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1 (* Title: HOLCF/lift1.ML |
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2 ID: $Id$ |
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3 Author: Franz Regensburger |
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4 Copyright 1993 Technische Universitaet Muenchen |
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5 *) |
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6 |
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7 open Lift1; |
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8 |
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9 val Exh_Lift = prove_goalw Lift1.thy [UU_lift_def,Iup_def ] |
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10 "z = UU_lift | (? x. z = Iup(x))" |
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11 (fn prems => |
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12 [ |
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13 (rtac (Rep_Lift_inverse RS subst) 1), |
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14 (res_inst_tac [("s","Rep_Lift(z)")] sumE 1), |
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15 (rtac disjI1 1), |
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16 (res_inst_tac [("f","Abs_Lift")] arg_cong 1), |
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17 (rtac (unique_void2 RS subst) 1), |
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18 (atac 1), |
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19 (rtac disjI2 1), |
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20 (rtac exI 1), |
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21 (res_inst_tac [("f","Abs_Lift")] arg_cong 1), |
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22 (atac 1) |
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23 ]); |
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24 |
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25 val inj_Abs_Lift = prove_goal Lift1.thy "inj(Abs_Lift)" |
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26 (fn prems => |
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27 [ |
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28 (rtac inj_inverseI 1), |
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29 (rtac Abs_Lift_inverse 1) |
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30 ]); |
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31 |
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32 val inj_Rep_Lift = prove_goal Lift1.thy "inj(Rep_Lift)" |
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33 (fn prems => |
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34 [ |
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35 (rtac inj_inverseI 1), |
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36 (rtac Rep_Lift_inverse 1) |
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37 ]); |
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38 |
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39 val inject_Iup = prove_goalw Lift1.thy [Iup_def] "Iup(x)=Iup(y) ==> x=y" |
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40 (fn prems => |
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41 [ |
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42 (cut_facts_tac prems 1), |
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43 (rtac (inj_Inr RS injD) 1), |
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44 (rtac (inj_Abs_Lift RS injD) 1), |
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45 (atac 1) |
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46 ]); |
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47 |
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48 val defined_Iup=prove_goalw Lift1.thy [Iup_def,UU_lift_def] "~ Iup(x)=UU_lift" |
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49 (fn prems => |
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50 [ |
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51 (rtac notI 1), |
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52 (rtac notE 1), |
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53 (rtac Inl_not_Inr 1), |
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54 (rtac sym 1), |
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55 (etac (inj_Abs_Lift RS injD) 1) |
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56 ]); |
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57 |
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58 |
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59 val liftE = prove_goal Lift1.thy |
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60 "[| p=UU_lift ==> Q; !!x. p=Iup(x)==>Q|] ==>Q" |
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61 (fn prems => |
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62 [ |
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63 (rtac (Exh_Lift RS disjE) 1), |
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64 (eresolve_tac prems 1), |
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65 (etac exE 1), |
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66 (eresolve_tac prems 1) |
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67 ]); |
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68 |
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69 val Ilift1 = prove_goalw Lift1.thy [Ilift_def,UU_lift_def] |
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70 "Ilift(f)(UU_lift)=UU" |
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71 (fn prems => |
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72 [ |
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73 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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74 (rtac (case_Inl RS ssubst) 1), |
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75 (rtac refl 1) |
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76 ]); |
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77 |
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78 val Ilift2 = prove_goalw Lift1.thy [Ilift_def,Iup_def] |
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79 "Ilift(f)(Iup(x))=f[x]" |
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80 (fn prems => |
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81 [ |
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82 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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83 (rtac (case_Inr RS ssubst) 1), |
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84 (rtac refl 1) |
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85 ]); |
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86 |
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87 val Lift_ss = Cfun_ss addsimps [Ilift1,Ilift2]; |
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88 |
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89 val less_lift1a = prove_goalw Lift1.thy [less_lift_def,UU_lift_def] |
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90 "less_lift(UU_lift)(z)" |
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91 (fn prems => |
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92 [ |
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93 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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94 (rtac (case_Inl RS ssubst) 1), |
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95 (rtac TrueI 1) |
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96 ]); |
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97 |
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98 val less_lift1b = prove_goalw Lift1.thy [Iup_def,less_lift_def,UU_lift_def] |
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99 "~less_lift(Iup(x),UU_lift)" |
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100 (fn prems => |
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101 [ |
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102 (rtac notI 1), |
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103 (rtac iffD1 1), |
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104 (atac 2), |
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105 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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106 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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107 (rtac (case_Inr RS ssubst) 1), |
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108 (rtac (case_Inl RS ssubst) 1), |
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109 (rtac refl 1) |
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110 ]); |
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111 |
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112 val less_lift1c = prove_goalw Lift1.thy [Iup_def,less_lift_def,UU_lift_def] |
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113 "less_lift(Iup(x),Iup(y))=(x<<y)" |
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114 (fn prems => |
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115 [ |
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116 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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117 (rtac (Abs_Lift_inverse RS ssubst) 1), |
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118 (rtac (case_Inr RS ssubst) 1), |
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119 (rtac (case_Inr RS ssubst) 1), |
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120 (rtac refl 1) |
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121 ]); |
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122 |
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123 |
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124 val refl_less_lift = prove_goal Lift1.thy "less_lift(p,p)" |
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125 (fn prems => |
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126 [ |
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127 (res_inst_tac [("p","p")] liftE 1), |
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128 (hyp_subst_tac 1), |
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129 (rtac less_lift1a 1), |
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130 (hyp_subst_tac 1), |
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131 (rtac (less_lift1c RS iffD2) 1), |
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132 (rtac refl_less 1) |
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133 ]); |
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134 |
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135 val antisym_less_lift = prove_goal Lift1.thy |
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136 "[|less_lift(p1,p2);less_lift(p2,p1)|] ==> p1=p2" |
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137 (fn prems => |
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138 [ |
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139 (cut_facts_tac prems 1), |
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140 (res_inst_tac [("p","p1")] liftE 1), |
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141 (hyp_subst_tac 1), |
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142 (res_inst_tac [("p","p2")] liftE 1), |
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143 (hyp_subst_tac 1), |
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144 (rtac refl 1), |
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145 (hyp_subst_tac 1), |
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146 (res_inst_tac [("P","less_lift(Iup(x),UU_lift)")] notE 1), |
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147 (rtac less_lift1b 1), |
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148 (atac 1), |
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149 (hyp_subst_tac 1), |
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150 (res_inst_tac [("p","p2")] liftE 1), |
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151 (hyp_subst_tac 1), |
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152 (res_inst_tac [("P","less_lift(Iup(x),UU_lift)")] notE 1), |
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153 (rtac less_lift1b 1), |
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154 (atac 1), |
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155 (hyp_subst_tac 1), |
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156 (rtac arg_cong 1), |
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157 (rtac antisym_less 1), |
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158 (etac (less_lift1c RS iffD1) 1), |
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159 (etac (less_lift1c RS iffD1) 1) |
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160 ]); |
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161 |
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162 val trans_less_lift = prove_goal Lift1.thy |
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163 "[|less_lift(p1,p2);less_lift(p2,p3)|] ==> less_lift(p1,p3)" |
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164 (fn prems => |
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165 [ |
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166 (cut_facts_tac prems 1), |
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167 (res_inst_tac [("p","p1")] liftE 1), |
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168 (hyp_subst_tac 1), |
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169 (rtac less_lift1a 1), |
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170 (hyp_subst_tac 1), |
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171 (res_inst_tac [("p","p2")] liftE 1), |
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172 (hyp_subst_tac 1), |
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173 (rtac notE 1), |
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174 (rtac less_lift1b 1), |
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175 (atac 1), |
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176 (hyp_subst_tac 1), |
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177 (res_inst_tac [("p","p3")] liftE 1), |
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178 (hyp_subst_tac 1), |
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179 (rtac notE 1), |
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180 (rtac less_lift1b 1), |
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181 (atac 1), |
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182 (hyp_subst_tac 1), |
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183 (rtac (less_lift1c RS iffD2) 1), |
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184 (rtac trans_less 1), |
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185 (etac (less_lift1c RS iffD1) 1), |
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186 (etac (less_lift1c RS iffD1) 1) |
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187 ]); |
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188 |