1 \begin{theindex} |
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2 |
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3 \item {\tt !} symbol, 4, 6, 13, 14, 26 |
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4 \item {\tt[]} symbol, 26 |
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5 \item {\tt\#} symbol, 26 |
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6 \item {\tt\&} symbol, 4 |
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7 \item {\tt *} symbol, 5, 23 |
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8 \item {\tt *} type, 21 |
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9 \item {\tt +} symbol, 5, 23 |
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10 \item {\tt +} type, 21 |
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11 \item {\tt -} symbol, 5, 23 |
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12 \item {\tt -->} symbol, 4 |
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13 \item {\tt :} symbol, 12 |
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14 \item {\tt <} constant, 24 |
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15 \item {\tt <} symbol, 23 |
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16 \item {\tt <=} constant, 24 |
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17 \item {\tt <=} symbol, 12 |
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18 \item {\tt =} symbol, 4 |
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19 \item {\tt ?} symbol, 4, 6, 13, 14 |
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20 \item {\tt ?!} symbol, 4 |
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21 \item {\tt\at} symbol, 4, 26 |
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22 \item {\tt ``} symbol, 12 |
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23 \item \verb'{}' symbol, 12 |
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24 \item {\tt |} symbol, 4 |
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25 |
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26 \indexspace |
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27 |
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28 \item {\tt 0} constant, 23 |
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29 |
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30 \indexspace |
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31 |
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32 \item {\tt Addsplits}, \bold{20} |
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33 \item {\tt addsplits}, \bold{20}, 25, 37 |
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34 \item {\tt ALL} symbol, 4, 6, 13, 14 |
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35 \item {\tt All} constant, 4 |
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36 \item {\tt All_def} theorem, 8 |
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37 \item {\tt all_dupE} theorem, 10 |
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38 \item {\tt allE} theorem, 10 |
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39 \item {\tt allI} theorem, 10 |
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40 \item {\tt and_def} theorem, 8 |
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41 \item {\tt arg_cong} theorem, 9 |
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42 \item {\tt Arith} theory, 24 |
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43 \item {\tt arith_tac}, 25 |
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44 |
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45 \indexspace |
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46 |
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47 \item {\tt Ball} constant, 12, 14 |
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48 \item {\tt Ball_def} theorem, 15 |
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49 \item {\tt ballE} theorem, 16 |
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50 \item {\tt ballI} theorem, 16 |
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51 \item {\tt Bex} constant, 12, 14 |
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52 \item {\tt Bex_def} theorem, 15 |
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53 \item {\tt bexCI} theorem, 14, 16 |
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54 \item {\tt bexE} theorem, 16 |
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55 \item {\tt bexI} theorem, 14, 16 |
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56 \item {\textit {bool}} type, 5 |
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57 \item {\tt box_equals} theorem, 9, 11 |
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58 \item {\tt bspec} theorem, 16 |
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59 \item {\tt butlast} constant, 26 |
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60 |
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61 \indexspace |
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62 |
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63 \item {\tt case} symbol, 7, 24, 25, 37 |
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64 \item {\tt case_tac}, \bold{11} |
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65 \item {\tt ccontr} theorem, 10 |
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66 \item {\tt classical} theorem, 10 |
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67 \item {\tt coinductive}, 49--51 |
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68 \item {\tt Collect} constant, 12, 14 |
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69 \item {\tt Collect_mem_eq} theorem, 14, 15 |
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70 \item {\tt CollectD} theorem, 16, 54 |
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71 \item {\tt CollectE} theorem, 16 |
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72 \item {\tt CollectI} theorem, 16, 55 |
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73 \item {\tt Compl} constant, 12 |
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74 \item {\tt Compl_def} theorem, 15 |
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75 \item {\tt Compl_disjoint} theorem, 18 |
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76 \item {\tt Compl_Int} theorem, 18 |
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77 \item {\tt Compl_partition} theorem, 18 |
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78 \item {\tt Compl_Un} theorem, 18 |
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79 \item {\tt ComplD} theorem, 17 |
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80 \item {\tt ComplI} theorem, 17 |
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81 \item {\tt concat} constant, 26 |
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82 \item {\tt cong} theorem, 9 |
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83 \item {\tt conj_cong}, 19 |
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84 \item {\tt conjE} theorem, 9 |
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85 \item {\tt conjI} theorem, 9 |
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86 \item {\tt conjunct1} theorem, 9 |
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87 \item {\tt conjunct2} theorem, 9 |
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88 \item {\tt context}, 55 |
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89 |
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90 \indexspace |
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91 |
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92 \item {\tt datatype}, 34--42 |
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93 \item {\tt Delsplits}, \bold{20} |
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94 \item {\tt delsplits}, \bold{20} |
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95 \item {\tt disjCI} theorem, 10 |
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96 \item {\tt disjE} theorem, 9 |
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97 \item {\tt disjI1} theorem, 9 |
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98 \item {\tt disjI2} theorem, 9 |
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99 \item {\tt div} symbol, 23 |
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100 \item {\tt div_geq} theorem, 24 |
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101 \item {\tt div_less} theorem, 24 |
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102 \item {\tt Divides} theory, 24 |
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103 \item {\tt double_complement} theorem, 18 |
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104 \item {\tt drop} constant, 26 |
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105 \item {\tt dropWhile} constant, 26 |
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106 |
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107 \indexspace |
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108 |
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109 \item {\tt empty_def} theorem, 15 |
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110 \item {\tt emptyE} theorem, 17 |
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111 \item {\tt Eps} constant, 4, 6 |
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112 \item {\tt equalityCE} theorem, 14, 16, 54, 55 |
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113 \item {\tt equalityD1} theorem, 16 |
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114 \item {\tt equalityD2} theorem, 16 |
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115 \item {\tt equalityE} theorem, 16 |
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116 \item {\tt equalityI} theorem, 16 |
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117 \item {\tt EX} symbol, 4, 6, 13, 14 |
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118 \item {\tt Ex} constant, 4 |
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119 \item {\tt EX!} symbol, 4 |
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120 \item {\tt Ex1} constant, 4 |
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121 \item {\tt Ex1_def} theorem, 8 |
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122 \item {\tt ex1E} theorem, 10 |
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123 \item {\tt ex1I} theorem, 10 |
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124 \item {\tt Ex_def} theorem, 8 |
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125 \item {\tt exCI} theorem, 10 |
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126 \item {\tt excluded_middle} theorem, 10 |
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127 \item {\tt exE} theorem, 10 |
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128 \item {\tt exhaust_tac}, \bold{38} |
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129 \item {\tt exI} theorem, 10 |
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130 \item {\tt Exp} theory, 53 |
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131 \item {\tt ext} theorem, 7, 8 |
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132 |
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133 \indexspace |
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134 |
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135 \item {\tt False} constant, 4 |
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136 \item {\tt False_def} theorem, 8 |
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137 \item {\tt FalseE} theorem, 9 |
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138 \item {\tt filter} constant, 26 |
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139 \item {\tt foldl} constant, 26 |
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140 \item {\tt fst} constant, 21 |
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141 \item {\tt fst_conv} theorem, 21 |
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142 \item {\tt Fun} theory, 19 |
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143 \item {\textit {fun}} type, 5 |
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144 \item {\tt fun_cong} theorem, 9 |
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145 |
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146 \indexspace |
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147 |
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148 \item {\tt hd} constant, 26 |
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149 \item higher-order logic, 3--55 |
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150 \item {\tt HOL} theory, 3 |
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151 \item {\sc hol} system, 3, 6 |
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152 \item {\tt HOL_basic_ss}, \bold{19} |
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153 \item {\tt HOL_cs}, \bold{20} |
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154 \item {\tt HOL_quantifiers}, \bold{6}, 14 |
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155 \item {\tt HOL_ss}, \bold{19} |
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156 \item {\tt hyp_subst_tac}, 19 |
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157 |
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158 \indexspace |
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159 |
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160 \item {\tt If} constant, 4 |
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161 \item {\tt if_def} theorem, 8 |
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162 \item {\tt if_not_P} theorem, 10 |
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163 \item {\tt if_P} theorem, 10 |
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164 \item {\tt iff} theorem, 7, 8 |
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165 \item {\tt iffCE} theorem, 10, 14 |
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166 \item {\tt iffD1} theorem, 9 |
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167 \item {\tt iffD2} theorem, 9 |
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168 \item {\tt iffE} theorem, 9 |
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169 \item {\tt iffI} theorem, 9 |
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170 \item {\tt image_def} theorem, 15 |
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171 \item {\tt imageE} theorem, 17 |
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172 \item {\tt imageI} theorem, 17 |
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173 \item {\tt impCE} theorem, 10 |
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174 \item {\tt impE} theorem, 9 |
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175 \item {\tt impI} theorem, 7 |
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176 \item {\tt in} symbol, 5 |
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177 \item {\textit {ind}} type, 22 |
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178 \item {\tt induct_tac}, 24, \bold{38} |
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179 \item {\tt inductive}, 49--51 |
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180 \item {\tt inj} constant, 19 |
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181 \item {\tt inj_def} theorem, 19 |
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182 \item {\tt inj_Inl} theorem, 23 |
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183 \item {\tt inj_Inr} theorem, 23 |
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184 \item {\tt inj_on} constant, 19 |
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185 \item {\tt inj_on_def} theorem, 19 |
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186 \item {\tt inj_Suc} theorem, 23 |
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187 \item {\tt Inl} constant, 23 |
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188 \item {\tt Inl_not_Inr} theorem, 23 |
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189 \item {\tt Inr} constant, 23 |
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190 \item {\tt insert} constant, 12 |
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191 \item {\tt insert_def} theorem, 15 |
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192 \item {\tt insertE} theorem, 17 |
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193 \item {\tt insertI1} theorem, 17 |
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194 \item {\tt insertI2} theorem, 17 |
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195 \item {\tt INT} symbol, 12--14 |
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196 \item {\tt Int} symbol, 12 |
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197 \item {\tt Int_absorb} theorem, 18 |
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198 \item {\tt Int_assoc} theorem, 18 |
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199 \item {\tt Int_commute} theorem, 18 |
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200 \item {\tt INT_D} theorem, 17 |
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201 \item {\tt Int_def} theorem, 15 |
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202 \item {\tt INT_E} theorem, 17 |
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203 \item {\tt Int_greatest} theorem, 18 |
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204 \item {\tt INT_I} theorem, 17 |
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205 \item {\tt Int_Inter_image} theorem, 18 |
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206 \item {\tt Int_lower1} theorem, 18 |
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207 \item {\tt Int_lower2} theorem, 18 |
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208 \item {\tt Int_Un_distrib} theorem, 18 |
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209 \item {\tt Int_Union} theorem, 18 |
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210 \item {\tt IntD1} theorem, 17 |
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211 \item {\tt IntD2} theorem, 17 |
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212 \item {\tt IntE} theorem, 17 |
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213 \item {\tt INTER} constant, 12 |
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214 \item {\tt Inter} constant, 12 |
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215 \item {\tt INTER1} constant, 12 |
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216 \item {\tt INTER1_def} theorem, 15 |
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217 \item {\tt INTER_def} theorem, 15 |
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218 \item {\tt Inter_def} theorem, 15 |
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219 \item {\tt Inter_greatest} theorem, 18 |
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220 \item {\tt Inter_lower} theorem, 18 |
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221 \item {\tt Inter_Un_distrib} theorem, 18 |
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222 \item {\tt InterD} theorem, 17 |
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223 \item {\tt InterE} theorem, 17 |
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224 \item {\tt InterI} theorem, 17 |
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225 \item {\tt IntI} theorem, 17 |
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226 \item {\tt inv} constant, 19 |
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227 \item {\tt inv_def} theorem, 19 |
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228 |
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229 \indexspace |
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230 |
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231 \item {\tt last} constant, 26 |
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232 \item {\tt LEAST} constant, 5, 6, 24 |
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233 \item {\tt Least} constant, 4 |
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234 \item {\tt Least_def} theorem, 8 |
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235 \item {\tt length} constant, 26 |
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236 \item {\tt less_induct} theorem, 25 |
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237 \item {\tt Let} constant, 4, 7 |
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238 \item {\tt let} symbol, 5, 7 |
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239 \item {\tt Let_def} theorem, 7, 8 |
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240 \item {\tt LFilter} theory, 53 |
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241 \item {\tt List} theory, 25, 26 |
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242 \item {\textit{list}} type, 25 |
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243 \item {\tt LList} theory, 52 |
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244 |
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245 \indexspace |
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246 |
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247 \item {\tt map} constant, 26 |
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248 \item {\tt max} constant, 5, 24 |
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249 \item {\tt mem} symbol, 26 |
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250 \item {\tt mem_Collect_eq} theorem, 14, 15 |
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251 \item {\tt min} constant, 5, 24 |
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252 \item {\tt minus} class, 5 |
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253 \item {\tt mod} symbol, 23 |
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254 \item {\tt mod_geq} theorem, 24 |
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255 \item {\tt mod_less} theorem, 24 |
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256 \item {\tt mono} constant, 5 |
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257 \item {\tt mp} theorem, 7 |
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258 \item {\tt mutual_induct_tac}, \bold{38} |
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259 |
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260 \indexspace |
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261 |
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262 \item {\tt n_not_Suc_n} theorem, 23 |
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263 \item {\tt Nat} theory, 24 |
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264 \item {\textit {nat}} type, 23, 24 |
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265 \item {\textit{nat}} type, 22--25 |
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266 \item {\tt nat_induct} theorem, 23 |
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267 \item {\tt nat_rec} constant, 24 |
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268 \item {\tt NatDef} theory, 22 |
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269 \item {\tt Not} constant, 4 |
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270 \item {\tt not_def} theorem, 8 |
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271 \item {\tt not_sym} theorem, 9 |
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272 \item {\tt notE} theorem, 9 |
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273 \item {\tt notI} theorem, 9 |
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274 \item {\tt notnotD} theorem, 10 |
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275 \item {\tt null} constant, 26 |
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276 |
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277 \indexspace |
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278 |
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279 \item {\tt o} symbol, 4, 15 |
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280 \item {\tt o_def} theorem, 8 |
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281 \item {\tt of} symbol, 7 |
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282 \item {\tt or_def} theorem, 8 |
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283 \item {\tt Ord} theory, 5 |
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284 \item {\tt ord} class, 5, 6, 24 |
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285 \item {\tt order} class, 5, 24 |
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286 |
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287 \indexspace |
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288 |
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289 \item {\tt Pair} constant, 21 |
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290 \item {\tt Pair_eq} theorem, 21 |
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291 \item {\tt Pair_inject} theorem, 21 |
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292 \item {\tt PairE} theorem, 21 |
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293 \item {\tt plus} class, 5 |
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294 \item {\tt Pow} constant, 12 |
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295 \item {\tt Pow_def} theorem, 15 |
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296 \item {\tt PowD} theorem, 17 |
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297 \item {\tt PowI} theorem, 17 |
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298 \item {\tt primrec}, 43--46 |
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299 \item {\tt primrec} symbol, 24 |
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300 \item priorities, 1 |
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301 \item {\tt Prod} theory, 21 |
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302 \item {\tt prop_cs}, \bold{20} |
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303 |
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304 \indexspace |
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305 |
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306 \item {\tt qed_spec_mp}, 41 |
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307 |
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308 \indexspace |
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309 |
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310 \item {\tt range} constant, 12, 54 |
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311 \item {\tt range_def} theorem, 15 |
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312 \item {\tt rangeE} theorem, 17, 54 |
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313 \item {\tt rangeI} theorem, 17 |
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314 \item {\tt recdef}, 46--49 |
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315 \item {\tt record}, 31 |
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316 \item {\tt record_split_tac}, 33, 34 |
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317 \item recursion |
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318 \subitem general, 46--49 |
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319 \subitem primitive, 43--46 |
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320 \item recursive functions, \see{recursion}{42} |
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321 \item {\tt refl} theorem, 7 |
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322 \item {\tt res_inst_tac}, 6 |
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323 \item {\tt rev} constant, 26 |
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324 |
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325 \indexspace |
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326 |
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327 \item search |
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328 \subitem best-first, 55 |
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329 \item {\tt select_equality} theorem, 8, 10 |
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330 \item {\tt selectI} theorem, 7, 8 |
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331 \item {\tt Set} theory, 11, 14 |
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332 \item {\tt set} constant, 26 |
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333 \item {\tt set} type, 11 |
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334 \item {\tt set_diff_def} theorem, 15 |
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335 \item {\tt show_sorts}, 6 |
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336 \item {\tt show_types}, 6 |
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337 \item {\tt Sigma} constant, 21 |
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338 \item {\tt Sigma_def} theorem, 21 |
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339 \item {\tt SigmaE} theorem, 21 |
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340 \item {\tt SigmaI} theorem, 21 |
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341 \item simplification |
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342 \subitem of conjunctions, 19 |
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343 \item {\tt size} constant, 38 |
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344 \item {\tt snd} constant, 21 |
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345 \item {\tt snd_conv} theorem, 21 |
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346 \item {\tt spec} theorem, 10 |
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347 \item {\tt split} constant, 21 |
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348 \item {\tt split} theorem, 21 |
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349 \item {\tt split_all_tac}, \bold{22} |
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350 \item {\tt split_if} theorem, 10, 20 |
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351 \item {\tt split_list_case} theorem, 25 |
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352 \item {\tt split_split} theorem, 21 |
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353 \item {\tt split_sum_case} theorem, 23 |
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354 \item {\tt ssubst} theorem, 9, 11 |
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355 \item {\tt stac}, \bold{19} |
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356 \item {\tt strip_tac}, \bold{11} |
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357 \item {\tt subset_def} theorem, 15 |
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358 \item {\tt subset_refl} theorem, 16 |
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359 \item {\tt subset_trans} theorem, 16 |
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360 \item {\tt subsetCE} theorem, 14, 16 |
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361 \item {\tt subsetD} theorem, 14, 16 |
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362 \item {\tt subsetI} theorem, 16 |
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363 \item {\tt subst} theorem, 7 |
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364 \item {\tt Suc} constant, 23 |
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365 \item {\tt Suc_not_Zero} theorem, 23 |
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366 \item {\tt Sum} theory, 22 |
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367 \item {\tt sum_case} constant, 23 |
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368 \item {\tt sum_case_Inl} theorem, 23 |
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369 \item {\tt sum_case_Inr} theorem, 23 |
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370 \item {\tt sumE} theorem, 23 |
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371 \item {\tt surj} constant, 15, 19 |
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372 \item {\tt surj_def} theorem, 19 |
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373 \item {\tt surjective_pairing} theorem, 21 |
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374 \item {\tt surjective_sum} theorem, 23 |
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375 \item {\tt swap} theorem, 10 |
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376 \item {\tt swap_res_tac}, 55 |
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377 \item {\tt sym} theorem, 9 |
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378 |
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379 \indexspace |
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380 |
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381 \item {\tt take} constant, 26 |
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382 \item {\tt takeWhile} constant, 26 |
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383 \item {\tt term} class, 5 |
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384 \item {\tt times} class, 5 |
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385 \item {\tt tl} constant, 26 |
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386 \item tracing |
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387 \subitem of unification, 6 |
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388 \item {\tt trans} theorem, 9 |
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389 \item {\tt True} constant, 4 |
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390 \item {\tt True_def} theorem, 8 |
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391 \item {\tt True_or_False} theorem, 7, 8 |
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392 \item {\tt TrueI} theorem, 9 |
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393 \item {\tt Trueprop} constant, 4 |
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394 \item type definition, \bold{28} |
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395 \item {\tt typedef}, 25 |
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396 |
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397 \indexspace |
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398 |
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399 \item {\tt UN} symbol, 12--14 |
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400 \item {\tt Un} symbol, 12 |
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401 \item {\tt Un1} theorem, 14 |
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402 \item {\tt Un2} theorem, 14 |
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403 \item {\tt Un_absorb} theorem, 18 |
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404 \item {\tt Un_assoc} theorem, 18 |
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405 \item {\tt Un_commute} theorem, 18 |
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406 \item {\tt Un_def} theorem, 15 |
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407 \item {\tt UN_E} theorem, 17 |
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408 \item {\tt UN_I} theorem, 17 |
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409 \item {\tt Un_Int_distrib} theorem, 18 |
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410 \item {\tt Un_Inter} theorem, 18 |
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411 \item {\tt Un_least} theorem, 18 |
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412 \item {\tt Un_Union_image} theorem, 18 |
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413 \item {\tt Un_upper1} theorem, 18 |
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414 \item {\tt Un_upper2} theorem, 18 |
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415 \item {\tt UnCI} theorem, 14, 17 |
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416 \item {\tt UnE} theorem, 17 |
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417 \item {\tt UnI1} theorem, 17 |
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418 \item {\tt UnI2} theorem, 17 |
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419 \item unification |
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420 \subitem incompleteness of, 6 |
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421 \item {\tt Unify.trace_types}, 6 |
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422 \item {\tt UNION} constant, 12 |
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423 \item {\tt Union} constant, 12 |
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424 \item {\tt UNION1} constant, 12 |
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425 \item {\tt UNION1_def} theorem, 15 |
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426 \item {\tt UNION_def} theorem, 15 |
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427 \item {\tt Union_def} theorem, 15 |
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428 \item {\tt Union_least} theorem, 18 |
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429 \item {\tt Union_Un_distrib} theorem, 18 |
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430 \item {\tt Union_upper} theorem, 18 |
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431 \item {\tt UnionE} theorem, 17 |
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432 \item {\tt UnionI} theorem, 17 |
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433 \item {\tt unit_eq} theorem, 22 |
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434 |
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435 \indexspace |
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436 |
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437 \item {\tt ZF} theory, 3 |
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438 |
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439 \end{theindex} |
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