author | paulson |
Wed, 16 Jan 2002 17:53:22 +0100 | |
changeset 12777 | 70b2651af635 |
parent 243 | c22b85994e17 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/sprod3.thy |
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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 Sprod3.thy |
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*) |
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|
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open Sprod3; |
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|
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(* ------------------------------------------------------------------------ *) |
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(* continuity of Ispair, Isfst, Issnd *) |
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(* ------------------------------------------------------------------------ *) |
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|
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val sprod3_lemma1 = prove_goal Sprod3.thy |
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"[| is_chain(Y); x~= UU; lub(range(Y))~= UU |] ==>\ |
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\ Ispair(lub(range(Y)),x) =\ |
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\ Ispair(lub(range(%i. Isfst(Ispair(Y(i),x)))),\ |
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\ lub(range(%i. Issnd(Ispair(Y(i),x)))))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(res_inst_tac [("f1","Ispair")] (arg_cong RS cong) 1), |
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(rtac lub_equal 1), |
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(atac 1), |
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(rtac (monofun_Isfst RS ch2ch_monofun) 1), |
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(rtac ch2ch_fun 1), |
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(rtac (monofun_Ispair1 RS ch2ch_monofun) 1), |
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(atac 1), |
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(rtac allI 1), |
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(asm_simp_tac Sprod_ss 1), |
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(rtac sym 1), |
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(rtac lub_chain_maxelem 1), |
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(rtac (monofun_Issnd RS ch2ch_monofun) 1), |
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(rtac ch2ch_fun 1), |
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(rtac (monofun_Ispair1 RS ch2ch_monofun) 1), |
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(atac 1), |
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(res_inst_tac [("P","%j.~Y(j)=UU")] exE 1), |
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(rtac (notall2ex RS iffD1) 1), |
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(res_inst_tac [("Q","lub(range(Y)) = UU")] contrapos 1), |
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(atac 1), |
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(rtac chain_UU_I_inverse 1), |
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(atac 1), |
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(rtac exI 1), |
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(etac Issnd2 1), |
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(rtac allI 1), |
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(res_inst_tac [("Q","Y(i)=UU")] (excluded_middle RS disjE) 1), |
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(asm_simp_tac Sprod_ss 1), |
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(rtac refl_less 1), |
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(res_inst_tac [("s","UU"),("t","Y(i)")] subst 1), |
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(etac sym 1), |
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(asm_simp_tac Sprod_ss 1), |
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(rtac minimal 1) |
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]); |
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val sprod3_lemma2 = prove_goal Sprod3.thy |
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"[| is_chain(Y); ~ x = UU; lub(range(Y)) = UU |] ==>\ |
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\ Ispair(lub(range(Y)),x) =\ |
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\ Ispair(lub(range(%i. Isfst(Ispair(Y(i),x)))),\ |
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\ lub(range(%i. Issnd(Ispair(Y(i),x)))))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1), |
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(atac 1), |
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(rtac trans 1), |
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(rtac strict_Ispair1 1), |
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(rtac (strict_Ispair RS sym) 1), |
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(rtac disjI1 1), |
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(rtac chain_UU_I_inverse 1), |
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(rtac allI 1), |
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(asm_simp_tac Sprod_ss 1), |
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(etac (chain_UU_I RS spec) 1), |
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(atac 1) |
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]); |
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val sprod3_lemma3 = prove_goal Sprod3.thy |
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"[| is_chain(Y); x = UU |] ==>\ |
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\ Ispair(lub(range(Y)),x) =\ |
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\ Ispair(lub(range(%i. Isfst(Ispair(Y(i),x)))),\ |
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\ lub(range(%i. Issnd(Ispair(Y(i),x)))))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(res_inst_tac [("s","UU"),("t","x")] ssubst 1), |
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(atac 1), |
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(rtac trans 1), |
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(rtac strict_Ispair2 1), |
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(rtac (strict_Ispair RS sym) 1), |
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(rtac disjI1 1), |
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(rtac chain_UU_I_inverse 1), |
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(rtac allI 1), |
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(simp_tac Sprod_ss 1) |
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]); |
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val contlub_Ispair1 = prove_goal Sprod3.thy "contlub(Ispair)" |
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(fn prems => |
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[ |
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(rtac contlubI 1), |
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(strip_tac 1), |
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(rtac (expand_fun_eq RS iffD2) 1), |
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(strip_tac 1), |
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(rtac (lub_fun RS thelubI RS ssubst) 1), |
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(etac (monofun_Ispair1 RS ch2ch_monofun) 1), |
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(rtac trans 1), |
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(rtac (thelub_sprod RS sym) 2), |
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(rtac ch2ch_fun 2), |
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(etac (monofun_Ispair1 RS ch2ch_monofun) 2), |
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(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1), |
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(res_inst_tac |
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[("Q","lub(range(Y))=UU")] (excluded_middle RS disjE) 1), |
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(etac sprod3_lemma1 1), |
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(atac 1), |
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(atac 1), |
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(etac sprod3_lemma2 1), |
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(atac 1), |
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(atac 1), |
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(etac sprod3_lemma3 1), |
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(atac 1) |
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]); |
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125 |
val sprod3_lemma4 = prove_goal Sprod3.thy |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
126 |
"[| is_chain(Y); ~ x = UU; ~ lub(range(Y)) = UU |] ==>\ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
127 |
\ Ispair(x,lub(range(Y))) =\ |
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|
128 |
\ Ispair(lub(range(%i. Isfst(Ispair(x,Y(i))))),\ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
129 |
\ lub(range(%i. Issnd(Ispair(x,Y(i))))))" |
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130 |
(fn prems => |
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|
131 |
[ |
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132 |
(cut_facts_tac prems 1), |
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|
133 |
(res_inst_tac [("f1","Ispair")] (arg_cong RS cong) 1), |
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134 |
(rtac sym 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
135 |
(rtac lub_chain_maxelem 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
136 |
(rtac (monofun_Isfst RS ch2ch_monofun) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
137 |
(rtac (monofun_Ispair2 RS ch2ch_monofun) 1), |
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|
138 |
(atac 1), |
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|
139 |
(res_inst_tac [("P","%j.~Y(j)=UU")] exE 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
140 |
(rtac (notall2ex RS iffD1) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
141 |
(res_inst_tac [("Q","lub(range(Y)) = UU")] contrapos 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
142 |
(atac 1), |
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|
143 |
(rtac chain_UU_I_inverse 1), |
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|
144 |
(atac 1), |
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|
145 |
(rtac exI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
146 |
(etac Isfst2 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
147 |
(rtac allI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
148 |
(res_inst_tac [("Q","Y(i)=UU")] (excluded_middle RS disjE) 1), |
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|
149 |
(asm_simp_tac Sprod_ss 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
150 |
(rtac refl_less 1), |
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|
151 |
(res_inst_tac [("s","UU"),("t","Y(i)")] subst 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
152 |
(etac sym 1), |
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|
153 |
(asm_simp_tac Sprod_ss 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
154 |
(rtac minimal 1), |
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|
155 |
(rtac lub_equal 1), |
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|
156 |
(atac 1), |
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|
157 |
(rtac (monofun_Issnd RS ch2ch_monofun) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
158 |
(rtac (monofun_Ispair2 RS ch2ch_monofun) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
159 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
160 |
(rtac allI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
161 |
(asm_simp_tac Sprod_ss 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
162 |
]); |
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|
163 |
|
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|
164 |
val sprod3_lemma5 = prove_goal Sprod3.thy |
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|
165 |
"[| is_chain(Y); ~ x = UU; lub(range(Y)) = UU |] ==>\ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
166 |
\ Ispair(x,lub(range(Y))) =\ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
167 |
\ Ispair(lub(range(%i. Isfst(Ispair(x,Y(i))))),\ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
168 |
\ lub(range(%i. Issnd(Ispair(x,Y(i))))))" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
169 |
(fn prems => |
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|
170 |
[ |
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|
171 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
172 |
(res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1), |
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|
173 |
(atac 1), |
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|
174 |
(rtac trans 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
175 |
(rtac strict_Ispair2 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
176 |
(rtac (strict_Ispair RS sym) 1), |
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|
177 |
(rtac disjI2 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
178 |
(rtac chain_UU_I_inverse 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
179 |
(rtac allI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
180 |
(asm_simp_tac Sprod_ss 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
181 |
(etac (chain_UU_I RS spec) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
182 |
(atac 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
183 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
184 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
185 |
val sprod3_lemma6 = prove_goal Sprod3.thy |
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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
|
186 |
"[| is_chain(Y); x = UU |] ==>\ |
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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
|
187 |
\ Ispair(x,lub(range(Y))) =\ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
188 |
\ Ispair(lub(range(%i. Isfst(Ispair(x,Y(i))))),\ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
189 |
\ lub(range(%i. Issnd(Ispair(x,Y(i))))))" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
190 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
191 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
192 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
193 |
(res_inst_tac [("s","UU"),("t","x")] ssubst 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
194 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
195 |
(rtac trans 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
196 |
(rtac strict_Ispair1 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
197 |
(rtac (strict_Ispair RS sym) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
198 |
(rtac disjI1 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
|
199 |
(rtac chain_UU_I_inverse 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
200 |
(rtac allI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
201 |
(simp_tac Sprod_ss 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
202 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
203 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
204 |
val contlub_Ispair2 = prove_goal Sprod3.thy "contlub(Ispair(x))" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
205 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
206 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
207 |
(rtac contlubI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
208 |
(strip_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
209 |
(rtac trans 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
210 |
(rtac (thelub_sprod RS sym) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
211 |
(etac (monofun_Ispair2 RS ch2ch_monofun) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
212 |
(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
213 |
(res_inst_tac [("Q","lub(range(Y))=UU")] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
214 |
(excluded_middle RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
215 |
(etac sprod3_lemma4 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
216 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
217 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
218 |
(etac sprod3_lemma5 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
219 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
220 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
221 |
(etac sprod3_lemma6 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
222 |
(atac 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
223 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
224 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
225 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
226 |
val contX_Ispair1 = prove_goal Sprod3.thy "contX(Ispair)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
227 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
228 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
229 |
(rtac monocontlub2contX 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
230 |
(rtac monofun_Ispair1 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
231 |
(rtac contlub_Ispair1 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
232 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
233 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
234 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
235 |
val contX_Ispair2 = prove_goal Sprod3.thy "contX(Ispair(x))" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
236 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
237 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
238 |
(rtac monocontlub2contX 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
239 |
(rtac monofun_Ispair2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
240 |
(rtac contlub_Ispair2 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
241 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
242 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
243 |
val contlub_Isfst = prove_goal Sprod3.thy "contlub(Isfst)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
244 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
245 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
246 |
(rtac contlubI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
247 |
(strip_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
248 |
(rtac (lub_sprod RS thelubI RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
249 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
250 |
(res_inst_tac [("Q","lub(range(%i. Issnd(Y(i))))=UU")] |
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parents:
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|
251 |
(excluded_middle RS disjE) 1), |
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parents:
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|
252 |
(asm_simp_tac Sprod_ss 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
253 |
(res_inst_tac [("s","UU"),("t","lub(range(%i. Issnd(Y(i))))")] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
254 |
ssubst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
255 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
256 |
(rtac trans 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
257 |
(asm_simp_tac Sprod_ss 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
258 |
(rtac sym 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
259 |
(rtac chain_UU_I_inverse 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
260 |
(rtac allI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
261 |
(rtac strict_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
262 |
(rtac swap 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
263 |
(etac (defined_IsfstIssnd RS conjunct2) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
264 |
(rtac notnotI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
265 |
(rtac (chain_UU_I RS spec) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
266 |
(rtac (monofun_Issnd RS ch2ch_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
267 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
268 |
(atac 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
269 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
270 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
271 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
272 |
val contlub_Issnd = prove_goal Sprod3.thy "contlub(Issnd)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
273 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
274 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
275 |
(rtac contlubI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
276 |
(strip_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
277 |
(rtac (lub_sprod RS thelubI RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
278 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
279 |
(res_inst_tac [("Q","lub(range(%i. Isfst(Y(i))))=UU")] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
280 |
(excluded_middle RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
281 |
(asm_simp_tac Sprod_ss 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
282 |
(res_inst_tac [("s","UU"),("t","lub(range(%i. Isfst(Y(i))))")] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
283 |
ssubst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
284 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
285 |
(asm_simp_tac Sprod_ss 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
286 |
(rtac sym 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
287 |
(rtac chain_UU_I_inverse 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
288 |
(rtac allI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
289 |
(rtac strict_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
290 |
(rtac swap 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
291 |
(etac (defined_IsfstIssnd RS conjunct1) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
292 |
(rtac notnotI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
293 |
(rtac (chain_UU_I RS spec) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
294 |
(rtac (monofun_Isfst RS ch2ch_monofun) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
295 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
296 |
(atac 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
297 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
298 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
299 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
300 |
val contX_Isfst = prove_goal Sprod3.thy "contX(Isfst)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
301 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
302 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
303 |
(rtac monocontlub2contX 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
304 |
(rtac monofun_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
305 |
(rtac contlub_Isfst 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
306 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
307 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
308 |
val contX_Issnd = prove_goal Sprod3.thy "contX(Issnd)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
309 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
310 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
311 |
(rtac monocontlub2contX 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
312 |
(rtac monofun_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
313 |
(rtac contlub_Issnd 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
314 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
315 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
316 |
(* |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
317 |
-------------------------------------------------------------------------- |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
318 |
more lemmas for Sprod3.thy |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
319 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
320 |
-------------------------------------------------------------------------- |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
321 |
*) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
322 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
323 |
val spair_eq = prove_goal Sprod3.thy "[|x1=x2;y1=y2|] ==> x1##y1 = x2##y2" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
324 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
325 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
326 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
327 |
(fast_tac HOL_cs 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
328 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
329 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
330 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
331 |
(* convert all lemmas to the continuous versions *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
332 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
333 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
334 |
val beta_cfun_sprod = prove_goalw Sprod3.thy [spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
335 |
"(LAM x y.Ispair(x,y))[a][b] = Ispair(a,b)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
336 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
337 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
338 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
339 |
(contX_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
340 |
(rtac contX_Ispair2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
341 |
(rtac contX2contX_CF1L 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
342 |
(rtac contX_Ispair1 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
343 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
344 |
(rtac contX_Ispair2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
345 |
(rtac refl 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
346 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
347 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
348 |
val inject_spair = prove_goalw Sprod3.thy [spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
349 |
"[|~aa=UU ; ~ba=UU ; (a##b)=(aa##ba) |] ==> a=aa & b=ba" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
350 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
351 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
352 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
353 |
(etac inject_Ispair 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
354 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
355 |
(etac box_equals 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
356 |
(rtac beta_cfun_sprod 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
357 |
(rtac beta_cfun_sprod 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
358 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
359 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
360 |
val inst_sprod_pcpo2 = prove_goalw Sprod3.thy [spair_def] "UU = (UU##UU)" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
361 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
362 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
363 |
(rtac sym 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
364 |
(rtac trans 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
365 |
(rtac beta_cfun_sprod 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
366 |
(rtac sym 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
367 |
(rtac inst_sprod_pcpo 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
368 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
369 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
370 |
val strict_spair = prove_goalw Sprod3.thy [spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
371 |
"(a=UU | b=UU) ==> (a##b)=UU" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
372 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
373 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
374 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
375 |
(rtac trans 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
376 |
(rtac beta_cfun_sprod 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
377 |
(rtac trans 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
378 |
(rtac (inst_sprod_pcpo RS sym) 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
379 |
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|
380 |
]); |
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|
381 |
|
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changeset
|
382 |
val strict_spair1 = prove_goalw Sprod3.thy [spair_def] "(UU##b) = UU" |
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|
383 |
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384 |
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|
385 |
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|
386 |
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|
387 |
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|
388 |
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|
389 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
390 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
391 |
val strict_spair2 = prove_goalw Sprod3.thy [spair_def] "(a##UU) = UU" |
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|
392 |
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|
393 |
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|
394 |
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|
395 |
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|
396 |
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|
397 |
(rtac strict_Ispair2 1) |
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|
398 |
]); |
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|
399 |
|
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changeset
|
400 |
val strict_spair_rev = prove_goalw Sprod3.thy [spair_def] |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
401 |
"~(x##y)=UU ==> ~x=UU & ~y=UU" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
402 |
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403 |
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404 |
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|
405 |
(rtac strict_Ispair_rev 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
406 |
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|
407 |
(rtac (inst_sprod_pcpo RS subst) 1), |
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|
408 |
(atac 1) |
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changeset
|
409 |
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changeset
|
410 |
|
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|
411 |
val defined_spair_rev = prove_goalw Sprod3.thy [spair_def] |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
412 |
"(a##b) = UU ==> (a = UU | b = UU)" |
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|
413 |
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414 |
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|
415 |
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|
416 |
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|
417 |
(rtac (beta_cfun_sprod RS subst) 1), |
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|
418 |
(rtac (inst_sprod_pcpo RS subst) 1), |
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|
419 |
(atac 1) |
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|
420 |
]); |
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changeset
|
421 |
|
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|
422 |
val defined_spair = prove_goalw Sprod3.thy [spair_def] |
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changeset
|
423 |
"[|~a=UU; ~b=UU|] ==> ~(a##b) = UU" |
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|
424 |
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425 |
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|
426 |
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|
427 |
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428 |
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|
429 |
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|
430 |
(atac 1) |
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|
431 |
]); |
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changeset
|
432 |
|
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|
433 |
val Exh_Sprod2 = prove_goalw Sprod3.thy [spair_def] |
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changeset
|
434 |
"z=UU | (? a b. z=(a##b) & ~a=UU & ~b=UU)" |
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|
435 |
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436 |
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|
437 |
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|
438 |
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|
439 |
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|
440 |
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|
441 |
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|
442 |
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|
443 |
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|
444 |
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445 |
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|
446 |
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|
447 |
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|
448 |
(fast_tac HOL_cs 1), |
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|
449 |
(fast_tac HOL_cs 1) |
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|
450 |
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|
451 |
|
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|
452 |
|
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|
453 |
val sprodE = prove_goalw Sprod3.thy [spair_def] |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
454 |
"[|p=UU ==> Q;!!x y. [|p=(x##y);~x=UU ; ~y=UU|] ==> Q|] ==> Q" |
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|
455 |
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|
456 |
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|
457 |
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|
458 |
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|
459 |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
460 |
(atac 1), |
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|
461 |
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|
462 |
(atac 2), |
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|
463 |
(atac 2), |
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|
464 |
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|
465 |
(atac 1) |
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parents:
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changeset
|
466 |
]); |
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|
467 |
|
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|
468 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
469 |
val strict_sfst = prove_goalw Sprod3.thy [sfst_def] |
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changeset
|
470 |
"p=UU==>sfst[p]=UU" |
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|
471 |
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|
472 |
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|
473 |
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|
474 |
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|
475 |
(rtac contX_Isfst 1), |
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|
476 |
(rtac strict_Isfst 1), |
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|
477 |
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|
478 |
(atac 1) |
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|
479 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
480 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
481 |
val strict_sfst1 = prove_goalw Sprod3.thy [sfst_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
482 |
"sfst[UU##y] = UU" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
483 |
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changeset
|
484 |
[ |
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|
485 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
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|
486 |
(rtac (beta_cfun RS ssubst) 1), |
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|
487 |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
488 |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
489 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
490 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
491 |
val strict_sfst2 = prove_goalw Sprod3.thy [sfst_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
492 |
"sfst[x##UU] = UU" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
493 |
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|
494 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
495 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
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|
496 |
(rtac (beta_cfun RS ssubst) 1), |
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changeset
|
497 |
(rtac contX_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
498 |
(rtac strict_Isfst2 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
499 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
500 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
501 |
val strict_ssnd = prove_goalw Sprod3.thy [ssnd_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
502 |
"p=UU==>ssnd[p]=UU" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
503 |
(fn prems => |
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|
504 |
[ |
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|
505 |
(cut_facts_tac prems 1), |
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|
506 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
507 |
(rtac contX_Issnd 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
508 |
(rtac strict_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
509 |
(rtac (inst_sprod_pcpo RS subst) 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
|
510 |
(atac 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
511 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
512 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
513 |
val strict_ssnd1 = prove_goalw Sprod3.thy [ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
514 |
"ssnd[UU##y] = UU" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
515 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
516 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
517 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
518 |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
519 |
(rtac contX_Issnd 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
520 |
(rtac strict_Issnd1 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
521 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
522 |
|
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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
|
523 |
val strict_ssnd2 = prove_goalw Sprod3.thy [ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
524 |
"ssnd[x##UU] = UU" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
525 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
526 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
527 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
528 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
529 |
(rtac contX_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
530 |
(rtac strict_Issnd2 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
|
531 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
532 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
533 |
val sfst2 = prove_goalw Sprod3.thy [sfst_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
534 |
"~y=UU ==>sfst[x##y]=x" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
535 |
(fn prems => |
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|
536 |
[ |
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|
537 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
538 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
539 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
540 |
(rtac contX_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
541 |
(etac Isfst2 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
|
542 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
543 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
544 |
val ssnd2 = prove_goalw Sprod3.thy [ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
545 |
"~x=UU ==>ssnd[x##y]=y" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
546 |
(fn prems => |
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|
547 |
[ |
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|
548 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
549 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
550 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
551 |
(rtac contX_Issnd 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
552 |
(etac Issnd2 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
553 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
554 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
555 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
556 |
val defined_sfstssnd = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
557 |
"~p=UU ==> ~sfst[p]=UU & ~ssnd[p]=UU" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
558 |
(fn prems => |
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|
559 |
[ |
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|
560 |
(cut_facts_tac prems 1), |
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|
561 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
562 |
(rtac contX_Issnd 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
changeset
|
563 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
564 |
(rtac contX_Isfst 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
565 |
(rtac defined_IsfstIssnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
566 |
(rtac (inst_sprod_pcpo RS subst) 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
|
567 |
(atac 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
568 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
569 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
570 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
571 |
val surjective_pairing_Sprod2 = prove_goalw Sprod3.thy |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
572 |
[sfst_def,ssnd_def,spair_def] "(sfst[p] ## ssnd[p]) = p" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
573 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
574 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
575 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
576 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
577 |
(rtac contX_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
578 |
(rtac (beta_cfun RS ssubst) 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
|
579 |
(rtac contX_Isfst 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
580 |
(rtac (surjective_pairing_Sprod RS sym) 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
581 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
582 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
583 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
584 |
val less_sprod5b = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
585 |
"~p1=UU ==> (p1<<p2) = (sfst[p1]<<sfst[p2] & ssnd[p1]<<ssnd[p2])" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
586 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
587 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
588 |
(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:
diff
changeset
|
589 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
590 |
(rtac contX_Issnd 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
591 |
(rtac (beta_cfun RS ssubst) 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
|
592 |
(rtac contX_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
593 |
(rtac (beta_cfun RS ssubst) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
594 |
(rtac contX_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
595 |
(rtac (beta_cfun RS ssubst) 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
|
596 |
(rtac contX_Isfst 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
597 |
(rtac less_sprod3b 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
598 |
(rtac (inst_sprod_pcpo RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
599 |
(atac 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
|
600 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
601 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
602 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
603 |
val less_sprod5c = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
604 |
"[|xa##ya<<x##y;~xa=UU;~ya=UU;~x=UU;~y=UU|] ==>xa<<x & ya << y" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
605 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
606 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
607 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
608 |
(rtac less_sprod4c 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
609 |
(REPEAT (atac 2)), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
610 |
(rtac (beta_cfun_sprod RS subst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
611 |
(rtac (beta_cfun_sprod RS subst) 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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|
612 |
(atac 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
613 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
614 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
615 |
val lub_sprod2 = prove_goalw Sprod3.thy [sfst_def,ssnd_def,spair_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
616 |
"[|is_chain(S)|] ==> range(S) <<| \ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
617 |
\ (lub(range(%i.sfst[S(i)])) ## lub(range(%i.ssnd[S(i)])))" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
618 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
619 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
620 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
621 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
622 |
(rtac (beta_cfun RS ext RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
623 |
(rtac contX_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
624 |
(rtac (beta_cfun RS ext RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
625 |
(rtac contX_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
626 |
(rtac lub_sprod 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
627 |
(resolve_tac prems 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
628 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
629 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
630 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
631 |
val thelub_sprod2 = (lub_sprod2 RS thelubI); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
632 |
(* is_chain(?S1) ==> lub(range(?S1)) = *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
633 |
(* (lub(range(%i. sfst[?S1(i)]))## lub(range(%i. ssnd[?S1(i)]))) *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
634 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
635 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
636 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
637 |
val ssplit1 = prove_goalw Sprod3.thy [ssplit_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
638 |
"ssplit[f][UU]=UU" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
639 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
640 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
641 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
642 |
(contX_tacR 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
643 |
(rtac (strictify1 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
644 |
(rtac refl 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
645 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
646 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
647 |
val ssplit2 = prove_goalw Sprod3.thy [ssplit_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
648 |
"[|~x=UU;~y=UU|] ==> ssplit[f][x##y]=f[x][y]" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
649 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
650 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
651 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
652 |
(contX_tacR 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
653 |
(rtac (strictify2 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
654 |
(rtac defined_spair 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
655 |
(resolve_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
656 |
(resolve_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
657 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
658 |
(contX_tacR 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
659 |
(rtac (sfst2 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
660 |
(resolve_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
661 |
(rtac (ssnd2 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
662 |
(resolve_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
663 |
(rtac refl 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
664 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
665 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
666 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
667 |
val ssplit3 = prove_goalw Sprod3.thy [ssplit_def] |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
668 |
"ssplit[spair][z]=z" |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
669 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
670 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
671 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
672 |
(contX_tacR 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
673 |
(res_inst_tac [("Q","z=UU")] classical2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
674 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
675 |
(rtac strictify1 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
676 |
(rtac trans 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
677 |
(rtac strictify2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
678 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
679 |
(rtac (beta_cfun RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
680 |
(contX_tacR 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
681 |
(rtac surjective_pairing_Sprod2 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
682 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
683 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
684 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
685 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
686 |
(* install simplifier for Sprod *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
687 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
688 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
689 |
val Sprod_rews = [strict_spair1,strict_spair2,strict_sfst1,strict_sfst2, |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
690 |
strict_ssnd1,strict_ssnd2,sfst2,ssnd2, |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
691 |
ssplit1,ssplit2]; |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
692 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
693 |
val Sprod_ss = Cfun_ss addsimps Sprod_rews; |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
694 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
695 |