author | huffman |
Fri, 04 Mar 2005 23:23:47 +0100 | |
changeset 15577 | e16da3068ad6 |
parent 15576 | efb95d0d01f7 |
child 15637 | d2a06007ebfa |
permissions | -rw-r--r-- |
2640 | 1 |
(* Title: HOLCF/Fix.thy |
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ID: $Id$ |
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Author: Franz Regensburger |
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License: GPL (GNU GENERAL PUBLIC LICENSE) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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definitions for fixed point operator and admissibility |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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*) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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header {* Fixed point operator and admissibility *} |
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||
11 |
theory Fix |
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12 |
imports Cfun |
|
13 |
begin |
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|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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consts |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
1990 | 17 |
iterate :: "nat=>('a->'a)=>'a=>'a" |
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Ifix :: "('a->'a)=>'a" |
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"fix" :: "('a->'a)->'a" |
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Added "discrete" CPOs and modified IMP to use those rather than "lift"
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adm :: "('a::cpo=>bool)=>bool" |
1990 | 21 |
admw :: "('a=>bool)=>bool" |
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5192 | 23 |
primrec |
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iterate_0: "iterate 0 F x = x" |
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iterate_Suc: "iterate (Suc n) F x = F$(iterate n F x)" |
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|
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The curried version of HOLCF is now just called HOLCF. The old
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defs |
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|
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Ifix_def: "Ifix F == lub(range(%i. iterate i F UU))" |
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fix_def: "fix == (LAM f. Ifix f)" |
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adm_def: "adm P == !Y. chain(Y) --> |
3842 | 33 |
(!i. P(Y i)) --> P(lub(range Y))" |
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admw_def: "admw P == !F. (!n. P (iterate n F UU)) --> |
1479 | 36 |
P (lub(range (%i. iterate i F UU)))" |
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(* Title: HOLCF/Fix.ML |
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ID: $Id$ |
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Author: Franz Regensburger |
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License: GPL (GNU GENERAL PUBLIC LICENSE) |
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|
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fixed point operator and admissibility |
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*) |
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|
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(* ------------------------------------------------------------------------ *) |
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(* derive inductive properties of iterate from primitive recursion *) |
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(* ------------------------------------------------------------------------ *) |
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|
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lemma iterate_Suc2: "iterate (Suc n) F x = iterate n F (F$x)" |
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apply (induct_tac "n") |
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52 |
apply auto |
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53 |
done |
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54 |
|
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(* ------------------------------------------------------------------------ *) |
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(* the sequence of function itertaions is a chain *) |
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(* This property is essential since monotonicity of iterate makes no sense *) |
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(* ------------------------------------------------------------------------ *) |
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59 |
|
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lemma chain_iterate2: "x << F$x ==> chain (%i. iterate i F x)" |
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61 |
|
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62 |
apply (unfold chain_def) |
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63 |
apply (intro strip) |
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64 |
apply (induct_tac "i") |
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65 |
apply auto |
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66 |
apply (erule monofun_cfun_arg) |
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67 |
done |
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68 |
|
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69 |
|
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70 |
lemma chain_iterate: "chain (%i. iterate i F UU)" |
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71 |
apply (rule chain_iterate2) |
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72 |
apply (rule minimal) |
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73 |
done |
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74 |
|
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75 |
|
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76 |
(* ------------------------------------------------------------------------ *) |
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77 |
(* Kleene's fixed point theorems for continuous functions in pointed *) |
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(* omega cpo's *) |
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(* ------------------------------------------------------------------------ *) |
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80 |
|
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81 |
|
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82 |
lemma Ifix_eq: "Ifix F =F$(Ifix F)" |
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83 |
|
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84 |
|
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85 |
apply (unfold Ifix_def) |
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86 |
apply (subst contlub_cfun_arg) |
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87 |
apply (rule chain_iterate) |
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88 |
apply (rule antisym_less) |
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89 |
apply (rule lub_mono) |
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90 |
apply (rule chain_iterate) |
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91 |
apply (rule ch2ch_Rep_CFunR) |
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92 |
apply (rule chain_iterate) |
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93 |
apply (rule allI) |
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94 |
apply (rule iterate_Suc [THEN subst]) |
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95 |
apply (rule chain_iterate [THEN chainE]) |
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96 |
apply (rule is_lub_thelub) |
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97 |
apply (rule ch2ch_Rep_CFunR) |
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98 |
apply (rule chain_iterate) |
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99 |
apply (rule ub_rangeI) |
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100 |
apply (rule iterate_Suc [THEN subst]) |
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101 |
apply (rule is_ub_thelub) |
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102 |
apply (rule chain_iterate) |
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103 |
done |
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104 |
|
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105 |
|
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106 |
lemma Ifix_least: "F$x=x ==> Ifix(F) << x" |
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107 |
|
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108 |
apply (unfold Ifix_def) |
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109 |
apply (rule is_lub_thelub) |
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110 |
apply (rule chain_iterate) |
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111 |
apply (rule ub_rangeI) |
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112 |
apply (induct_tac "i") |
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113 |
apply (simp (no_asm_simp)) |
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114 |
apply (simp (no_asm_simp)) |
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115 |
apply (rule_tac t = "x" in subst) |
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116 |
apply assumption |
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117 |
apply (erule monofun_cfun_arg) |
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118 |
done |
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119 |
|
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120 |
|
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121 |
(* ------------------------------------------------------------------------ *) |
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122 |
(* monotonicity and continuity of iterate *) |
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123 |
(* ------------------------------------------------------------------------ *) |
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124 |
|
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125 |
lemma monofun_iterate: "monofun(iterate(i))" |
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126 |
apply (unfold monofun) |
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127 |
apply (intro strip) |
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128 |
apply (induct_tac "i") |
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129 |
apply (simp (no_asm_simp)) |
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130 |
apply (simp add: less_fun monofun_cfun) |
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131 |
done |
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132 |
|
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133 |
(* ------------------------------------------------------------------------ *) |
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134 |
(* the following lemma uses contlub_cfun which itself is based on a *) |
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135 |
(* diagonalisation lemma for continuous functions with two arguments. *) |
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136 |
(* In this special case it is the application function Rep_CFun *) |
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137 |
(* ------------------------------------------------------------------------ *) |
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138 |
|
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139 |
lemma contlub_iterate: "contlub(iterate(i))" |
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diff
changeset
|
140 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
141 |
apply (unfold contlub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
142 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
143 |
apply (induct_tac "i") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
144 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
145 |
apply (rule lub_const [THEN thelubI, symmetric]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
146 |
apply (simp (no_asm_simp) del: range_composition) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
147 |
apply (rule ext) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
148 |
apply (simplesubst thelub_fun) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
149 |
apply (rule chainI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
150 |
apply (rule less_fun [THEN iffD2]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
151 |
apply (rule allI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
152 |
apply (rule chainE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
153 |
apply (rule monofun_Rep_CFun1 [THEN ch2ch_MF2LR]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
154 |
apply (rule allI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
155 |
apply (rule monofun_Rep_CFun2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
156 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
157 |
apply (rule ch2ch_fun) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
158 |
apply (rule monofun_iterate [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
159 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
160 |
apply (subst thelub_fun) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
161 |
apply (rule monofun_iterate [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
162 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
163 |
apply (rule contlub_cfun) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
164 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
165 |
apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
166 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
167 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
168 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
169 |
lemma cont_iterate: "cont(iterate(i))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
170 |
apply (rule monocontlub2cont) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
171 |
apply (rule monofun_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
172 |
apply (rule contlub_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
173 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
174 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
175 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
176 |
(* a lemma about continuity of iterate in its third argument *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
177 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
178 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
179 |
lemma monofun_iterate2: "monofun(iterate n F)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
180 |
apply (rule monofunI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
181 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
182 |
apply (induct_tac "n") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
183 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
184 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
185 |
apply (erule monofun_cfun_arg) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
186 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
187 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
188 |
lemma contlub_iterate2: "contlub(iterate n F)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
189 |
apply (rule contlubI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
190 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
191 |
apply (induct_tac "n") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
192 |
apply (simp (no_asm)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
193 |
apply (simp (no_asm)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
194 |
apply (rule_tac t = "iterate n F (lub (range (%u. Y u))) " and s = "lub (range (%i. iterate n F (Y i))) " in ssubst) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
195 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
196 |
apply (rule contlub_cfun_arg) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
197 |
apply (erule monofun_iterate2 [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
198 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
199 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
200 |
lemma cont_iterate2: "cont (iterate n F)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
201 |
apply (rule monocontlub2cont) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
202 |
apply (rule monofun_iterate2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
203 |
apply (rule contlub_iterate2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
204 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
205 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
206 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
207 |
(* monotonicity and continuity of Ifix *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
208 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
209 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
210 |
lemma monofun_Ifix: "monofun(Ifix)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
211 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
212 |
apply (unfold monofun Ifix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
213 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
214 |
apply (rule lub_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
215 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
216 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
217 |
apply (rule allI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
218 |
apply (rule less_fun [THEN iffD1, THEN spec], erule monofun_iterate [THEN monofunE, THEN spec, THEN spec, THEN mp]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
219 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
220 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
221 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
222 |
(* since iterate is not monotone in its first argument, special lemmas must *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
223 |
(* be derived for lubs in this argument *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
224 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
225 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
226 |
lemma chain_iterate_lub: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
227 |
"chain(Y) ==> chain(%i. lub(range(%ia. iterate ia (Y i) UU)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
228 |
apply (rule chainI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
229 |
apply (rule lub_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
230 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
231 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
232 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
233 |
apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun, THEN chainE]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
234 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
235 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
236 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
237 |
(* this exchange lemma is analog to the one for monotone functions *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
238 |
(* observe that monotonicity is not really needed. The propagation of *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
239 |
(* chains is the essential argument which is usually derived from monot. *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
240 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
241 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
242 |
lemma contlub_Ifix_lemma1: "chain(Y) ==>iterate n (lub(range Y)) y = lub(range(%i. iterate n (Y i) y))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
243 |
apply (rule thelub_fun [THEN subst]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
244 |
apply (erule monofun_iterate [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
245 |
apply (simp (no_asm_simp) add: contlub_iterate [THEN contlubE]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
246 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
247 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
248 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
249 |
lemma ex_lub_iterate: "chain(Y) ==> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
250 |
lub(range(%i. lub(range(%ia. iterate i (Y ia) UU)))) = |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
251 |
lub(range(%i. lub(range(%ia. iterate ia (Y i) UU))))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
252 |
apply (rule antisym_less) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
253 |
apply (rule is_lub_thelub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
254 |
apply (rule contlub_Ifix_lemma1 [THEN ext, THEN subst]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
255 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
256 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
257 |
apply (rule ub_rangeI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
258 |
apply (rule lub_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
259 |
apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
260 |
apply (erule chain_iterate_lub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
261 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
262 |
apply (rule is_ub_thelub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
263 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
264 |
apply (rule is_lub_thelub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
265 |
apply (erule chain_iterate_lub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
266 |
apply (rule ub_rangeI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
267 |
apply (rule lub_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
268 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
269 |
apply (rule contlub_Ifix_lemma1 [THEN ext, THEN subst]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
270 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
271 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
272 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
273 |
apply (rule is_ub_thelub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
274 |
apply (erule monofun_iterate [THEN ch2ch_monofun, THEN ch2ch_fun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
275 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
276 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
277 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
278 |
lemma contlub_Ifix: "contlub(Ifix)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
279 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
280 |
apply (unfold contlub Ifix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
281 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
282 |
apply (subst contlub_Ifix_lemma1 [THEN ext]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
283 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
284 |
apply (erule ex_lub_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
285 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
286 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
287 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
288 |
lemma cont_Ifix: "cont(Ifix)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
289 |
apply (rule monocontlub2cont) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
290 |
apply (rule monofun_Ifix) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
291 |
apply (rule contlub_Ifix) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
292 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
293 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
294 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
295 |
(* propagate properties of Ifix to its continuous counterpart *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
296 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
297 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
298 |
lemma fix_eq: "fix$F = F$(fix$F)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
299 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
300 |
apply (unfold fix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
301 |
apply (simp (no_asm_simp) add: cont_Ifix) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
302 |
apply (rule Ifix_eq) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
303 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
304 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
305 |
lemma fix_least: "F$x = x ==> fix$F << x" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
306 |
apply (unfold fix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
307 |
apply (simp (no_asm_simp) add: cont_Ifix) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
308 |
apply (erule Ifix_least) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
309 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
310 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
311 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
312 |
lemma fix_eqI: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
313 |
"[| F$x = x; !z. F$z = z --> x << z |] ==> x = fix$F" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
314 |
apply (rule antisym_less) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
315 |
apply (erule allE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
316 |
apply (erule mp) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
317 |
apply (rule fix_eq [symmetric]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
318 |
apply (erule fix_least) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
319 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
320 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
321 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
322 |
lemma fix_eq2: "f == fix$F ==> f = F$f" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
323 |
apply (simp (no_asm_simp) add: fix_eq [symmetric]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
324 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
325 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
326 |
lemma fix_eq3: "f == fix$F ==> f$x = F$f$x" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
327 |
apply (erule fix_eq2 [THEN cfun_fun_cong]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
328 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
329 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
330 |
(* fun fix_tac3 thm i = ((rtac trans i) THEN (rtac (thm RS fix_eq3) i)) *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
331 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
332 |
lemma fix_eq4: "f = fix$F ==> f = F$f" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
333 |
apply (erule ssubst) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
334 |
apply (rule fix_eq) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
335 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
336 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
337 |
lemma fix_eq5: "f = fix$F ==> f$x = F$f$x" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
338 |
apply (rule trans) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
339 |
apply (erule fix_eq4 [THEN cfun_fun_cong]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
340 |
apply (rule refl) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
341 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
342 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
343 |
(* fun fix_tac5 thm i = ((rtac trans i) THEN (rtac (thm RS fix_eq5) i)) *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
344 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
345 |
(* proves the unfolding theorem for function equations f = fix$... *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
346 |
(* |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
347 |
fun fix_prover thy fixeq s = prove_goal thy s (fn prems => [ |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
348 |
(rtac trans 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
349 |
(rtac (fixeq RS fix_eq4) 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
350 |
(rtac trans 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
351 |
(rtac beta_cfun 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
352 |
(Simp_tac 1) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
353 |
]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
354 |
*) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
355 |
(* proves the unfolding theorem for function definitions f == fix$... *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
356 |
(* |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
357 |
fun fix_prover2 thy fixdef s = prove_goal thy s (fn prems => [ |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
358 |
(rtac trans 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
359 |
(rtac (fix_eq2) 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
360 |
(rtac fixdef 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
361 |
(rtac beta_cfun 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
362 |
(Simp_tac 1) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
363 |
]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
364 |
*) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
365 |
(* proves an application case for a function from its unfolding thm *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
366 |
(* |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
367 |
fun case_prover thy unfold s = prove_goal thy s (fn prems => [ |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
368 |
(cut_facts_tac prems 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
369 |
(rtac trans 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
370 |
(stac unfold 1), |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
371 |
Auto_tac |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
372 |
]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
373 |
*) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
374 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
375 |
(* better access to definitions *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
376 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
377 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
378 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
379 |
lemma Ifix_def2: "Ifix=(%x. lub(range(%i. iterate i x UU)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
380 |
apply (rule ext) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
381 |
apply (unfold Ifix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
382 |
apply (rule refl) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
383 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
384 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
385 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
386 |
(* direct connection between fix and iteration without Ifix *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
387 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
388 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
389 |
lemma fix_def2: "fix$F = lub(range(%i. iterate i F UU))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
390 |
apply (unfold fix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
391 |
apply (fold Ifix_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
392 |
apply (simp (no_asm_simp) add: cont_Ifix) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
393 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
394 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
395 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
396 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
397 |
(* Lemmas about admissibility and fixed point induction *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
398 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
399 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
400 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
401 |
(* access to definitions *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
402 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
403 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
404 |
lemma admI: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
405 |
"(!!Y. [| chain Y; !i. P (Y i) |] ==> P (lub (range Y))) ==> adm P" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
406 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
407 |
apply blast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
408 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
409 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
410 |
lemma triv_admI: "!x. P x ==> adm P" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
411 |
apply (rule admI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
412 |
apply (erule spec) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
413 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
414 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
415 |
lemma admD: "[| adm(P); chain(Y); !i. P(Y(i)) |] ==> P(lub(range(Y)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
416 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
417 |
apply blast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
418 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
419 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
420 |
lemma admw_def2: "admw(P) = (!F.(!n. P(iterate n F UU)) --> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
421 |
P (lub(range(%i. iterate i F UU))))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
422 |
apply (unfold admw_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
423 |
apply (rule refl) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
424 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
425 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
426 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
427 |
(* an admissible formula is also weak admissible *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
428 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
429 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
430 |
lemma adm_impl_admw: "adm(P)==>admw(P)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
431 |
apply (unfold admw_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
432 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
433 |
apply (erule admD) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
434 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
435 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
436 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
437 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
438 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
439 |
(* fixed point induction *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
440 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
441 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
442 |
lemma fix_ind: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
443 |
"[| adm(P); P(UU); !!x. P(x) ==> P(F$x)|] ==> P(fix$F)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
444 |
apply (subst fix_def2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
445 |
apply (erule admD) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
446 |
apply (rule chain_iterate) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
447 |
apply (rule allI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
448 |
apply (induct_tac "i") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
449 |
apply simp |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
450 |
apply simp |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
451 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
452 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
453 |
lemma def_fix_ind: "[| f == fix$F; adm(P); |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
454 |
P(UU); !!x. P(x) ==> P(F$x)|] ==> P f" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
455 |
apply simp |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
456 |
apply (erule fix_ind) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
457 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
458 |
apply fast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
459 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
460 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
461 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
462 |
(* computational induction for weak admissible formulae *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
463 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
464 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
465 |
lemma wfix_ind: "[| admw(P); !n. P(iterate n F UU)|] ==> P(fix$F)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
466 |
apply (subst fix_def2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
467 |
apply (rule admw_def2 [THEN iffD1, THEN spec, THEN mp]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
468 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
469 |
apply (rule allI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
470 |
apply (erule spec) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
471 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
472 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
473 |
lemma def_wfix_ind: "[| f == fix$F; admw(P); |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
474 |
!n. P(iterate n F UU) |] ==> P f" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
475 |
apply simp |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
476 |
apply (erule wfix_ind) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
477 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
478 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
479 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
480 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
481 |
(* for chain-finite (easy) types every formula is admissible *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
482 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
483 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
484 |
lemma adm_max_in_chain: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
485 |
"!Y. chain(Y::nat=>'a) --> (? n. max_in_chain n Y) ==> adm(P::'a=>bool)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
486 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
487 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
488 |
apply (rule exE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
489 |
apply (rule mp) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
490 |
apply (erule spec) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
491 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
492 |
apply (subst lub_finch1 [THEN thelubI]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
493 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
494 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
495 |
apply (erule spec) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
496 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
497 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
498 |
lemmas adm_chfin = chfin [THEN adm_max_in_chain, standard] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
499 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
500 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
501 |
(* some lemmata for functions with flat/chfin domain/range types *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
502 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
503 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
504 |
lemma adm_chfindom: "adm (%(u::'a::cpo->'b::chfin). P(u$s))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
505 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
506 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
507 |
apply (drule chfin_Rep_CFunR) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
508 |
apply (erule_tac x = "s" in allE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
509 |
apply clarsimp |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
510 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
511 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
512 |
(* adm_flat not needed any more, since it is a special case of adm_chfindom *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
513 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
514 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
515 |
(* improved admisibility introduction *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
516 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
517 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
518 |
lemma admI2: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
519 |
"(!!Y. [| chain Y; !i. P (Y i); !i. ? j. i < j & Y i ~= Y j & Y i << Y j |] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
520 |
==> P(lub (range Y))) ==> adm P" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
521 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
522 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
523 |
apply (erule increasing_chain_adm_lemma) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
524 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
525 |
apply fast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
526 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
527 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
528 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
529 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
530 |
(* admissibility of special formulae and propagation *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
531 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
532 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
533 |
lemma adm_less: "[|cont u;cont v|]==> adm(%x. u x << v x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
534 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
535 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
536 |
apply (frule_tac f = "u" in cont2mono [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
537 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
538 |
apply (frule_tac f = "v" in cont2mono [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
539 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
540 |
apply (erule cont2contlub [THEN contlubE, THEN spec, THEN mp, THEN ssubst]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
541 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
542 |
apply (erule cont2contlub [THEN contlubE, THEN spec, THEN mp, THEN ssubst]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
543 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
544 |
apply (blast intro: lub_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
545 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
546 |
declare adm_less [simp] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
547 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
548 |
lemma adm_conj: "[| adm P; adm Q |] ==> adm(%x. P x & Q x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
549 |
apply (fast elim: admD intro: admI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
550 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
551 |
declare adm_conj [simp] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
552 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
553 |
lemma adm_not_free: "adm(%x. t)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
554 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
555 |
apply fast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
556 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
557 |
declare adm_not_free [simp] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
558 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
559 |
lemma adm_not_less: "cont t ==> adm(%x.~ (t x) << u)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
560 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
561 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
562 |
apply (rule contrapos_nn) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
563 |
apply (erule spec) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
564 |
apply (rule trans_less) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
565 |
prefer 2 apply (assumption) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
566 |
apply (erule cont2mono [THEN monofun_fun_arg]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
567 |
apply (rule is_ub_thelub) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
568 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
569 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
570 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
571 |
lemma adm_all: "!y. adm(P y) ==> adm(%x.!y. P y x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
572 |
apply (fast intro: admI elim: admD) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
573 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
574 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
575 |
lemmas adm_all2 = allI [THEN adm_all, standard] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
576 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
577 |
lemma adm_subst: "[|cont t; adm P|] ==> adm(%x. P (t x))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
578 |
apply (rule admI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
579 |
apply (simplesubst cont2contlub [THEN contlubE, THEN spec, THEN mp]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
580 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
581 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
582 |
apply (erule admD) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
583 |
apply (erule cont2mono [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
584 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
585 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
586 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
587 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
588 |
lemma adm_UU_not_less: "adm(%x.~ UU << t(x))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
589 |
apply (simp (no_asm)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
590 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
591 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
592 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
593 |
lemma adm_not_UU: "cont(t)==> adm(%x.~ (t x) = UU)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
594 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
595 |
apply (unfold adm_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
596 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
597 |
apply (rule contrapos_nn) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
598 |
apply (erule spec) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
599 |
apply (rule chain_UU_I [THEN spec]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
600 |
apply (erule cont2mono [THEN ch2ch_monofun]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
601 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
602 |
apply (erule cont2contlub [THEN contlubE, THEN spec, THEN mp, THEN subst]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
603 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
604 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
605 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
606 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
607 |
lemma adm_eq: "[|cont u ; cont v|]==> adm(%x. u x = v x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
608 |
apply (simp (no_asm_simp) add: po_eq_conv) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
609 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
610 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
611 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
612 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
613 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
614 |
(* admissibility for disjunction is hard to prove. It takes 10 Lemmas *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
615 |
(* ------------------------------------------------------------------------ *) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
616 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
617 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
618 |
lemma adm_disj_lemma1: "!n. P(Y n)|Q(Y n) ==> (? i.!j. R i j --> Q(Y(j))) | (!i.? j. R i j & P(Y(j)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
619 |
apply fast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
620 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
621 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
622 |
lemma adm_disj_lemma2: "[| adm(Q); ? X. chain(X) & (!n. Q(X(n))) & |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
623 |
lub(range(Y))=lub(range(X))|] ==> Q(lub(range(Y)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
624 |
apply (force elim: admD) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
625 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
626 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
627 |
lemma adm_disj_lemma3: "chain Y ==> chain (%m. if m < Suc i then Y (Suc i) else Y m)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
628 |
apply (unfold chain_def) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
629 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
630 |
apply safe |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
631 |
apply (subgoal_tac "ia = i") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
632 |
apply (simp_all (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
633 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
634 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
635 |
lemma adm_disj_lemma4: "!j. i < j --> Q(Y(j)) ==> !n. Q( if n < Suc i then Y(Suc i) else Y n)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
636 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
637 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
638 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
639 |
lemma adm_disj_lemma5: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
640 |
"!!Y::nat=>'a::cpo. [| chain(Y); ! j. i < j --> Q(Y(j)) |] ==> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
641 |
lub(range(Y)) = lub(range(%m. if m< Suc(i) then Y(Suc(i)) else Y m))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
642 |
apply (safe intro!: lub_equal2 adm_disj_lemma3) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
643 |
prefer 2 apply (assumption) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
644 |
apply (rule_tac x = "i" in exI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
645 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
646 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
647 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
648 |
lemma adm_disj_lemma6: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
649 |
"[| chain(Y::nat=>'a::cpo); ? i. ! j. i < j --> Q(Y(j)) |] ==> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
650 |
? X. chain(X) & (! n. Q(X(n))) & lub(range(Y)) = lub(range(X))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
651 |
apply (erule exE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
652 |
apply (rule_tac x = "%m. if m<Suc (i) then Y (Suc (i)) else Y m" in exI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
653 |
apply (rule conjI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
654 |
apply (rule adm_disj_lemma3) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
655 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
656 |
apply (rule conjI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
657 |
apply (rule adm_disj_lemma4) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
658 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
659 |
apply (rule adm_disj_lemma5) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
660 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
661 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
662 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
663 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
664 |
lemma adm_disj_lemma7: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
665 |
"[| chain(Y::nat=>'a::cpo); ! i. ? j. i < j & P(Y(j)) |] ==> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
666 |
chain(%m. Y(Least(%j. m<j & P(Y(j)))))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
667 |
apply (rule chainI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
668 |
apply (rule chain_mono3) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
669 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
670 |
apply (rule Least_le) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
671 |
apply (rule conjI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
672 |
apply (rule Suc_lessD) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
673 |
apply (erule allE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
674 |
apply (erule exE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
675 |
apply (rule LeastI [THEN conjunct1]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
676 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
677 |
apply (erule allE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
678 |
apply (erule exE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
679 |
apply (rule LeastI [THEN conjunct2]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
680 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
681 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
682 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
683 |
lemma adm_disj_lemma8: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
684 |
"[| ! i. ? j. i < j & P(Y(j)) |] ==> ! m. P(Y(LEAST j::nat. m<j & P(Y(j))))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
685 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
686 |
apply (erule allE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
687 |
apply (erule exE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
688 |
apply (erule LeastI [THEN conjunct2]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
689 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
690 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
691 |
lemma adm_disj_lemma9: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
692 |
"[| chain(Y::nat=>'a::cpo); ! i. ? j. i < j & P(Y(j)) |] ==> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
693 |
lub(range(Y)) = lub(range(%m. Y(Least(%j. m<j & P(Y(j))))))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
694 |
apply (rule antisym_less) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
695 |
apply (rule lub_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
696 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
697 |
apply (rule adm_disj_lemma7) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
698 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
699 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
700 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
701 |
apply (rule chain_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
702 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
703 |
apply (erule allE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
704 |
apply (erule exE) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
705 |
apply (rule LeastI [THEN conjunct1]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
706 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
707 |
apply (rule lub_mono3) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
708 |
apply (rule adm_disj_lemma7) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
709 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
710 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
711 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
712 |
apply (intro strip) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
713 |
apply (rule exI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
714 |
apply (rule chain_mono) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
715 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
716 |
apply (rule lessI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
717 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
718 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
719 |
lemma adm_disj_lemma10: "[| chain(Y::nat=>'a::cpo); ! i. ? j. i < j & P(Y(j)) |] ==> |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
720 |
? X. chain(X) & (! n. P(X(n))) & lub(range(Y)) = lub(range(X))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
721 |
apply (rule_tac x = "%m. Y (Least (%j. m<j & P (Y (j))))" in exI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
722 |
apply (rule conjI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
723 |
apply (rule adm_disj_lemma7) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
724 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
725 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
726 |
apply (rule conjI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
727 |
apply (rule adm_disj_lemma8) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
728 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
729 |
apply (rule adm_disj_lemma9) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
730 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
731 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
732 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
733 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
734 |
lemma adm_disj_lemma12: "[| adm(P); chain(Y);? i. ! j. i < j --> P(Y(j))|]==>P(lub(range(Y)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
735 |
apply (erule adm_disj_lemma2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
736 |
apply (erule adm_disj_lemma6) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
737 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
738 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
739 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
740 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
741 |
lemma adm_lemma11: |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
742 |
"[| adm(P); chain(Y); ! i. ? j. i < j & P(Y(j)) |]==>P(lub(range(Y)))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
743 |
apply (erule adm_disj_lemma2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
744 |
apply (erule adm_disj_lemma10) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
745 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
746 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
747 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
748 |
lemma adm_disj: "[| adm P; adm Q |] ==> adm(%x. P x | Q x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
749 |
apply (rule admI) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
750 |
apply (rule adm_disj_lemma1 [THEN disjE]) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
751 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
752 |
apply (rule disjI2) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
753 |
apply (erule adm_disj_lemma12) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
754 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
755 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
756 |
apply (rule disjI1) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
757 |
apply (erule adm_lemma11) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
758 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
759 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
760 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
761 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
762 |
lemma adm_imp: "[| adm(%x.~(P x)); adm Q |] ==> adm(%x. P x --> Q x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
763 |
apply (subgoal_tac " (%x. P x --> Q x) = (%x. ~P x | Q x) ") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
764 |
apply (erule ssubst) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
765 |
apply (erule adm_disj) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
766 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
767 |
apply (simp (no_asm)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
768 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
769 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
770 |
lemma adm_iff: "[| adm (%x. P x --> Q x); adm (%x. Q x --> P x) |] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
771 |
==> adm (%x. P x = Q x)" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
772 |
apply (subgoal_tac " (%x. P x = Q x) = (%x. (P x --> Q x) & (Q x --> P x))") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
773 |
apply (simp (no_asm_simp)) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
774 |
apply (rule ext) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
775 |
apply fast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
776 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
777 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
778 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
779 |
lemma adm_not_conj: "[| adm (%x. ~ P x); adm (%x. ~ Q x) |] ==> adm (%x. ~ (P x & Q x))" |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
780 |
apply (subgoal_tac " (%x. ~ (P x & Q x)) = (%x. ~ P x | ~ Q x) ") |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
781 |
apply (rule_tac [2] ext) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
782 |
prefer 2 apply fast |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
783 |
apply (erule ssubst) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
784 |
apply (erule adm_disj) |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
785 |
apply assumption |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
786 |
done |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
787 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
788 |
lemmas adm_lemmas = adm_not_free adm_imp adm_disj adm_eq adm_not_UU |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
789 |
adm_UU_not_less adm_all2 adm_not_less adm_not_conj adm_iff |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
790 |
|
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
791 |
declare adm_lemmas [simp] |
efb95d0d01f7
converted to new-style theories, and combined numbered files
huffman
parents:
14981
diff
changeset
|
792 |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
793 |
end |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
794 |