author | wenzelm |
Fri, 13 Dec 1996 17:34:32 +0100 | |
changeset 2383 | 4127499d9b52 |
parent 2033 | 639de962ded4 |
child 2566 | cbf02fc74332 |
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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qed_goal "sprod3_lemma1" 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 Sprod0_ss 1), |
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(rtac sym 1), |
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(rtac lub_chain_maxelem 1), |
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(res_inst_tac [("P","%j.~Y(j)=UU")] exE 1), |
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(rtac (not_all 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 Sprod0_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 Sprod0_ss 1), |
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(rtac minimal 1) |
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]); |
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qed_goal "sprod3_lemma2" 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 Sprod0_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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qed_goal "sprod3_lemma3" 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 Sprod0_ss 1) |
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]); |
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qed_goal "contlub_Ispair1" 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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(stac (lub_fun RS thelubI) 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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qed_goal "sprod3_lemma4" Sprod3.thy |
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"[| is_chain(Y); x ~= UU; lub(range(Y)) ~= UU |] ==>\ |
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\ Ispair x (lub(range Y)) =\ |
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\ Ispair (lub(range(%i. Isfst (Ispair x (Y i)))))\ |
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\ (lub(range(%i. Issnd (Ispair x (Y i)))))" |
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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 sym 1), |
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(rtac lub_chain_maxelem 1), |
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(res_inst_tac [("P","%j.Y(j)~=UU")] exE 1), |
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(rtac (not_all 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 Isfst2 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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corrected some errors that occurred after introduction of local simpsets
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parents:
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(asm_simp_tac Sprod0_ss 1), |
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142 |
(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), |
|
1277
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corrected some errors that occurred after introduction of local simpsets
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145 |
(asm_simp_tac Sprod0_ss 1), |
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(rtac minimal 1), |
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(rtac lub_equal 1), |
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(atac 1), |
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(rtac (monofun_Issnd RS ch2ch_monofun) 1), |
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(rtac (monofun_Ispair2 RS ch2ch_monofun) 1), |
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(atac 1), |
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(rtac allI 1), |
|
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corrected some errors that occurred after introduction of local simpsets
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(asm_simp_tac Sprod0_ss 1) |
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]); |
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892 | 156 |
qed_goal "sprod3_lemma5" Sprod3.thy |
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"[| is_chain(Y); x ~= UU; lub(range(Y)) = UU |] ==>\ |
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158 |
\ Ispair x (lub(range Y)) =\ |
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\ Ispair (lub(range(%i. Isfst(Ispair x (Y i)))))\ |
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\ (lub(range(%i. Issnd(Ispair x (Y i)))))" |
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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_Ispair2 1), |
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(rtac (strict_Ispair RS sym) 1), |
|
169 |
(rtac disjI2 1), |
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170 |
(rtac chain_UU_I_inverse 1), |
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(rtac allI 1), |
|
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(asm_simp_tac Sprod0_ss 1), |
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(etac (chain_UU_I RS spec) 1), |
174 |
(atac 1) |
|
175 |
]); |
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|
892 | 177 |
qed_goal "sprod3_lemma6" Sprod3.thy |
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"[| is_chain(Y); x = UU |] ==>\ |
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\ Ispair x (lub(range Y)) =\ |
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\ Ispair (lub(range(%i. Isfst (Ispair x (Y i)))))\ |
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\ (lub(range(%i. Issnd (Ispair x (Y i)))))" |
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(fn prems => |
1461 | 183 |
[ |
184 |
(cut_facts_tac prems 1), |
|
185 |
(res_inst_tac [("s","UU"),("t","x")] ssubst 1), |
|
186 |
(atac 1), |
|
187 |
(rtac trans 1), |
|
188 |
(rtac strict_Ispair1 1), |
|
189 |
(rtac (strict_Ispair RS sym) 1), |
|
190 |
(rtac disjI1 1), |
|
191 |
(rtac chain_UU_I_inverse 1), |
|
192 |
(rtac allI 1), |
|
1277
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corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
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193 |
(simp_tac Sprod0_ss 1) |
1461 | 194 |
]); |
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195 |
|
892 | 196 |
qed_goal "contlub_Ispair2" Sprod3.thy "contlub(Ispair(x))" |
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(fn prems => |
1461 | 198 |
[ |
199 |
(rtac contlubI 1), |
|
200 |
(strip_tac 1), |
|
201 |
(rtac trans 1), |
|
202 |
(rtac (thelub_sprod RS sym) 2), |
|
203 |
(etac (monofun_Ispair2 RS ch2ch_monofun) 2), |
|
204 |
(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1), |
|
205 |
(res_inst_tac [("Q","lub(range(Y))=UU")] |
|
206 |
(excluded_middle RS disjE) 1), |
|
207 |
(etac sprod3_lemma4 1), |
|
208 |
(atac 1), |
|
209 |
(atac 1), |
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210 |
(etac sprod3_lemma5 1), |
|
211 |
(atac 1), |
|
212 |
(atac 1), |
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(etac sprod3_lemma6 1), |
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214 |
(atac 1) |
|
215 |
]); |
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|
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qed_goal "cont_Ispair1" Sprod3.thy "cont(Ispair)" |
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219 |
(fn prems => |
1461 | 220 |
[ |
221 |
(rtac monocontlub2cont 1), |
|
222 |
(rtac monofun_Ispair1 1), |
|
223 |
(rtac contlub_Ispair1 1) |
|
224 |
]); |
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225 |
|
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|
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qed_goal "cont_Ispair2" Sprod3.thy "cont(Ispair(x))" |
243
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|
228 |
(fn prems => |
1461 | 229 |
[ |
230 |
(rtac monocontlub2cont 1), |
|
231 |
(rtac monofun_Ispair2 1), |
|
232 |
(rtac contlub_Ispair2 1) |
|
233 |
]); |
|
243
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234 |
|
892 | 235 |
qed_goal "contlub_Isfst" Sprod3.thy "contlub(Isfst)" |
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236 |
(fn prems => |
1461 | 237 |
[ |
238 |
(rtac contlubI 1), |
|
239 |
(strip_tac 1), |
|
2033 | 240 |
(stac (lub_sprod RS thelubI) 1), |
1461 | 241 |
(atac 1), |
242 |
(res_inst_tac [("Q","lub(range(%i. Issnd(Y(i))))=UU")] |
|
243 |
(excluded_middle RS disjE) 1), |
|
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244 |
(asm_simp_tac Sprod0_ss 1), |
1461 | 245 |
(res_inst_tac [("s","UU"),("t","lub(range(%i. Issnd(Y(i))))")] |
246 |
ssubst 1), |
|
247 |
(atac 1), |
|
248 |
(rtac trans 1), |
|
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249 |
(asm_simp_tac Sprod0_ss 1), |
1461 | 250 |
(rtac sym 1), |
251 |
(rtac chain_UU_I_inverse 1), |
|
252 |
(rtac allI 1), |
|
253 |
(rtac strict_Isfst 1), |
|
254 |
(rtac swap 1), |
|
255 |
(etac (defined_IsfstIssnd RS conjunct2) 2), |
|
2033 | 256 |
(fast_tac (HOL_cs addSDs [monofun_Issnd RS ch2ch_monofun RS |
257 |
chain_UU_I RS spec]) 1) |
|
258 |
]); |
|
243
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|
892 | 260 |
qed_goal "contlub_Issnd" Sprod3.thy "contlub(Issnd)" |
243
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|
261 |
(fn prems => |
1461 | 262 |
[ |
263 |
(rtac contlubI 1), |
|
264 |
(strip_tac 1), |
|
2033 | 265 |
(stac (lub_sprod RS thelubI) 1), |
1461 | 266 |
(atac 1), |
267 |
(res_inst_tac [("Q","lub(range(%i. Isfst(Y(i))))=UU")] |
|
268 |
(excluded_middle RS disjE) 1), |
|
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269 |
(asm_simp_tac Sprod0_ss 1), |
1461 | 270 |
(res_inst_tac [("s","UU"),("t","lub(range(%i. Isfst(Y(i))))")] |
271 |
ssubst 1), |
|
272 |
(atac 1), |
|
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|
273 |
(asm_simp_tac Sprod0_ss 1), |
1461 | 274 |
(rtac sym 1), |
275 |
(rtac chain_UU_I_inverse 1), |
|
276 |
(rtac allI 1), |
|
277 |
(rtac strict_Issnd 1), |
|
278 |
(rtac swap 1), |
|
279 |
(etac (defined_IsfstIssnd RS conjunct1) 2), |
|
1675 | 280 |
(fast_tac (HOL_cs addSDs [monofun_Isfst RS ch2ch_monofun RS |
2033 | 281 |
chain_UU_I RS spec]) 1) |
282 |
]); |
|
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283 |
|
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284 |
qed_goal "cont_Isfst" Sprod3.thy "cont(Isfst)" |
243
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|
285 |
(fn prems => |
1461 | 286 |
[ |
287 |
(rtac monocontlub2cont 1), |
|
288 |
(rtac monofun_Isfst 1), |
|
289 |
(rtac contlub_Isfst 1) |
|
290 |
]); |
|
243
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291 |
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292 |
qed_goal "cont_Issnd" Sprod3.thy "cont(Issnd)" |
243
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|
293 |
(fn prems => |
1461 | 294 |
[ |
295 |
(rtac monocontlub2cont 1), |
|
296 |
(rtac monofun_Issnd 1), |
|
297 |
(rtac contlub_Issnd 1) |
|
298 |
]); |
|
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|
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300 |
(* |
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-------------------------------------------------------------------------- |
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302 |
more lemmas for Sprod3.thy |
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|
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-------------------------------------------------------------------------- |
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*) |
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306 |
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|
307 |
qed_goal "spair_eq" Sprod3.thy "[|x1=x2;y1=y2|] ==> (|x1,y1|) = (|x2,y2|)" |
243
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|
308 |
(fn prems => |
1461 | 309 |
[ |
310 |
(cut_facts_tac prems 1), |
|
311 |
(fast_tac HOL_cs 1) |
|
312 |
]); |
|
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|
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314 |
(* ------------------------------------------------------------------------ *) |
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(* convert all lemmas to the continuous versions *) |
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316 |
(* ------------------------------------------------------------------------ *) |
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|
317 |
|
892 | 318 |
qed_goalw "beta_cfun_sprod" Sprod3.thy [spair_def] |
1461 | 319 |
"(LAM x y.Ispair x y)`a`b = Ispair a b" |
243
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|
320 |
(fn prems => |
1461 | 321 |
[ |
2033 | 322 |
(stac beta_cfun 1), |
1461 | 323 |
(cont_tac 1), |
324 |
(rtac cont_Ispair2 1), |
|
325 |
(rtac cont2cont_CF1L 1), |
|
326 |
(rtac cont_Ispair1 1), |
|
2033 | 327 |
(stac beta_cfun 1), |
1461 | 328 |
(rtac cont_Ispair2 1), |
329 |
(rtac refl 1) |
|
330 |
]); |
|
243
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|
331 |
|
892 | 332 |
qed_goalw "inject_spair" Sprod3.thy [spair_def] |
1461 | 333 |
"[| aa~=UU ; ba~=UU ; (|a,b|)=(|aa,ba|) |] ==> a=aa & b=ba" |
243
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|
334 |
(fn prems => |
1461 | 335 |
[ |
336 |
(cut_facts_tac prems 1), |
|
337 |
(etac inject_Ispair 1), |
|
338 |
(atac 1), |
|
339 |
(etac box_equals 1), |
|
340 |
(rtac beta_cfun_sprod 1), |
|
341 |
(rtac beta_cfun_sprod 1) |
|
342 |
]); |
|
243
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|
343 |
|
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|
344 |
qed_goalw "inst_sprod_pcpo2" Sprod3.thy [spair_def] "UU = (|UU,UU|)" |
243
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|
345 |
(fn prems => |
1461 | 346 |
[ |
347 |
(rtac sym 1), |
|
348 |
(rtac trans 1), |
|
349 |
(rtac beta_cfun_sprod 1), |
|
350 |
(rtac sym 1), |
|
351 |
(rtac inst_sprod_pcpo 1) |
|
352 |
]); |
|
243
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|
353 |
|
892 | 354 |
qed_goalw "strict_spair" Sprod3.thy [spair_def] |
1461 | 355 |
"(a=UU | b=UU) ==> (|a,b|)=UU" |
243
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|
356 |
(fn prems => |
1461 | 357 |
[ |
358 |
(cut_facts_tac prems 1), |
|
359 |
(rtac trans 1), |
|
360 |
(rtac beta_cfun_sprod 1), |
|
361 |
(rtac trans 1), |
|
362 |
(rtac (inst_sprod_pcpo RS sym) 2), |
|
363 |
(etac strict_Ispair 1) |
|
364 |
]); |
|
243
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|
365 |
|
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|
366 |
qed_goalw "strict_spair1" Sprod3.thy [spair_def] "(|UU,b|) = UU" |
243
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|
367 |
(fn prems => |
1461 | 368 |
[ |
2033 | 369 |
(stac beta_cfun_sprod 1), |
1461 | 370 |
(rtac trans 1), |
371 |
(rtac (inst_sprod_pcpo RS sym) 2), |
|
372 |
(rtac strict_Ispair1 1) |
|
373 |
]); |
|
243
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|
374 |
|
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|
375 |
qed_goalw "strict_spair2" Sprod3.thy [spair_def] "(|a,UU|) = UU" |
243
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|
376 |
(fn prems => |
1461 | 377 |
[ |
2033 | 378 |
(stac beta_cfun_sprod 1), |
1461 | 379 |
(rtac trans 1), |
380 |
(rtac (inst_sprod_pcpo RS sym) 2), |
|
381 |
(rtac strict_Ispair2 1) |
|
382 |
]); |
|
243
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|
383 |
|
892 | 384 |
qed_goalw "strict_spair_rev" Sprod3.thy [spair_def] |
1461 | 385 |
"(|x,y|)~=UU ==> ~x=UU & ~y=UU" |
243
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|
386 |
(fn prems => |
1461 | 387 |
[ |
388 |
(cut_facts_tac prems 1), |
|
389 |
(rtac strict_Ispair_rev 1), |
|
390 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
391 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
392 |
(atac 1) |
|
393 |
]); |
|
243
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|
394 |
|
892 | 395 |
qed_goalw "defined_spair_rev" Sprod3.thy [spair_def] |
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|
396 |
"(|a,b|) = UU ==> (a = UU | b = UU)" |
243
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|
397 |
(fn prems => |
1461 | 398 |
[ |
399 |
(cut_facts_tac prems 1), |
|
400 |
(rtac defined_Ispair_rev 1), |
|
401 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
402 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
403 |
(atac 1) |
|
404 |
]); |
|
243
c22b85994e17
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|
405 |
|
892 | 406 |
qed_goalw "defined_spair" Sprod3.thy [spair_def] |
1461 | 407 |
"[|a~=UU; b~=UU|] ==> (|a,b|) ~= UU" |
243
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|
408 |
(fn prems => |
1461 | 409 |
[ |
410 |
(cut_facts_tac prems 1), |
|
2033 | 411 |
(stac beta_cfun_sprod 1), |
412 |
(stac inst_sprod_pcpo 1), |
|
1461 | 413 |
(etac defined_Ispair 1), |
414 |
(atac 1) |
|
415 |
]); |
|
243
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|
416 |
|
892 | 417 |
qed_goalw "Exh_Sprod2" Sprod3.thy [spair_def] |
1461 | 418 |
"z=UU | (? a b. z=(|a,b|) & a~=UU & b~=UU)" |
243
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|
419 |
(fn prems => |
1461 | 420 |
[ |
421 |
(rtac (Exh_Sprod RS disjE) 1), |
|
422 |
(rtac disjI1 1), |
|
2033 | 423 |
(stac inst_sprod_pcpo 1), |
1461 | 424 |
(atac 1), |
425 |
(rtac disjI2 1), |
|
426 |
(etac exE 1), |
|
427 |
(etac exE 1), |
|
428 |
(rtac exI 1), |
|
429 |
(rtac exI 1), |
|
430 |
(rtac conjI 1), |
|
2033 | 431 |
(stac beta_cfun_sprod 1), |
1461 | 432 |
(fast_tac HOL_cs 1), |
433 |
(fast_tac HOL_cs 1) |
|
434 |
]); |
|
243
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|
435 |
|
c22b85994e17
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|
436 |
|
892 | 437 |
qed_goalw "sprodE" Sprod3.thy [spair_def] |
1168
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regensbu
parents:
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changeset
|
438 |
"[|p=UU ==> Q;!!x y. [|p=(|x,y|);x~=UU ; y~=UU|] ==> Q|] ==> Q" |
243
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|
439 |
(fn prems => |
1461 | 440 |
[ |
441 |
(rtac IsprodE 1), |
|
442 |
(resolve_tac prems 1), |
|
2033 | 443 |
(stac inst_sprod_pcpo 1), |
1461 | 444 |
(atac 1), |
445 |
(resolve_tac prems 1), |
|
446 |
(atac 2), |
|
447 |
(atac 2), |
|
2033 | 448 |
(stac beta_cfun_sprod 1), |
1461 | 449 |
(atac 1) |
450 |
]); |
|
243
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|
451 |
|
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changeset
|
452 |
|
892 | 453 |
qed_goalw "strict_sfst" Sprod3.thy [sfst_def] |
1461 | 454 |
"p=UU==>sfst`p=UU" |
243
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|
455 |
(fn prems => |
1461 | 456 |
[ |
457 |
(cut_facts_tac prems 1), |
|
2033 | 458 |
(stac beta_cfun 1), |
1461 | 459 |
(rtac cont_Isfst 1), |
460 |
(rtac strict_Isfst 1), |
|
461 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
462 |
(atac 1) |
|
463 |
]); |
|
243
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|
464 |
|
892 | 465 |
qed_goalw "strict_sfst1" Sprod3.thy [sfst_def,spair_def] |
1461 | 466 |
"sfst`(|UU,y|) = UU" |
243
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|
467 |
(fn prems => |
1461 | 468 |
[ |
2033 | 469 |
(stac beta_cfun_sprod 1), |
470 |
(stac beta_cfun 1), |
|
1461 | 471 |
(rtac cont_Isfst 1), |
472 |
(rtac strict_Isfst1 1) |
|
473 |
]); |
|
243
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|
474 |
|
892 | 475 |
qed_goalw "strict_sfst2" Sprod3.thy [sfst_def,spair_def] |
1461 | 476 |
"sfst`(|x,UU|) = UU" |
243
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|
477 |
(fn prems => |
1461 | 478 |
[ |
2033 | 479 |
(stac beta_cfun_sprod 1), |
480 |
(stac beta_cfun 1), |
|
1461 | 481 |
(rtac cont_Isfst 1), |
482 |
(rtac strict_Isfst2 1) |
|
483 |
]); |
|
243
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|
484 |
|
892 | 485 |
qed_goalw "strict_ssnd" Sprod3.thy [ssnd_def] |
1461 | 486 |
"p=UU==>ssnd`p=UU" |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
487 |
(fn prems => |
1461 | 488 |
[ |
489 |
(cut_facts_tac prems 1), |
|
2033 | 490 |
(stac beta_cfun 1), |
1461 | 491 |
(rtac cont_Issnd 1), |
492 |
(rtac strict_Issnd 1), |
|
493 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
494 |
(atac 1) |
|
495 |
]); |
|
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
496 |
|
892 | 497 |
qed_goalw "strict_ssnd1" Sprod3.thy [ssnd_def,spair_def] |
1461 | 498 |
"ssnd`(|UU,y|) = UU" |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
499 |
(fn prems => |
1461 | 500 |
[ |
2033 | 501 |
(stac beta_cfun_sprod 1), |
502 |
(stac beta_cfun 1), |
|
1461 | 503 |
(rtac cont_Issnd 1), |
504 |
(rtac strict_Issnd1 1) |
|
505 |
]); |
|
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
506 |
|
892 | 507 |
qed_goalw "strict_ssnd2" Sprod3.thy [ssnd_def,spair_def] |
1461 | 508 |
"ssnd`(|x,UU|) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
509 |
(fn prems => |
1461 | 510 |
[ |
2033 | 511 |
(stac beta_cfun_sprod 1), |
512 |
(stac beta_cfun 1), |
|
1461 | 513 |
(rtac cont_Issnd 1), |
514 |
(rtac strict_Issnd2 1) |
|
515 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
516 |
|
892 | 517 |
qed_goalw "sfst2" Sprod3.thy [sfst_def,spair_def] |
1461 | 518 |
"y~=UU ==>sfst`(|x,y|)=x" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
519 |
(fn prems => |
1461 | 520 |
[ |
521 |
(cut_facts_tac prems 1), |
|
2033 | 522 |
(stac beta_cfun_sprod 1), |
523 |
(stac beta_cfun 1), |
|
1461 | 524 |
(rtac cont_Isfst 1), |
525 |
(etac Isfst2 1) |
|
526 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
527 |
|
892 | 528 |
qed_goalw "ssnd2" Sprod3.thy [ssnd_def,spair_def] |
1461 | 529 |
"x~=UU ==>ssnd`(|x,y|)=y" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
530 |
(fn prems => |
1461 | 531 |
[ |
532 |
(cut_facts_tac prems 1), |
|
2033 | 533 |
(stac beta_cfun_sprod 1), |
534 |
(stac beta_cfun 1), |
|
1461 | 535 |
(rtac cont_Issnd 1), |
536 |
(etac Issnd2 1) |
|
537 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
538 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
539 |
|
892 | 540 |
qed_goalw "defined_sfstssnd" Sprod3.thy [sfst_def,ssnd_def,spair_def] |
1461 | 541 |
"p~=UU ==> sfst`p ~=UU & ssnd`p ~=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
542 |
(fn prems => |
1461 | 543 |
[ |
544 |
(cut_facts_tac prems 1), |
|
2033 | 545 |
(stac beta_cfun 1), |
1461 | 546 |
(rtac cont_Issnd 1), |
2033 | 547 |
(stac beta_cfun 1), |
1461 | 548 |
(rtac cont_Isfst 1), |
549 |
(rtac defined_IsfstIssnd 1), |
|
550 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
551 |
(atac 1) |
|
552 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
553 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
554 |
|
892 | 555 |
qed_goalw "surjective_pairing_Sprod2" Sprod3.thy |
1461 | 556 |
[sfst_def,ssnd_def,spair_def] "(|sfst`p , ssnd`p|) = p" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
557 |
(fn prems => |
1461 | 558 |
[ |
2033 | 559 |
(stac beta_cfun_sprod 1), |
560 |
(stac beta_cfun 1), |
|
1461 | 561 |
(rtac cont_Issnd 1), |
2033 | 562 |
(stac beta_cfun 1), |
1461 | 563 |
(rtac cont_Isfst 1), |
564 |
(rtac (surjective_pairing_Sprod RS sym) 1) |
|
565 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
566 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
567 |
|
892 | 568 |
qed_goalw "less_sprod5b" Sprod3.thy [sfst_def,ssnd_def,spair_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
569 |
"p1~=UU ==> (p1<<p2) = (sfst`p1<<sfst`p2 & ssnd`p1<<ssnd`p2)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
570 |
(fn prems => |
1461 | 571 |
[ |
572 |
(cut_facts_tac prems 1), |
|
2033 | 573 |
(stac beta_cfun 1), |
1461 | 574 |
(rtac cont_Issnd 1), |
2033 | 575 |
(stac beta_cfun 1), |
1461 | 576 |
(rtac cont_Issnd 1), |
2033 | 577 |
(stac beta_cfun 1), |
1461 | 578 |
(rtac cont_Isfst 1), |
2033 | 579 |
(stac beta_cfun 1), |
1461 | 580 |
(rtac cont_Isfst 1), |
581 |
(rtac less_sprod3b 1), |
|
582 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
583 |
(atac 1) |
|
584 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
585 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
586 |
|
892 | 587 |
qed_goalw "less_sprod5c" Sprod3.thy [sfst_def,ssnd_def,spair_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
588 |
"[|(|xa,ya|) << (|x,y|);xa~=UU;ya~=UU;x~=UU;y~=UU|] ==>xa<<x & ya << y" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
589 |
(fn prems => |
1461 | 590 |
[ |
591 |
(cut_facts_tac prems 1), |
|
592 |
(rtac less_sprod4c 1), |
|
593 |
(REPEAT (atac 2)), |
|
594 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
595 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
596 |
(atac 1) |
|
597 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
598 |
|
892 | 599 |
qed_goalw "lub_sprod2" Sprod3.thy [sfst_def,ssnd_def,spair_def] |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
600 |
"[|is_chain(S)|] ==> range(S) <<| \ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
601 |
\ (| lub(range(%i.sfst`(S i))), lub(range(%i.ssnd`(S i))) |)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
602 |
(fn prems => |
1461 | 603 |
[ |
604 |
(cut_facts_tac prems 1), |
|
2033 | 605 |
(stac beta_cfun_sprod 1), |
606 |
(stac (beta_cfun RS ext) 1), |
|
1461 | 607 |
(rtac cont_Issnd 1), |
2033 | 608 |
(stac (beta_cfun RS ext) 1), |
1461 | 609 |
(rtac cont_Isfst 1), |
610 |
(rtac lub_sprod 1), |
|
611 |
(resolve_tac prems 1) |
|
612 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
613 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
614 |
|
1779 | 615 |
bind_thm ("thelub_sprod2", lub_sprod2 RS thelubI); |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
616 |
(* |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
617 |
"is_chain ?S1 ==> |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
618 |
lub (range ?S1) = |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
619 |
(|lub (range (%i. sfst`(?S1 i))), lub (range (%i. ssnd`(?S1 i)))|)" : thm |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
620 |
*) |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
621 |
|
892 | 622 |
qed_goalw "ssplit1" Sprod3.thy [ssplit_def] |
1461 | 623 |
"ssplit`f`UU=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
624 |
(fn prems => |
1461 | 625 |
[ |
2033 | 626 |
(stac beta_cfun 1), |
1461 | 627 |
(cont_tacR 1), |
2033 | 628 |
(stac strictify1 1), |
1461 | 629 |
(rtac refl 1) |
630 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
631 |
|
892 | 632 |
qed_goalw "ssplit2" Sprod3.thy [ssplit_def] |
1461 | 633 |
"[|x~=UU;y~=UU|] ==> ssplit`f`(|x,y|)= f`x`y" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
634 |
(fn prems => |
1461 | 635 |
[ |
2033 | 636 |
(stac beta_cfun 1), |
1461 | 637 |
(cont_tacR 1), |
2033 | 638 |
(stac strictify2 1), |
1461 | 639 |
(rtac defined_spair 1), |
640 |
(resolve_tac prems 1), |
|
641 |
(resolve_tac prems 1), |
|
2033 | 642 |
(stac beta_cfun 1), |
1461 | 643 |
(cont_tacR 1), |
2033 | 644 |
(stac sfst2 1), |
1461 | 645 |
(resolve_tac prems 1), |
2033 | 646 |
(stac ssnd2 1), |
1461 | 647 |
(resolve_tac prems 1), |
648 |
(rtac refl 1) |
|
649 |
]); |
|
243
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 |
|
892 | 652 |
qed_goalw "ssplit3" Sprod3.thy [ssplit_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
653 |
"ssplit`spair`z=z" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
654 |
(fn prems => |
1461 | 655 |
[ |
2033 | 656 |
(stac beta_cfun 1), |
1461 | 657 |
(cont_tacR 1), |
1675 | 658 |
(case_tac "z=UU" 1), |
1461 | 659 |
(hyp_subst_tac 1), |
660 |
(rtac strictify1 1), |
|
661 |
(rtac trans 1), |
|
662 |
(rtac strictify2 1), |
|
663 |
(atac 1), |
|
2033 | 664 |
(stac beta_cfun 1), |
1461 | 665 |
(cont_tacR 1), |
666 |
(rtac surjective_pairing_Sprod2 1) |
|
667 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
668 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
669 |
|
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 |
(* install simplifier for Sprod *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
672 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
673 |
|
1274 | 674 |
val Sprod_rews = [strict_spair1,strict_spair2,strict_sfst1,strict_sfst2, |
1461 | 675 |
strict_ssnd1,strict_ssnd2,sfst2,ssnd2,defined_spair, |
676 |
ssplit1,ssplit2]; |
|
1274 | 677 |
|
1267 | 678 |
Addsimps [strict_spair1,strict_spair2,strict_sfst1,strict_sfst2, |
1461 | 679 |
strict_ssnd1,strict_ssnd2,sfst2,ssnd2,defined_spair, |
680 |
ssplit1,ssplit2]; |