author | clasohm |
Tue, 24 Oct 1995 14:45:35 +0100 | |
changeset 1294 | 1358dc040edb |
parent 1277 | caef3601c0b2 |
child 1461 | 6bcb44e4d6e5 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/ssum2.ML |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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|
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Lemmas for ssum2.thy |
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*) |
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|
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open Ssum2; |
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|
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(* ------------------------------------------------------------------------ *) |
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(* access to less_ssum in class po *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "less_ssum3a" Ssum2.thy |
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"(Isinl(x) << Isinl(y)) = (x << y)" |
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(fn prems => |
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[ |
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(rtac (inst_ssum_po RS ssubst) 1), |
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(rtac less_ssum2a 1) |
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]); |
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qed_goal "less_ssum3b" Ssum2.thy |
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"(Isinr(x) << Isinr(y)) = (x << y)" |
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(fn prems => |
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[ |
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(rtac (inst_ssum_po RS ssubst) 1), |
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(rtac less_ssum2b 1) |
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]); |
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qed_goal "less_ssum3c" Ssum2.thy |
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"(Isinl(x) << Isinr(y)) = (x = UU)" |
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(fn prems => |
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[ |
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(rtac (inst_ssum_po RS ssubst) 1), |
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(rtac less_ssum2c 1) |
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]); |
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qed_goal "less_ssum3d" Ssum2.thy |
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"(Isinr(x) << Isinl(y)) = (x = UU)" |
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(fn prems => |
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[ |
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(rtac (inst_ssum_po RS ssubst) 1), |
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(rtac less_ssum2d 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* type ssum ++ is pointed *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "minimal_ssum" Ssum2.thy "Isinl(UU) << s" |
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(fn prems => |
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[ |
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(res_inst_tac [("p","s")] IssumE2 1), |
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(hyp_subst_tac 1), |
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(rtac (less_ssum3a RS iffD2) 1), |
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(rtac minimal 1), |
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(hyp_subst_tac 1), |
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(rtac (strict_IsinlIsinr RS ssubst) 1), |
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(rtac (less_ssum3b RS iffD2) 1), |
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(rtac minimal 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* Isinl, Isinr are monotone *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "monofun_Isinl" Ssum2.thy [monofun] "monofun(Isinl)" |
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(fn prems => |
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[ |
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(strip_tac 1), |
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(etac (less_ssum3a RS iffD2) 1) |
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qed_goalw "monofun_Isinr" Ssum2.thy [monofun] "monofun(Isinr)" |
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(fn prems => |
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[ |
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(strip_tac 1), |
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(etac (less_ssum3b RS iffD2) 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* Iwhen is monotone in all arguments *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "monofun_Iwhen1" Ssum2.thy [monofun] "monofun(Iwhen)" |
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(fn prems => |
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[ |
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(strip_tac 1), |
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(strip_tac 1), |
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(res_inst_tac [("p","xb")] IssumE 1), |
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(hyp_subst_tac 1), |
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(asm_simp_tac Ssum0_ss 1), |
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(etac monofun_cfun_fun 1), |
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qed_goalw "monofun_Iwhen2" Ssum2.thy [monofun] "monofun(Iwhen(f))" |
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[ |
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(strip_tac 1), |
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(etac monofun_cfun_fun 1) |
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qed_goalw "monofun_Iwhen3" Ssum2.thy [monofun] "monofun(Iwhen(f)(g))" |
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[ |
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(res_inst_tac [("P","xa=UU")] notE 1), |
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(atac 1), |
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(rtac UU_I 1), |
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(atac 1), |
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136 |
(hyp_subst_tac 1), |
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137 |
(asm_simp_tac Ssum0_ss 1), |
243
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138 |
(rtac monofun_cfun_arg 1), |
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139 |
(etac (less_ssum3a RS iffD1) 1), |
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140 |
(hyp_subst_tac 1), |
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141 |
(res_inst_tac [("s","UU"),("t","xa")] subst 1), |
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142 |
(etac (less_ssum3c RS iffD1 RS sym) 1), |
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143 |
(asm_simp_tac Ssum0_ss 1), |
243
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144 |
(hyp_subst_tac 1), |
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145 |
(res_inst_tac [("p","y")] IssumE 1), |
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146 |
(hyp_subst_tac 1), |
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147 |
(res_inst_tac [("s","UU"),("t","ya")] subst 1), |
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148 |
(etac (less_ssum3d RS iffD1 RS sym) 1), |
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149 |
(asm_simp_tac Ssum0_ss 1), |
243
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150 |
(hyp_subst_tac 1), |
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151 |
(res_inst_tac [("s","UU"),("t","ya")] subst 1), |
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152 |
(etac (less_ssum3d RS iffD1 RS sym) 1), |
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153 |
(asm_simp_tac Ssum0_ss 1), |
243
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154 |
(hyp_subst_tac 1), |
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155 |
(asm_simp_tac Ssum0_ss 1), |
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156 |
(rtac monofun_cfun_arg 1), |
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157 |
(etac (less_ssum3b RS iffD1) 1) |
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158 |
]); |
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159 |
|
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160 |
|
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161 |
|
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162 |
|
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163 |
(* ------------------------------------------------------------------------ *) |
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164 |
(* some kind of exhaustion rules for chains in 'a ++ 'b *) |
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165 |
(* ------------------------------------------------------------------------ *) |
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166 |
|
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167 |
|
892 | 168 |
qed_goal "ssum_lemma1" Ssum2.thy |
1168
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169 |
"[|~(!i.? x.Y(i::nat)=Isinl(x))|] ==> (? i.! x.Y(i)~=Isinl(x))" |
243
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(fn prems => |
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171 |
[ |
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172 |
(cut_facts_tac prems 1), |
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173 |
(fast_tac HOL_cs 1) |
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174 |
]); |
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175 |
|
892 | 176 |
qed_goal "ssum_lemma2" Ssum2.thy |
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177 |
"[|(? i.!x.(Y::nat => 'a++'b)(i::nat)~=Isinl(x::'a))|] ==>\ |
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178 |
\ (? i y. (Y::nat => 'a++'b)(i::nat)=Isinr(y::'b) & y~=UU)" |
243
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179 |
(fn prems => |
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180 |
[ |
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181 |
(cut_facts_tac prems 1), |
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182 |
(etac exE 1), |
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183 |
(res_inst_tac [("p","Y(i)")] IssumE 1), |
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184 |
(dtac spec 1), |
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185 |
(contr_tac 1), |
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186 |
(dtac spec 1), |
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187 |
(contr_tac 1), |
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188 |
(fast_tac HOL_cs 1) |
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189 |
]); |
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190 |
|
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191 |
|
892 | 192 |
qed_goal "ssum_lemma3" Ssum2.thy |
961
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|
193 |
"[|is_chain(Y);(? i x. Y(i)=Isinr(x::'b) & (x::'b)~=UU)|] ==>\ |
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|
194 |
\ (!i.? y.Y(i)=Isinr(y))" |
243
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195 |
(fn prems => |
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196 |
[ |
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197 |
(cut_facts_tac prems 1), |
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198 |
(etac exE 1), |
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|
199 |
(etac exE 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
200 |
(rtac allI 1), |
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|
201 |
(res_inst_tac [("p","Y(ia)")] IssumE 1), |
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202 |
(rtac exI 1), |
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|
203 |
(rtac trans 1), |
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204 |
(rtac strict_IsinlIsinr 2), |
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|
205 |
(atac 1), |
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|
206 |
(etac exI 2), |
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|
207 |
(etac conjE 1), |
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|
208 |
(res_inst_tac [("m","i"),("n","ia")] nat_less_cases 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
209 |
(hyp_subst_tac 2), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
210 |
(etac exI 2), |
961
932784dfa671
Removed bugs which occurred due to new generation mechanism for type variables
regensbu
parents:
892
diff
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|
211 |
(eres_inst_tac [("P","x=UU")] notE 1), |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
212 |
(rtac (less_ssum3d RS iffD1) 1), |
961
932784dfa671
Removed bugs which occurred due to new generation mechanism for type variables
regensbu
parents:
892
diff
changeset
|
213 |
(eres_inst_tac [("s","Y(i)"),("t","Isinr(x)::'a++'b")] subst 1), |
932784dfa671
Removed bugs which occurred due to new generation mechanism for type variables
regensbu
parents:
892
diff
changeset
|
214 |
(eres_inst_tac [("s","Y(ia)"),("t","Isinl(xa)::'a++'b")] subst 1), |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
215 |
(etac (chain_mono RS mp) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
216 |
(atac 1), |
961
932784dfa671
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regensbu
parents:
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diff
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|
217 |
(eres_inst_tac [("P","xa=UU")] notE 1), |
243
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|
218 |
(rtac (less_ssum3c RS iffD1) 1), |
961
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parents:
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diff
changeset
|
219 |
(eres_inst_tac [("s","Y(i)"),("t","Isinr(x)::'a++'b")] subst 1), |
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regensbu
parents:
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|
220 |
(eres_inst_tac [("s","Y(ia)"),("t","Isinl(xa)::'a++'b")] subst 1), |
243
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221 |
(etac (chain_mono RS mp) 1), |
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|
222 |
(atac 1) |
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|
223 |
]); |
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|
224 |
|
892 | 225 |
qed_goal "ssum_lemma4" Ssum2.thy |
243
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226 |
"is_chain(Y) ==> (!i.? x.Y(i)=Isinl(x))|(!i.? y.Y(i)=Isinr(y))" |
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227 |
(fn prems => |
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|
228 |
[ |
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229 |
(cut_facts_tac prems 1), |
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230 |
(rtac classical2 1), |
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231 |
(etac disjI1 1), |
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|
232 |
(rtac disjI2 1), |
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|
233 |
(etac ssum_lemma3 1), |
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|
234 |
(rtac ssum_lemma2 1), |
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|
235 |
(etac ssum_lemma1 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
236 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
237 |
|
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238 |
|
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239 |
(* ------------------------------------------------------------------------ *) |
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|
240 |
(* restricted surjectivity of Isinl *) |
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|
241 |
(* ------------------------------------------------------------------------ *) |
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|
242 |
|
892 | 243 |
qed_goal "ssum_lemma5" Ssum2.thy |
243
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|
244 |
"z=Isinl(x)==> Isinl((Iwhen (LAM x.x) (LAM y.UU))(z)) = z" |
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|
245 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
246 |
[ |
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247 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
248 |
(hyp_subst_tac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
249 |
(res_inst_tac [("Q","x=UU")] classical2 1), |
1277
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corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
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|
250 |
(asm_simp_tac Ssum0_ss 1), |
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corrected some errors that occurred after introduction of local simpsets
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251 |
(asm_simp_tac Ssum0_ss 1) |
243
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252 |
]); |
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|
253 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
254 |
(* ------------------------------------------------------------------------ *) |
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|
255 |
(* restricted surjectivity of Isinr *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
256 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
257 |
|
892 | 258 |
qed_goal "ssum_lemma6" Ssum2.thy |
243
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|
259 |
"z=Isinr(x)==> Isinr((Iwhen (LAM y.UU) (LAM x.x))(z)) = z" |
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260 |
(fn prems => |
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|
261 |
[ |
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|
262 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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263 |
(hyp_subst_tac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
264 |
(res_inst_tac [("Q","x=UU")] classical2 1), |
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1267
diff
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|
265 |
(asm_simp_tac Ssum0_ss 1), |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
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|
266 |
(asm_simp_tac Ssum0_ss 1) |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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267 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
268 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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269 |
(* ------------------------------------------------------------------------ *) |
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270 |
(* technical lemmas *) |
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271 |
(* ------------------------------------------------------------------------ *) |
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272 |
|
892 | 273 |
qed_goal "ssum_lemma7" Ssum2.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
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parents:
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|
274 |
"[|Isinl(x) << z; x~=UU|] ==> ? y.z=Isinl(y) & y~=UU" |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
275 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
276 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
277 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
278 |
(res_inst_tac [("p","z")] IssumE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
279 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
280 |
(etac notE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
281 |
(rtac antisym_less 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
282 |
(etac (less_ssum3a RS iffD1) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
283 |
(rtac minimal 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
284 |
(fast_tac HOL_cs 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
285 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
286 |
(rtac notE 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
287 |
(etac (less_ssum3c RS iffD1) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
288 |
(atac 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
289 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
290 |
|
892 | 291 |
qed_goal "ssum_lemma8" Ssum2.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
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|
292 |
"[|Isinr(x) << z; x~=UU|] ==> ? y.z=Isinr(y) & y~=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
293 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
294 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
295 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
296 |
(res_inst_tac [("p","z")] IssumE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
297 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
298 |
(etac notE 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
299 |
(etac (less_ssum3d RS iffD1) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
300 |
(hyp_subst_tac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
301 |
(rtac notE 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
302 |
(etac (less_ssum3d RS iffD1) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
303 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
304 |
(fast_tac HOL_cs 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
305 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
306 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
307 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
308 |
(* the type 'a ++ 'b is a cpo in three steps *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
309 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
310 |
|
892 | 311 |
qed_goal "lub_ssum1a" Ssum2.thy |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
312 |
"[|is_chain(Y);(!i.? x.Y(i)=Isinl(x))|] ==>\ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
313 |
\ range(Y) <<|\ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
314 |
\ Isinl(lub(range(%i.(Iwhen (LAM x.x) (LAM y.UU))(Y i))))" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
315 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
316 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
317 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
318 |
(rtac is_lubI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
319 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
320 |
(rtac ub_rangeI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
321 |
(rtac allI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
322 |
(etac allE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
323 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
324 |
(res_inst_tac [("t","Y(i)")] (ssum_lemma5 RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
325 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
326 |
(rtac (monofun_Isinl RS monofunE RS spec RS spec RS mp) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
327 |
(rtac is_ub_thelub 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
328 |
(etac (monofun_Iwhen3 RS ch2ch_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
329 |
(strip_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
330 |
(res_inst_tac [("p","u")] IssumE2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
331 |
(res_inst_tac [("t","u")] (ssum_lemma5 RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
332 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
333 |
(rtac (monofun_Isinl RS monofunE RS spec RS spec RS mp) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
334 |
(rtac is_lub_thelub 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
335 |
(etac (monofun_Iwhen3 RS ch2ch_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
336 |
(etac (monofun_Iwhen3 RS ub2ub_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
337 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
338 |
(rtac (less_ssum3c RS iffD2) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
339 |
(rtac chain_UU_I_inverse 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
340 |
(rtac allI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
341 |
(res_inst_tac [("p","Y(i)")] IssumE 1), |
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1267
diff
changeset
|
342 |
(asm_simp_tac Ssum0_ss 1), |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1267
diff
changeset
|
343 |
(asm_simp_tac Ssum0_ss 2), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
344 |
(etac notE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
345 |
(rtac (less_ssum3c RS iffD1) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
346 |
(res_inst_tac [("t","Isinl(x)")] subst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
347 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
348 |
(etac (ub_rangeE RS spec) 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
349 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
350 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
351 |
|
892 | 352 |
qed_goal "lub_ssum1b" Ssum2.thy |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
353 |
"[|is_chain(Y);(!i.? x.Y(i)=Isinr(x))|] ==>\ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
354 |
\ range(Y) <<|\ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
355 |
\ Isinr(lub(range(%i.(Iwhen (LAM y.UU) (LAM x.x))(Y i))))" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
356 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
357 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
358 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
359 |
(rtac is_lubI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
360 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
361 |
(rtac ub_rangeI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
362 |
(rtac allI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
363 |
(etac allE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
364 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
365 |
(res_inst_tac [("t","Y(i)")] (ssum_lemma6 RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
366 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
367 |
(rtac (monofun_Isinr RS monofunE RS spec RS spec RS mp) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
368 |
(rtac is_ub_thelub 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
369 |
(etac (monofun_Iwhen3 RS ch2ch_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
370 |
(strip_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
371 |
(res_inst_tac [("p","u")] IssumE2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
372 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
373 |
(rtac (less_ssum3d RS iffD2) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
374 |
(rtac chain_UU_I_inverse 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
375 |
(rtac allI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
376 |
(res_inst_tac [("p","Y(i)")] IssumE 1), |
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1267
diff
changeset
|
377 |
(asm_simp_tac Ssum0_ss 1), |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1267
diff
changeset
|
378 |
(asm_simp_tac Ssum0_ss 1), |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1267
diff
changeset
|
379 |
(etac notE 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
380 |
(rtac (less_ssum3d RS iffD1) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
381 |
(res_inst_tac [("t","Isinr(y)")] subst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
382 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
383 |
(etac (ub_rangeE RS spec) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
384 |
(res_inst_tac [("t","u")] (ssum_lemma6 RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
385 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
386 |
(rtac (monofun_Isinr RS monofunE RS spec RS spec RS mp) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
387 |
(rtac is_lub_thelub 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
388 |
(etac (monofun_Iwhen3 RS ch2ch_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
389 |
(etac (monofun_Iwhen3 RS ub2ub_monofun) 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
390 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
391 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
392 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
393 |
val thelub_ssum1a = lub_ssum1a RS thelubI; |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
394 |
(* |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
395 |
[| is_chain ?Y1; ! i. ? x. ?Y1 i = Isinl x |] ==> |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
396 |
lub (range ?Y1) = Isinl |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
397 |
(lub (range (%i. Iwhen (LAM x. x) (LAM y. UU) (?Y1 i)))) |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
398 |
*) |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
399 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
400 |
val thelub_ssum1b = lub_ssum1b RS thelubI; |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
401 |
(* |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
402 |
[| is_chain ?Y1; ! i. ? x. ?Y1 i = Isinr x |] ==> |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
403 |
lub (range ?Y1) = Isinr |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
404 |
(lub (range (%i. Iwhen (LAM y. UU) (LAM x. x) (?Y1 i)))) |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
405 |
*) |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
406 |
|
892 | 407 |
qed_goal "cpo_ssum" Ssum2.thy |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
408 |
"is_chain(Y::nat=>'a ++'b) ==> ? x.range(Y) <<|x" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
409 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
410 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
411 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
412 |
(rtac (ssum_lemma4 RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
413 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
414 |
(rtac exI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
415 |
(etac lub_ssum1a 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
416 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
417 |
(rtac exI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
418 |
(etac lub_ssum1b 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
419 |
(atac 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
420 |
]); |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
961
diff
changeset
|
421 |