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1 \begin{theindex} |
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2 |
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3 \item \ttall, \bold{209} |
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4 \item \texttt{?}, \bold{209} |
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5 \item \isasymuniqex, \bold{209} |
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6 \item \ttuniquex, \bold{209} |
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7 \item {\texttt {\&}}, \bold{209} |
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8 \item \verb$~$, \bold{209} |
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9 \item \verb$~=$, \bold{209} |
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10 \item \ttor, \bold{209} |
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11 \item \texttt{[]}, \bold{9} |
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12 \item \texttt{\#}, \bold{9} |
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13 \item \texttt{\at}, \bold{10}, \hyperpage{209} |
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14 \item \isasymnotin, \bold{209} |
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15 \item \verb$~:$, \bold{209} |
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16 \item \isasymInter, \bold{209} |
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17 \item \isasymUnion, \bold{209} |
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18 \item \isasyminverse, \bold{209} |
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19 \item \verb$^-1$, \bold{209} |
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20 \item \isactrlsup{\isacharasterisk}, \bold{209} |
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21 \item \verb$^$\texttt{*}, \bold{209} |
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22 \item \isasymAnd, \bold{12}, \bold{209} |
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23 \item \ttAnd, \bold{209} |
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24 \item \emph {$\Rightarrow $}, \bold{5} |
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25 \item \ttlbr, \bold{209} |
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26 \item \ttrbr, \bold{209} |
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27 \item \texttt {\%}, \bold{209} |
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28 \item \texttt {;}, \bold{7} |
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29 \item \isa {()} (constant), \hyperpage{24} |
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30 \item \isa {+} (tactical), \hyperpage{99} |
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31 \item \isa {<*lex*>}, \see{lexicographic product}{1} |
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32 \item \isa {?} (tactical), \hyperpage{99} |
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33 \item \texttt{|} (tactical), \hyperpage{99} |
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34 |
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35 \indexspace |
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36 |
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37 \item \isa {0} (constant), \hyperpage{22, 23}, \hyperpage{150} |
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38 \item \isa {1} (constant), \hyperpage{23}, \hyperpage{150, 151} |
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39 |
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40 \indexspace |
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41 |
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42 \item abandoning a proof, \bold{13} |
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43 \item abandoning a theory, \bold{16} |
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44 \item \isa {abs} (constant), \hyperpage{153} |
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45 \item \texttt {abs}, \bold{209} |
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46 \item absolute value, \hyperpage{153} |
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47 \item \isa {add} (modifier), \hyperpage{29} |
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48 \item \isa {add_ac} (theorems), \hyperpage{152} |
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49 \item \isa {add_assoc} (theorem), \bold{152} |
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50 \item \isa {add_commute} (theorem), \bold{152} |
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51 \item \isa {add_mult_distrib} (theorem), \bold{151} |
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52 \item \texttt {ALL}, \bold{209} |
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53 \item \isa {All} (constant), \hyperpage{109} |
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54 \item \isa {allE} (theorem), \bold{81} |
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55 \item \isa {allI} (theorem), \bold{80} |
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56 \item antiquotation, \bold{61} |
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57 \item append function, 10--14 |
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58 \item \isacommand {apply} (command), \hyperpage{15} |
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59 \item \isa {arg_cong} (theorem), \bold{96} |
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60 \item \isa {arith} (method), \hyperpage{23}, \hyperpage{149} |
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61 \item arithmetic operations |
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62 \subitem for \protect\isa{nat}, \hyperpage{23} |
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63 \item \textsc {ascii} symbols, \bold{209} |
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64 \item Aspinall, David, \hyperpage{viii} |
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65 \item associative-commutative function, \hyperpage{176} |
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66 \item \isa {assumption} (method), \hyperpage{69} |
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67 \item assumptions |
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68 \subitem of subgoal, \hyperpage{12} |
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69 \subitem renaming, 82--83 |
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70 \subitem reusing, 83 |
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71 \item \isa {auto} (method), \hyperpage{38}, \hyperpage{92} |
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72 \item \isa {axclass}, 164--170 |
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73 \item axiom of choice, \hyperpage{86} |
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74 \item axiomatic type classes, 164--170 |
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75 |
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76 \indexspace |
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77 |
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78 \item \isacommand {back} (command), \hyperpage{78} |
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79 \item \isa {Ball} (constant), \hyperpage{109} |
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80 \item \isa {ballI} (theorem), \bold{108} |
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81 \item \isa {best} (method), \hyperpage{92} |
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82 \item \isa {Bex} (constant), \hyperpage{109} |
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83 \item \isa {bexE} (theorem), \bold{108} |
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84 \item \isa {bexI} (theorem), \bold{108} |
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85 \item \isa {bij_def} (theorem), \bold{110} |
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86 \item bijections, \hyperpage{110} |
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87 \item binary trees, \hyperpage{18} |
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88 \item binomial coefficients, \hyperpage{109} |
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89 \item bisimulations, \hyperpage{116} |
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90 \item \isa {blast} (method), 89--90, \hyperpage{92} |
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91 \item \isa {bool} (type), \hyperpage{4, 5} |
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92 \item boolean expressions example, 20--22 |
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93 \item \isa {bspec} (theorem), \bold{108} |
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94 \item \isacommand{by} (command), 73 |
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95 |
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96 \indexspace |
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97 |
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98 \item \isa {card} (constant), \hyperpage{109} |
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99 \item \isa {card_Pow} (theorem), \bold{109} |
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100 \item \isa {card_Un_Int} (theorem), \bold{109} |
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101 \item cardinality, \hyperpage{109} |
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102 \item \isa {case} (symbol), \hyperpage{32, 33} |
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103 \item \isa {case} expressions, \hyperpage{5, 6}, \hyperpage{18} |
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104 \item case distinctions, \hyperpage{19} |
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105 \item case splits, \bold{31} |
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106 \item \isa {case_tac} (method), \hyperpage{19}, \hyperpage{101}, |
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107 \hyperpage{157} |
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108 \item \isa {cases} (method), \hyperpage{162} |
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109 \item \isacommand {chapter} (command), \hyperpage{59} |
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110 \item \isa {clarify} (method), \hyperpage{91, 92} |
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111 \item \isa {clarsimp} (method), \hyperpage{91, 92} |
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112 \item \isa {classical} (theorem), \bold{73} |
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113 \item coinduction, \bold{116} |
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114 \item \isa {Collect} (constant), \hyperpage{109} |
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115 \item compiling expressions example, 36--38 |
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116 \item \isa {Compl_iff} (theorem), \bold{106} |
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117 \item complement |
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118 \subitem of a set, \hyperpage{105} |
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119 \item composition |
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120 \subitem of functions, \bold{110} |
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121 \subitem of relations, \bold{112} |
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122 \item conclusion |
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123 \subitem of subgoal, \hyperpage{12} |
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124 \item conditional expressions, \see{\isa{if} expressions}{1} |
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125 \item conditional simplification rules, \hyperpage{31} |
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126 \item \isa {cong} (attribute), \hyperpage{176} |
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127 \item congruence rules, \bold{175} |
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128 \item \isa {conjE} (theorem), \bold{71} |
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129 \item \isa {conjI} (theorem), \bold{68} |
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130 \item \isa {Cons} (constant), \hyperpage{9} |
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131 \item \isacommand {constdefs} (command), \hyperpage{25} |
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132 \item \isacommand {consts} (command), \hyperpage{10} |
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133 \item contrapositives, 73 |
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134 \item converse |
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135 \subitem of a relation, \bold{112} |
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136 \item \isa {converse_iff} (theorem), \bold{112} |
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137 \item CTL, 121--126, 191--193 |
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138 |
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139 \indexspace |
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140 |
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141 \item \isacommand {datatype} (command), \hyperpage{9}, 38--43 |
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142 \item datatypes, 17--22 |
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143 \subitem and nested recursion, \hyperpage{40}, \hyperpage{44} |
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144 \subitem mutually recursive, \hyperpage{38} |
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145 \subitem nested, \hyperpage{180} |
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146 \item \isacommand {defer} (command), \hyperpage{16}, \hyperpage{100} |
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147 \item Definitional Approach, \hyperpage{26} |
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148 \item definitions, \bold{25} |
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149 \subitem unfolding, \bold{30} |
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150 \item \isacommand {defs} (command), \hyperpage{25} |
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151 \item \isa {del} (modifier), \hyperpage{29} |
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152 \item description operators, 85--87 |
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153 \item descriptions |
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154 \subitem definite, \hyperpage{85} |
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155 \subitem indefinite, \hyperpage{86} |
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156 \item \isa {dest} (attribute), \hyperpage{102} |
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157 \item destruction rules, 71 |
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158 \item \isa {diff_mult_distrib} (theorem), \bold{151} |
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159 \item difference |
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160 \subitem of sets, \bold{106} |
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161 \item \isa {disjCI} (theorem), \bold{74} |
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162 \item \isa {disjE} (theorem), \bold{70} |
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163 \item \isa {div} (symbol), \hyperpage{23} |
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164 \item divides relation, \hyperpage{84}, \hyperpage{95}, 101--104, |
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165 \hyperpage{152} |
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166 \item division |
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167 \subitem by negative numbers, \hyperpage{153} |
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168 \subitem by zero, \hyperpage{152} |
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169 \subitem for type \protect\isa{nat}, \hyperpage{151} |
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170 \item documents, \bold{57} |
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171 \item domain |
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172 \subitem of a relation, \hyperpage{112} |
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173 \item \isa {Domain_iff} (theorem), \bold{112} |
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174 \item \isacommand {done} (command), \hyperpage{13} |
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175 \item \isa {drule_tac} (method), \hyperpage{76}, \hyperpage{96} |
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176 \item \isa {dvd_add} (theorem), \bold{152} |
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177 \item \isa {dvd_anti_sym} (theorem), \bold{152} |
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178 \item \isa {dvd_def} (theorem), \bold{152} |
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179 |
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180 \indexspace |
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181 |
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182 \item \isa {elim!} (attribute), \hyperpage{131} |
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183 \item elimination rules, 69--70 |
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184 \item \isacommand {end} (command), \hyperpage{14} |
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185 \item \isa {Eps} (constant), \hyperpage{109} |
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186 \item equality, \hyperpage{5} |
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187 \subitem of functions, \bold{109} |
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188 \subitem of records, \hyperpage{161} |
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189 \subitem of sets, \bold{106} |
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190 \item \isa {equalityE} (theorem), \bold{106} |
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191 \item \isa {equalityI} (theorem), \bold{106} |
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192 \item \isa {erule} (method), \hyperpage{70} |
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193 \item \isa {erule_tac} (method), \hyperpage{76} |
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194 \item Euclid's algorithm, 101--104 |
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195 \item even numbers |
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196 \subitem defining inductively, 127--131 |
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197 \item \texttt {EX}, \bold{209} |
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198 \item \isa {Ex} (constant), \hyperpage{109} |
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199 \item \isa {exE} (theorem), \bold{82} |
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200 \item \isa {exI} (theorem), \bold{82} |
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201 \item \isa {ext} (theorem), \bold{109} |
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202 \item \isa {extend} (constant), \hyperpage{163} |
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203 \item extensionality |
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204 \subitem for functions, \bold{109, 110} |
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205 \subitem for records, \hyperpage{162} |
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206 \subitem for sets, \bold{106} |
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207 \item \ttEXU, \bold{209} |
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208 |
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209 \indexspace |
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210 |
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211 \item \isa {False} (constant), \hyperpage{5} |
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212 \item \isa {fast} (method), \hyperpage{92}, \hyperpage{124} |
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213 \item Fibonacci function, \hyperpage{47} |
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214 \item \isa {fields} (constant), \hyperpage{163} |
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215 \item \isa {finite} (symbol), \hyperpage{109} |
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216 \item \isa {Finites} (constant), \hyperpage{109} |
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217 \item fixed points, 116 |
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218 \item flags, \hyperpage{5, 6}, \hyperpage{33} |
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219 \subitem setting and resetting, \hyperpage{5} |
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220 \item \isa {force} (method), \hyperpage{91, 92} |
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221 \item formal comments, \bold{60} |
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222 \item formal proof documents, \bold{57} |
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223 \item formulae, 5--6 |
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224 \item forward proof, 92--98 |
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225 \item \isa {frule} (method), 83 |
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226 \item \isa {frule_tac} (method), \hyperpage{76} |
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227 \item \isa {fst} (constant), \hyperpage{24} |
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228 \item function types, \hyperpage{5} |
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229 \item functions, 109--111 |
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230 \subitem partial, \hyperpage{182} |
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231 \subitem total, \hyperpage{11}, 47--52 |
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232 \subitem underdefined, \hyperpage{183} |
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233 |
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234 \indexspace |
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235 |
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236 \item \isa {gcd} (constant), 93--94, 101--104 |
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237 \item generalizing for induction, \hyperpage{129} |
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238 \item generalizing induction formulae, \hyperpage{35} |
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239 \item Girard, Jean-Yves, \fnote{71} |
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240 \item Gordon, Mike, \hyperpage{3} |
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241 \item grammars |
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242 \subitem defining inductively, 140--145 |
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243 \item ground terms example, 135--140 |
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244 |
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245 \indexspace |
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246 |
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247 \item \isa {hd} (constant), \hyperpage{17}, \hyperpage{37} |
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248 \item \isacommand {header} (command), \hyperpage{59} |
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249 \item Hilbert's $\varepsilon$-operator, \hyperpage{86} |
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250 \item HOLCF, \hyperpage{43} |
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251 \item Hopcroft, J. E., \hyperpage{145} |
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252 \item \isa {hypreal} (type), \hyperpage{155} |
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253 |
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254 \indexspace |
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255 |
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256 \item \isa {Id_def} (theorem), \bold{112} |
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257 \item \isa {id_def} (theorem), \bold{110} |
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258 \item identifiers, \bold{6} |
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259 \subitem qualified, \bold{4} |
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260 \item identity function, \bold{110} |
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261 \item identity relation, \bold{112} |
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262 \item \isa {if} expressions, \hyperpage{5, 6} |
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263 \subitem simplification of, \hyperpage{33} |
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264 \subitem splitting of, \hyperpage{31}, \hyperpage{49} |
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265 \item if-and-only-if, \hyperpage{6} |
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266 \item \isa {iff} (attribute), \hyperpage{90}, \hyperpage{102}, |
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267 \hyperpage{130} |
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268 \item \isa {iffD1} (theorem), \bold{94} |
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269 \item \isa {iffD2} (theorem), \bold{94} |
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270 \item ignored material, \bold{64} |
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271 \item image |
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272 \subitem under a function, \bold{111} |
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273 \subitem under a relation, \bold{112} |
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274 \item \isa {image_def} (theorem), \bold{111} |
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275 \item \isa {Image_iff} (theorem), \bold{112} |
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276 \item \isa {impI} (theorem), \bold{72} |
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277 \item implication, 72--73 |
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278 \item \isa {ind_cases} (method), \hyperpage{131} |
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279 \item \isa {induct_tac} (method), \hyperpage{12}, \hyperpage{19}, |
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280 \hyperpage{52}, \hyperpage{190} |
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281 \item induction, 186--193 |
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282 \subitem complete, \hyperpage{188} |
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283 \subitem deriving new schemas, \hyperpage{190} |
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284 \subitem on a term, \hyperpage{187} |
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285 \subitem recursion, 51--52 |
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286 \subitem structural, \hyperpage{19} |
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287 \subitem well-founded, 115 |
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288 \item induction heuristics, 34--36 |
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289 \item \isacommand {inductive} (command), \hyperpage{127} |
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290 \item inductive definition |
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291 \subitem simultaneous, \hyperpage{141} |
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292 \item inductive definitions, 127--145 |
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293 \item \isacommand {inductive\_cases} (command), \hyperpage{131}, |
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294 \hyperpage{139} |
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295 \item infinitely branching trees, \hyperpage{43} |
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296 \item infix annotations, \hyperpage{53} |
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297 \item \isacommand{infixr} (annotation), \hyperpage{10} |
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298 \item \isa {inj_on_def} (theorem), \bold{110} |
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299 \item injections, \hyperpage{110} |
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300 \item \isa {insert} (constant), \hyperpage{107} |
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301 \item \isa {insert} (method), \hyperpage{97}, 97, \hyperpage{98} |
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302 \item instance, \bold{166} |
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303 \item \texttt {INT}, \bold{209} |
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304 \item \texttt {Int}, \bold{209} |
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305 \item \isa {int} (type), 153--154 |
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306 \item \isa {INT_iff} (theorem), \bold{108} |
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307 \item \isa {IntD1} (theorem), \bold{105} |
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308 \item \isa {IntD2} (theorem), \bold{105} |
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309 \item integers, 153--154 |
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310 \item \isa {INTER} (constant), \hyperpage{109} |
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311 \item \texttt {Inter}, \bold{209} |
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312 \item \isa {Inter_iff} (theorem), \bold{108} |
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313 \item intersection, \hyperpage{105} |
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314 \subitem indexed, \hyperpage{108} |
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315 \item \isa {IntI} (theorem), \bold{105} |
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316 \item \isa {intro} (method), \hyperpage{74} |
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317 \item \isa {intro!} (attribute), \hyperpage{128} |
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318 \item \isa {intro_classes} (method), \hyperpage{166} |
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319 \item introduction rules, 68--69 |
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320 \item \isa {inv} (constant), \hyperpage{86} |
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321 \item \isa {inv_image_def} (theorem), \bold{115} |
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322 \item inverse |
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323 \subitem of a function, \bold{110} |
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324 \subitem of a relation, \bold{112} |
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325 \item inverse image |
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326 \subitem of a function, \hyperpage{111} |
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327 \subitem of a relation, \hyperpage{114} |
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328 \item \isa {itrev} (constant), \hyperpage{34} |
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329 |
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330 \indexspace |
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331 |
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332 \item \isacommand {kill} (command), \hyperpage{16} |
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333 |
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334 \indexspace |
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335 |
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336 \item $\lambda$ expressions, \hyperpage{5} |
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337 \item LCF, \hyperpage{43} |
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338 \item \isa {LEAST} (symbol), \hyperpage{23}, \hyperpage{85} |
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339 \item least number operator, \see{\protect\isa{LEAST}}{85} |
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340 \item Leibniz, Gottfried Wilhelm, \hyperpage{53} |
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341 \item \isacommand {lemma} (command), \hyperpage{13} |
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342 \item \isacommand {lemmas} (command), \hyperpage{93}, \hyperpage{102} |
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343 \item \isa {length} (symbol), \hyperpage{18} |
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344 \item \isa {length_induct}, \bold{190} |
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345 \item \isa {less_than} (constant), \hyperpage{114} |
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346 \item \isa {less_than_iff} (theorem), \bold{114} |
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347 \item \isa {let} expressions, \hyperpage{5, 6}, \hyperpage{31} |
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348 \item \isa {Let_def} (theorem), \hyperpage{31} |
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349 \item \isa {lex_prod_def} (theorem), \bold{115} |
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350 \item lexicographic product, \bold{115}, \hyperpage{178} |
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351 \item {\texttt{lfp}} |
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352 \subitem applications of, \see{CTL}{116} |
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353 \item Library, \hyperpage{4} |
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354 \item linear arithmetic, 22--24, \hyperpage{149} |
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355 \item \isa {List} (theory), \hyperpage{17} |
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356 \item \isa {list} (type), \hyperpage{5}, \hyperpage{9}, |
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357 \hyperpage{17} |
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358 \item \isa {list.split} (theorem), \hyperpage{32} |
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359 \item \isa {lists_mono} (theorem), \bold{137} |
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360 \item Lowe, Gavin, 196--197 |
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361 |
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362 \indexspace |
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363 |
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364 \item \isa {Main} (theory), \hyperpage{4} |
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365 \item major premise, \bold{75} |
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366 \item \isa {make} (constant), \hyperpage{163} |
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367 \item marginal comments, \bold{60} |
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368 \item markup commands, \bold{59} |
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369 \item \isa {max} (constant), \hyperpage{23, 24} |
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370 \item measure functions, \hyperpage{47}, \hyperpage{114} |
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371 \item \isa {measure_def} (theorem), \bold{115} |
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372 \item meta-logic, \bold{80} |
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373 \item methods, \bold{16} |
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374 \item \isa {min} (constant), \hyperpage{23, 24} |
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375 \item mixfix annotations, \bold{53} |
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376 \item \isa {mod} (symbol), \hyperpage{23} |
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377 \item \isa {mod_div_equality} (theorem), \bold{151} |
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378 \item \isa {mod_mult_distrib} (theorem), \bold{151} |
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379 \item model checking example, 116--126 |
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380 \item \emph{modus ponens}, \hyperpage{67}, \hyperpage{72} |
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381 \item \isa {mono_def} (theorem), \bold{116} |
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382 \item monotone functions, \bold{116}, \hyperpage{139} |
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383 \subitem and inductive definitions, 137--138 |
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384 \item \isa {more} (constant), \hyperpage{158}, \hyperpage{160} |
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385 \item \isa {mp} (theorem), \bold{72} |
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386 \item \isa {mult_ac} (theorems), \hyperpage{152} |
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387 \item multiple inheritance, \bold{169} |
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388 \item multiset ordering, \bold{115} |
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389 |
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390 \indexspace |
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391 |
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392 \item \isa {nat} (type), \hyperpage{4}, \hyperpage{22}, 151--153 |
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393 \item \isa {nat_less_induct} (theorem), \hyperpage{188} |
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394 \item natural deduction, 67--68 |
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395 \item natural numbers, \hyperpage{22}, 151--153 |
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396 \item Needham-Schroeder protocol, 195--197 |
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397 \item negation, 73--75 |
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398 \item \isa {Nil} (constant), \hyperpage{9} |
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399 \item \isa {no_asm} (modifier), \hyperpage{29} |
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400 \item \isa {no_asm_simp} (modifier), \hyperpage{30} |
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401 \item \isa {no_asm_use} (modifier), \hyperpage{30} |
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402 \item \isa {no_vars} (attribute), \hyperpage{62} |
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403 \item non-standard reals, \hyperpage{155} |
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404 \item \isa {None} (constant), \bold{24} |
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405 \item \isa {notE} (theorem), \bold{73} |
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406 \item \isa {notI} (theorem), \bold{73} |
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407 \item numbers, 149--155 |
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408 \item numeric literals, 150 |
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409 \subitem for type \protect\isa{nat}, \hyperpage{151} |
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410 \subitem for type \protect\isa{real}, \hyperpage{155} |
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411 |
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412 \indexspace |
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413 |
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414 \item \isa {O} (symbol), \hyperpage{112} |
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415 \item \texttt {o}, \bold{209} |
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416 \item \isa {o_def} (theorem), \bold{110} |
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417 \item \isa {OF} (attribute), 95--96, \hyperpage{96} |
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418 \item \isa {of} (attribute), \hyperpage{93}, \hyperpage{96} |
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419 \item \isa {only} (modifier), \hyperpage{29} |
|
420 \item \isacommand {oops} (command), \hyperpage{13} |
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421 \item \isa {option} (type), \bold{24} |
|
422 \item ordered rewriting, \bold{176} |
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423 \item overloading, \hyperpage{23}, 165--167 |
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424 \subitem and arithmetic, \hyperpage{150} |
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425 |
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426 \indexspace |
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427 |
|
428 \item pairs and tuples, \hyperpage{24}, 155--158 |
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429 \item parent theories, \bold{4} |
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430 \item pattern matching |
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431 \subitem and \isacommand{recdef}, \hyperpage{47} |
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432 \item patterns |
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433 \subitem higher-order, \bold{177} |
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434 \item PDL, 118--120 |
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435 \item \isacommand {pr} (command), \hyperpage{16}, \hyperpage{100} |
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436 \item \isacommand {prefer} (command), \hyperpage{16}, \hyperpage{100} |
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437 \item prefix annotation, \hyperpage{56} |
|
438 \item primitive recursion, \see{recursion, primitive}{1} |
|
439 \item \isacommand {primrec} (command), \hyperpage{10}, \hyperpage{18}, |
|
440 \hyperpage{41}, 38--43 |
|
441 \item print mode, \bold{55} |
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442 \item \isacommand {print\_syntax} (command), \hyperpage{54} |
|
443 \item product type, \see{pairs and tuples}{1} |
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444 \item Proof General, \bold{7} |
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445 \item proof state, \hyperpage{12} |
|
446 \item proofs |
|
447 \subitem abandoning, \bold{13} |
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448 \subitem examples of failing, 87--89 |
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449 \item protocols |
|
450 \subitem security, 195--205 |
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451 |
|
452 \indexspace |
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453 |
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454 \item quantifiers, \hyperpage{6} |
|
455 \subitem and inductive definitions, 135--137 |
|
456 \subitem existential, 82 |
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457 \subitem for sets, 108 |
|
458 \subitem instantiating, \hyperpage{84} |
|
459 \subitem universal, 79--82 |
|
460 |
|
461 \indexspace |
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462 |
|
463 \item \isa {r_into_rtrancl} (theorem), \bold{112} |
|
464 \item \isa {r_into_trancl} (theorem), \bold{113} |
|
465 \item range |
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466 \subitem of a function, \hyperpage{111} |
|
467 \subitem of a relation, \hyperpage{112} |
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468 \item \isa {range} (symbol), \hyperpage{111} |
|
469 \item \isa {Range_iff} (theorem), \bold{112} |
|
470 \item \isa {Real} (theory), \hyperpage{155} |
|
471 \item \isa {real} (type), 154--155 |
|
472 \item real numbers, 154--155 |
|
473 \item \isacommand {recdef} (command), 47--52, \hyperpage{114}, |
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474 178--186 |
|
475 \subitem and numeric literals, \hyperpage{150} |
|
476 \item \isa {recdef_cong} (attribute), \hyperpage{182} |
|
477 \item \isa {recdef_simp} (attribute), \hyperpage{49} |
|
478 \item \isa {recdef_wf} (attribute), \hyperpage{180} |
|
479 \item \isacommand {record} (command), \hyperpage{159} |
|
480 \item records, 158--164 |
|
481 \subitem extensible, 160--161 |
|
482 \item recursion |
|
483 \subitem guarded, \hyperpage{183} |
|
484 \subitem primitive, \hyperpage{18} |
|
485 \subitem well-founded, \bold{179} |
|
486 \item recursion induction, 51--52 |
|
487 \item \isacommand {redo} (command), \hyperpage{16} |
|
488 \item reflexive and transitive closure, 112--114 |
|
489 \item reflexive transitive closure |
|
490 \subitem defining inductively, 132--135 |
|
491 \item \isa {rel_comp_def} (theorem), \bold{112} |
|
492 \item relations, 111--114 |
|
493 \subitem well-founded, 114--115 |
|
494 \item \isa {rename_tac} (method), 82--83 |
|
495 \item \isa {rev} (constant), \hyperpage{10}, 10--14, \hyperpage{34} |
|
496 \item rewrite rules, \bold{27} |
|
497 \subitem permutative, \bold{176} |
|
498 \item rewriting, \bold{27} |
|
499 \item \isa {rotate_tac} (method), \hyperpage{30} |
|
500 \item \isa {rtrancl_refl} (theorem), \bold{112} |
|
501 \item \isa {rtrancl_trans} (theorem), \bold{112} |
|
502 \item rule induction, 128--130 |
|
503 \item rule inversion, 130--131, 139--140 |
|
504 \item \isa {rule_format} (attribute), \hyperpage{187} |
|
505 \item \isa {rule_tac} (method), \hyperpage{76} |
|
506 \subitem and renaming, \hyperpage{83} |
|
507 |
|
508 \indexspace |
|
509 |
|
510 \item \isa {safe} (method), \hyperpage{91, 92} |
|
511 \item safe rules, \bold{90} |
|
512 \item \isacommand {sect} (command), \hyperpage{59} |
|
513 \item \isacommand {section} (command), \hyperpage{59} |
|
514 \item selector |
|
515 \subitem record, \hyperpage{159} |
|
516 \item session, \bold{58} |
|
517 \item \isa {set} (type), \hyperpage{5}, \hyperpage{105} |
|
518 \item set comprehensions, 107--108 |
|
519 \item \isa {set_ext} (theorem), \bold{106} |
|
520 \item sets, 105--109 |
|
521 \subitem finite, \hyperpage{109} |
|
522 \subitem notation for finite, \bold{107} |
|
523 \item settings, \see{flags}{1} |
|
524 \item \isa {show_brackets} (flag), \hyperpage{6} |
|
525 \item \isa {show_types} (flag), \hyperpage{5}, \hyperpage{16} |
|
526 \item \isa {simp} (attribute), \hyperpage{11}, \hyperpage{28} |
|
527 \item \isa {simp} (method), \bold{28} |
|
528 \item \isa {simp} del (attribute), \hyperpage{28} |
|
529 \item \isa {simp_all} (method), \hyperpage{29}, \hyperpage{38} |
|
530 \item simplification, 27--33, 175--178 |
|
531 \subitem of \isa{let}-expressions, \hyperpage{31} |
|
532 \subitem with definitions, \hyperpage{30} |
|
533 \subitem with/of assumptions, \hyperpage{29} |
|
534 \item simplification rule, 177--178 |
|
535 \item simplification rules, \hyperpage{28} |
|
536 \subitem adding and deleting, \hyperpage{29} |
|
537 \item \isa {simplified} (attribute), \hyperpage{93}, \hyperpage{96} |
|
538 \item \isa {size} (constant), \hyperpage{17} |
|
539 \item \isa {snd} (constant), \hyperpage{24} |
|
540 \item \isa {SOME} (symbol), \hyperpage{86} |
|
541 \item \texttt {SOME}, \bold{209} |
|
542 \item \isa {Some} (constant), \bold{24} |
|
543 \item \isa {some_equality} (theorem), \bold{86} |
|
544 \item \isa {someI} (theorem), \bold{86} |
|
545 \item \isa {someI2} (theorem), \bold{86} |
|
546 \item \isa {someI_ex} (theorem), \bold{87} |
|
547 \item sorts, \hyperpage{170} |
|
548 \item \isa {spec} (theorem), \bold{80} |
|
549 \item \isa {split} (attribute), \hyperpage{32} |
|
550 \item \isa {split} (constant), \hyperpage{156} |
|
551 \item \isa {split} (method), \hyperpage{31}, \hyperpage{156} |
|
552 \item \isa {split} (modifier), \hyperpage{32} |
|
553 \item split rule, \bold{32} |
|
554 \item \isa {split_if} (theorem), \hyperpage{32} |
|
555 \item \isa {split_if_asm} (theorem), \hyperpage{32} |
|
556 \item \isa {ssubst} (theorem), \bold{77} |
|
557 \item structural induction, \see{induction, structural}{1} |
|
558 \item subclasses, \hyperpage{164}, \hyperpage{169} |
|
559 \item subgoal numbering, \hyperpage{46} |
|
560 \item \isa {subgoal_tac} (method), \hyperpage{98} |
|
561 \item subgoals, \hyperpage{12} |
|
562 \item \isacommand {subsect} (command), \hyperpage{59} |
|
563 \item \isacommand {subsection} (command), \hyperpage{59} |
|
564 \item subset relation, \bold{106} |
|
565 \item \isa {subsetD} (theorem), \bold{106} |
|
566 \item \isa {subsetI} (theorem), \bold{106} |
|
567 \item \isa {subst} (method), \hyperpage{77} |
|
568 \item substitution, 77--79 |
|
569 \item \isacommand {subsubsect} (command), \hyperpage{59} |
|
570 \item \isacommand {subsubsection} (command), \hyperpage{59} |
|
571 \item \isa {Suc} (constant), \hyperpage{22} |
|
572 \item \isa {surj_def} (theorem), \bold{110} |
|
573 \item surjections, \hyperpage{110} |
|
574 \item \isa {sym} (theorem), \bold{94} |
|
575 \item symbols, \bold{54} |
|
576 \item syntax, \hyperpage{6}, \hyperpage{11} |
|
577 \item \isacommand {syntax} (command), \hyperpage{55} |
|
578 \item syntax (command), \hyperpage{56} |
|
579 \item syntax translations, \bold{56} |
|
580 |
|
581 \indexspace |
|
582 |
|
583 \item tacticals, 99 |
|
584 \item tactics, \hyperpage{12} |
|
585 \item \isacommand {term} (command), \hyperpage{16} |
|
586 \item term rewriting, \bold{27} |
|
587 \item termination, \see{functions, total}{1} |
|
588 \item terms, 5 |
|
589 \item text, \bold{61} |
|
590 \item text blocks, \bold{60} |
|
591 \item \isa {THE} (symbol), \hyperpage{85} |
|
592 \item \isa {the_equality} (theorem), \bold{85} |
|
593 \item \isa {THEN} (attribute), \bold{94}, \hyperpage{96}, |
|
594 \hyperpage{102} |
|
595 \item \isacommand {theorem} (command), \bold{11}, \hyperpage{13} |
|
596 \item theories, 4 |
|
597 \subitem abandoning, \bold{16} |
|
598 \item \isacommand {theory} (command), \hyperpage{16} |
|
599 \item theory files, \hyperpage{4} |
|
600 \item \isacommand {thm} (command), \hyperpage{16} |
|
601 \item \isa {tl} (constant), \hyperpage{17} |
|
602 \item \isa {ToyList} example, 9--14 |
|
603 \item \isa {trace_simp} (flag), \hyperpage{33} |
|
604 \item tracing the simplifier, \bold{33} |
|
605 \item \isa {trancl_trans} (theorem), \bold{113} |
|
606 \item transition systems, \hyperpage{117} |
|
607 \item \isacommand {translations} (command), \hyperpage{56} |
|
608 \item tries, 44--46 |
|
609 \item \isa {True} (constant), \hyperpage{5} |
|
610 \item \isa {truncate} (constant), \hyperpage{163} |
|
611 \item tuples, \see{pairs and tuples}{1} |
|
612 \item txt, \bold{61} |
|
613 \item \isacommand {typ} (command), \hyperpage{16} |
|
614 \item type constraints, \bold{6} |
|
615 \item type constructors, \hyperpage{5} |
|
616 \item type inference, \bold{5} |
|
617 \item type synonyms, \hyperpage{25} |
|
618 \item type variables, \hyperpage{5} |
|
619 \item \isacommand {typedecl} (command), \hyperpage{117}, |
|
620 \hyperpage{171} |
|
621 \item \isacommand {typedef} (command), 171--174 |
|
622 \item types, 4--5 |
|
623 \subitem declaring, 171 |
|
624 \subitem defining, 171--174 |
|
625 \item \isacommand {types} (command), \hyperpage{25} |
|
626 |
|
627 \indexspace |
|
628 |
|
629 \item Ullman, J. D., \hyperpage{145} |
|
630 \item \texttt {UN}, \bold{209} |
|
631 \item \texttt {Un}, \bold{209} |
|
632 \item \isa {UN_E} (theorem), \bold{108} |
|
633 \item \isa {UN_I} (theorem), \bold{108} |
|
634 \item \isa {UN_iff} (theorem), \bold{108} |
|
635 \item \isa {Un_subset_iff} (theorem), \bold{106} |
|
636 \item \isacommand {undo} (command), \hyperpage{16} |
|
637 \item \isa {unfold} (method), \bold{31} |
|
638 \item unification, 76--79 |
|
639 \item \isa {UNION} (constant), \hyperpage{109} |
|
640 \item \texttt {Union}, \bold{209} |
|
641 \item union |
|
642 \subitem indexed, \hyperpage{108} |
|
643 \item \isa {Union_iff} (theorem), \bold{108} |
|
644 \item \isa {unit} (type), \hyperpage{24} |
|
645 \item unknowns, \hyperpage{7}, \bold{68} |
|
646 \item unsafe rules, \bold{90} |
|
647 \item update |
|
648 \subitem record, \hyperpage{159} |
|
649 \item updating a function, \bold{109} |
|
650 |
|
651 \indexspace |
|
652 |
|
653 \item variables, 7 |
|
654 \subitem schematic, \hyperpage{7} |
|
655 \subitem type, \hyperpage{5} |
|
656 \item \isa {vimage_def} (theorem), \bold{111} |
|
657 |
|
658 \indexspace |
|
659 |
|
660 \item Wenzel, Markus, \hyperpage{vii} |
|
661 \item \isa {wf_induct} (theorem), \bold{115} |
|
662 \item \isa {wf_inv_image} (theorem), \bold{115} |
|
663 \item \isa {wf_less_than} (theorem), \bold{114} |
|
664 \item \isa {wf_lex_prod} (theorem), \bold{115} |
|
665 \item \isa {wf_measure} (theorem), \bold{115} |
|
666 \item \isa {wf_subset} (theorem), \hyperpage{180} |
|
667 \item \isa {while} (constant), \hyperpage{185} |
|
668 \item \isa {While_Combinator} (theory), \hyperpage{185} |
|
669 \item \isa {while_rule} (theorem), \hyperpage{185} |
|
670 |
|
671 \indexspace |
|
672 |
|
673 \item \isa {zadd_ac} (theorems), \hyperpage{153} |
|
674 \item \isa {zmult_ac} (theorems), \hyperpage{153} |
|
675 |
|
676 \end{theindex} |