unique l' ==> unique l -->  
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   313
  (!(x,y):set l. !(x',y'):set l'. x' ~= x) --> unique (l @ l')"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   314
apply (induct_tac "l")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   315
apply  (auto dest: fst_in_set_lemma)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   316
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   317
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   318
lemma unique_map_inj [rule_format (no_asm)]: "unique l --> inj f --> unique (map (%(k,x). (f k, g k x)) l)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   319
apply (induct_tac "l")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   320
apply  (auto dest: fst_in_set_lemma simp add: inj_eq)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   321
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   322
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   323
lemma map_of_SomeI [rule_format (no_asm)]: "unique l --> (k, x) : set l --> map_of l k = Some x"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   324
apply (induct_tac "l")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   325
apply auto
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   326
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   327
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   328
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   329
section "list patterns"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   330
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   331
consts
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   332
  lsplit         :: "[['a, 'a list] => 'b, 'a list] => 'b"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   333
defs
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   334
  lsplit_def:    "lsplit == %f l. f (hd l) (tl l)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   335
(*  list patterns -- extends pre-defined type "pttrn" used in abstractions *)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   336
syntax
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   337
  "_lpttrn"    :: "[pttrn,pttrn] => pttrn"     ("_#/_" [901,900] 900)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   338
translations
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   339
  "%y#x#xs. b"  == "lsplit (%y x#xs. b)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   340
  "%x#xs  . b"  == "lsplit (%x xs  . b)"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   341
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   342
lemma lsplit [simp]: "lsplit c (x#xs) = c x xs"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   343
apply (unfold lsplit_def)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   344
apply (simp (no_asm))
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   345
done
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   346
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   347
lemma lsplit2 [simp]: "lsplit P (x#xs) y z = P x xs y z"
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   348
apply (unfold lsplit_def)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   349
apply simp
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   350
done 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   351
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   352
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   353
section "dummy pattern for quantifiers, let, etc."
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   354
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   355
syntax
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   356
  "@dummy_pat"   :: pttrn    ("'_")
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   357
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   358
parse_translation {*
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   359
let fun dummy_pat_tr [] = Free ("_",dummyT)
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   360
  | dummy_pat_tr ts = raise TERM ("dummy_pat_tr", ts);
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   361
in [("@dummy_pat", dummy_pat_tr)] 
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   362
end
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   363
*}
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   364
00d4a435777f Isabelle/Bali sources;
schirmer
parents:
diff changeset
   365
end