author | clasohm |
Tue, 30 Jan 1996 13:42:57 +0100 | |
changeset 1461 | 6bcb44e4d6e5 |
parent 1277 | caef3601c0b2 |
child 1675 | 36ba4da350c3 |
permissions | -rw-r--r-- |
1461 | 1 |
(* 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 (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 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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(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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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 (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 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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(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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parents:
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(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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(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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\ 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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166 |
(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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171 |
(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 => |
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[ |
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
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parents:
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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 => |
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[ |
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), |
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207 |
(etac sprod3_lemma4 1), |
|
208 |
(atac 1), |
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209 |
(atac 1), |
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210 |
(etac sprod3_lemma5 1), |
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211 |
(atac 1), |
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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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|
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qed_goal "cont_Ispair1" Sprod3.thy "cont(Ispair)" |
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(fn prems => |
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[ |
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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227 |
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)" |
243
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|
236 |
(fn prems => |
1461 | 237 |
[ |
238 |
(rtac contlubI 1), |
|
239 |
(strip_tac 1), |
|
240 |
(rtac (lub_sprod RS thelubI RS ssubst) 1), |
|
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), |
|
256 |
(rtac notnotI 1), |
|
257 |
(rtac (chain_UU_I RS spec) 1), |
|
258 |
(rtac (monofun_Issnd RS ch2ch_monofun) 1), |
|
259 |
(atac 1), |
|
260 |
(atac 1) |
|
261 |
]); |
|
243
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|
262 |
|
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263 |
|
892 | 264 |
qed_goal "contlub_Issnd" Sprod3.thy "contlub(Issnd)" |
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|
265 |
(fn prems => |
1461 | 266 |
[ |
267 |
(rtac contlubI 1), |
|
268 |
(strip_tac 1), |
|
269 |
(rtac (lub_sprod RS thelubI RS ssubst) 1), |
|
270 |
(atac 1), |
|
271 |
(res_inst_tac [("Q","lub(range(%i. Isfst(Y(i))))=UU")] |
|
272 |
(excluded_middle RS disjE) 1), |
|
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|
273 |
(asm_simp_tac Sprod0_ss 1), |
1461 | 274 |
(res_inst_tac [("s","UU"),("t","lub(range(%i. Isfst(Y(i))))")] |
275 |
ssubst 1), |
|
276 |
(atac 1), |
|
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277 |
(asm_simp_tac Sprod0_ss 1), |
1461 | 278 |
(rtac sym 1), |
279 |
(rtac chain_UU_I_inverse 1), |
|
280 |
(rtac allI 1), |
|
281 |
(rtac strict_Issnd 1), |
|
282 |
(rtac swap 1), |
|
283 |
(etac (defined_IsfstIssnd RS conjunct1) 2), |
|
284 |
(rtac notnotI 1), |
|
285 |
(rtac (chain_UU_I RS spec) 1), |
|
286 |
(rtac (monofun_Isfst RS ch2ch_monofun) 1), |
|
287 |
(atac 1), |
|
288 |
(atac 1) |
|
289 |
]); |
|
243
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290 |
|
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291 |
|
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|
292 |
qed_goal "cont_Isfst" Sprod3.thy "cont(Isfst)" |
243
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|
293 |
(fn prems => |
1461 | 294 |
[ |
295 |
(rtac monocontlub2cont 1), |
|
296 |
(rtac monofun_Isfst 1), |
|
297 |
(rtac contlub_Isfst 1) |
|
298 |
]); |
|
243
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299 |
|
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300 |
qed_goal "cont_Issnd" Sprod3.thy "cont(Issnd)" |
243
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|
301 |
(fn prems => |
1461 | 302 |
[ |
303 |
(rtac monocontlub2cont 1), |
|
304 |
(rtac monofun_Issnd 1), |
|
305 |
(rtac contlub_Issnd 1) |
|
306 |
]); |
|
243
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|
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|
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|
308 |
(* |
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309 |
-------------------------------------------------------------------------- |
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|
310 |
more lemmas for Sprod3.thy |
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|
311 |
|
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-------------------------------------------------------------------------- |
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313 |
*) |
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|
314 |
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|
315 |
qed_goal "spair_eq" Sprod3.thy "[|x1=x2;y1=y2|] ==> (|x1,y1|) = (|x2,y2|)" |
243
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|
316 |
(fn prems => |
1461 | 317 |
[ |
318 |
(cut_facts_tac prems 1), |
|
319 |
(fast_tac HOL_cs 1) |
|
320 |
]); |
|
243
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|
321 |
|
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322 |
(* ------------------------------------------------------------------------ *) |
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323 |
(* convert all lemmas to the continuous versions *) |
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|
324 |
(* ------------------------------------------------------------------------ *) |
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|
325 |
|
892 | 326 |
qed_goalw "beta_cfun_sprod" Sprod3.thy [spair_def] |
1461 | 327 |
"(LAM x y.Ispair x y)`a`b = Ispair a b" |
243
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|
328 |
(fn prems => |
1461 | 329 |
[ |
330 |
(rtac (beta_cfun RS ssubst) 1), |
|
331 |
(cont_tac 1), |
|
332 |
(rtac cont_Ispair2 1), |
|
333 |
(rtac cont2cont_CF1L 1), |
|
334 |
(rtac cont_Ispair1 1), |
|
335 |
(rtac (beta_cfun RS ssubst) 1), |
|
336 |
(rtac cont_Ispair2 1), |
|
337 |
(rtac refl 1) |
|
338 |
]); |
|
243
c22b85994e17
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|
339 |
|
892 | 340 |
qed_goalw "inject_spair" Sprod3.thy [spair_def] |
1461 | 341 |
"[| aa~=UU ; ba~=UU ; (|a,b|)=(|aa,ba|) |] ==> a=aa & b=ba" |
243
c22b85994e17
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|
342 |
(fn prems => |
1461 | 343 |
[ |
344 |
(cut_facts_tac prems 1), |
|
345 |
(etac inject_Ispair 1), |
|
346 |
(atac 1), |
|
347 |
(etac box_equals 1), |
|
348 |
(rtac beta_cfun_sprod 1), |
|
349 |
(rtac beta_cfun_sprod 1) |
|
350 |
]); |
|
243
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|
351 |
|
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|
352 |
qed_goalw "inst_sprod_pcpo2" Sprod3.thy [spair_def] "UU = (|UU,UU|)" |
243
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|
353 |
(fn prems => |
1461 | 354 |
[ |
355 |
(rtac sym 1), |
|
356 |
(rtac trans 1), |
|
357 |
(rtac beta_cfun_sprod 1), |
|
358 |
(rtac sym 1), |
|
359 |
(rtac inst_sprod_pcpo 1) |
|
360 |
]); |
|
243
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|
361 |
|
892 | 362 |
qed_goalw "strict_spair" Sprod3.thy [spair_def] |
1461 | 363 |
"(a=UU | b=UU) ==> (|a,b|)=UU" |
243
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|
364 |
(fn prems => |
1461 | 365 |
[ |
366 |
(cut_facts_tac prems 1), |
|
367 |
(rtac trans 1), |
|
368 |
(rtac beta_cfun_sprod 1), |
|
369 |
(rtac trans 1), |
|
370 |
(rtac (inst_sprod_pcpo RS sym) 2), |
|
371 |
(etac strict_Ispair 1) |
|
372 |
]); |
|
243
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|
373 |
|
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74be52691d62
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|
374 |
qed_goalw "strict_spair1" Sprod3.thy [spair_def] "(|UU,b|) = UU" |
243
c22b85994e17
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|
375 |
(fn prems => |
1461 | 376 |
[ |
377 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
378 |
(rtac trans 1), |
|
379 |
(rtac (inst_sprod_pcpo RS sym) 2), |
|
380 |
(rtac strict_Ispair1 1) |
|
381 |
]); |
|
243
c22b85994e17
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|
382 |
|
1168
74be52691d62
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|
383 |
qed_goalw "strict_spair2" Sprod3.thy [spair_def] "(|a,UU|) = UU" |
243
c22b85994e17
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|
384 |
(fn prems => |
1461 | 385 |
[ |
386 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
387 |
(rtac trans 1), |
|
388 |
(rtac (inst_sprod_pcpo RS sym) 2), |
|
389 |
(rtac strict_Ispair2 1) |
|
390 |
]); |
|
243
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|
391 |
|
892 | 392 |
qed_goalw "strict_spair_rev" Sprod3.thy [spair_def] |
1461 | 393 |
"(|x,y|)~=UU ==> ~x=UU & ~y=UU" |
243
c22b85994e17
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|
394 |
(fn prems => |
1461 | 395 |
[ |
396 |
(cut_facts_tac prems 1), |
|
397 |
(rtac strict_Ispair_rev 1), |
|
398 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
399 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
400 |
(atac 1) |
|
401 |
]); |
|
243
c22b85994e17
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|
402 |
|
892 | 403 |
qed_goalw "defined_spair_rev" Sprod3.thy [spair_def] |
1168
74be52691d62
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regensbu
parents:
1043
diff
changeset
|
404 |
"(|a,b|) = UU ==> (a = UU | b = UU)" |
243
c22b85994e17
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|
405 |
(fn prems => |
1461 | 406 |
[ |
407 |
(cut_facts_tac prems 1), |
|
408 |
(rtac defined_Ispair_rev 1), |
|
409 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
410 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
411 |
(atac 1) |
|
412 |
]); |
|
243
c22b85994e17
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|
413 |
|
892 | 414 |
qed_goalw "defined_spair" Sprod3.thy [spair_def] |
1461 | 415 |
"[|a~=UU; b~=UU|] ==> (|a,b|) ~= UU" |
243
c22b85994e17
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|
416 |
(fn prems => |
1461 | 417 |
[ |
418 |
(cut_facts_tac prems 1), |
|
419 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
420 |
(rtac (inst_sprod_pcpo RS ssubst) 1), |
|
421 |
(etac defined_Ispair 1), |
|
422 |
(atac 1) |
|
423 |
]); |
|
243
c22b85994e17
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|
424 |
|
892 | 425 |
qed_goalw "Exh_Sprod2" Sprod3.thy [spair_def] |
1461 | 426 |
"z=UU | (? a b. z=(|a,b|) & a~=UU & b~=UU)" |
243
c22b85994e17
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|
427 |
(fn prems => |
1461 | 428 |
[ |
429 |
(rtac (Exh_Sprod RS disjE) 1), |
|
430 |
(rtac disjI1 1), |
|
431 |
(rtac (inst_sprod_pcpo RS ssubst) 1), |
|
432 |
(atac 1), |
|
433 |
(rtac disjI2 1), |
|
434 |
(etac exE 1), |
|
435 |
(etac exE 1), |
|
436 |
(rtac exI 1), |
|
437 |
(rtac exI 1), |
|
438 |
(rtac conjI 1), |
|
439 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
440 |
(fast_tac HOL_cs 1), |
|
441 |
(fast_tac HOL_cs 1) |
|
442 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
443 |
|
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changeset
|
444 |
|
892 | 445 |
qed_goalw "sprodE" Sprod3.thy [spair_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
446 |
"[|p=UU ==> Q;!!x y. [|p=(|x,y|);x~=UU ; y~=UU|] ==> Q|] ==> Q" |
243
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|
447 |
(fn prems => |
1461 | 448 |
[ |
449 |
(rtac IsprodE 1), |
|
450 |
(resolve_tac prems 1), |
|
451 |
(rtac (inst_sprod_pcpo RS ssubst) 1), |
|
452 |
(atac 1), |
|
453 |
(resolve_tac prems 1), |
|
454 |
(atac 2), |
|
455 |
(atac 2), |
|
456 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
457 |
(atac 1) |
|
458 |
]); |
|
243
c22b85994e17
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|
459 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
460 |
|
892 | 461 |
qed_goalw "strict_sfst" Sprod3.thy [sfst_def] |
1461 | 462 |
"p=UU==>sfst`p=UU" |
243
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|
463 |
(fn prems => |
1461 | 464 |
[ |
465 |
(cut_facts_tac prems 1), |
|
466 |
(rtac (beta_cfun RS ssubst) 1), |
|
467 |
(rtac cont_Isfst 1), |
|
468 |
(rtac strict_Isfst 1), |
|
469 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
470 |
(atac 1) |
|
471 |
]); |
|
243
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|
472 |
|
892 | 473 |
qed_goalw "strict_sfst1" Sprod3.thy [sfst_def,spair_def] |
1461 | 474 |
"sfst`(|UU,y|) = UU" |
243
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|
475 |
(fn prems => |
1461 | 476 |
[ |
477 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
478 |
(rtac (beta_cfun RS ssubst) 1), |
|
479 |
(rtac cont_Isfst 1), |
|
480 |
(rtac strict_Isfst1 1) |
|
481 |
]); |
|
243
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|
482 |
|
892 | 483 |
qed_goalw "strict_sfst2" Sprod3.thy [sfst_def,spair_def] |
1461 | 484 |
"sfst`(|x,UU|) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
485 |
(fn prems => |
1461 | 486 |
[ |
487 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
488 |
(rtac (beta_cfun RS ssubst) 1), |
|
489 |
(rtac cont_Isfst 1), |
|
490 |
(rtac strict_Isfst2 1) |
|
491 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
492 |
|
892 | 493 |
qed_goalw "strict_ssnd" Sprod3.thy [ssnd_def] |
1461 | 494 |
"p=UU==>ssnd`p=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
495 |
(fn prems => |
1461 | 496 |
[ |
497 |
(cut_facts_tac prems 1), |
|
498 |
(rtac (beta_cfun RS ssubst) 1), |
|
499 |
(rtac cont_Issnd 1), |
|
500 |
(rtac strict_Issnd 1), |
|
501 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
502 |
(atac 1) |
|
503 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
504 |
|
892 | 505 |
qed_goalw "strict_ssnd1" Sprod3.thy [ssnd_def,spair_def] |
1461 | 506 |
"ssnd`(|UU,y|) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
507 |
(fn prems => |
1461 | 508 |
[ |
509 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
510 |
(rtac (beta_cfun RS ssubst) 1), |
|
511 |
(rtac cont_Issnd 1), |
|
512 |
(rtac strict_Issnd1 1) |
|
513 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
514 |
|
892 | 515 |
qed_goalw "strict_ssnd2" Sprod3.thy [ssnd_def,spair_def] |
1461 | 516 |
"ssnd`(|x,UU|) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
517 |
(fn prems => |
1461 | 518 |
[ |
519 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
520 |
(rtac (beta_cfun RS ssubst) 1), |
|
521 |
(rtac cont_Issnd 1), |
|
522 |
(rtac strict_Issnd2 1) |
|
523 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
524 |
|
892 | 525 |
qed_goalw "sfst2" Sprod3.thy [sfst_def,spair_def] |
1461 | 526 |
"y~=UU ==>sfst`(|x,y|)=x" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
527 |
(fn prems => |
1461 | 528 |
[ |
529 |
(cut_facts_tac prems 1), |
|
530 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
531 |
(rtac (beta_cfun RS ssubst) 1), |
|
532 |
(rtac cont_Isfst 1), |
|
533 |
(etac Isfst2 1) |
|
534 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
535 |
|
892 | 536 |
qed_goalw "ssnd2" Sprod3.thy [ssnd_def,spair_def] |
1461 | 537 |
"x~=UU ==>ssnd`(|x,y|)=y" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
538 |
(fn prems => |
1461 | 539 |
[ |
540 |
(cut_facts_tac prems 1), |
|
541 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
542 |
(rtac (beta_cfun RS ssubst) 1), |
|
543 |
(rtac cont_Issnd 1), |
|
544 |
(etac Issnd2 1) |
|
545 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
546 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
547 |
|
892 | 548 |
qed_goalw "defined_sfstssnd" Sprod3.thy [sfst_def,ssnd_def,spair_def] |
1461 | 549 |
"p~=UU ==> sfst`p ~=UU & ssnd`p ~=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
550 |
(fn prems => |
1461 | 551 |
[ |
552 |
(cut_facts_tac prems 1), |
|
553 |
(rtac (beta_cfun RS ssubst) 1), |
|
554 |
(rtac cont_Issnd 1), |
|
555 |
(rtac (beta_cfun RS ssubst) 1), |
|
556 |
(rtac cont_Isfst 1), |
|
557 |
(rtac defined_IsfstIssnd 1), |
|
558 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
559 |
(atac 1) |
|
560 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
561 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
562 |
|
892 | 563 |
qed_goalw "surjective_pairing_Sprod2" Sprod3.thy |
1461 | 564 |
[sfst_def,ssnd_def,spair_def] "(|sfst`p , ssnd`p|) = p" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
565 |
(fn prems => |
1461 | 566 |
[ |
567 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
568 |
(rtac (beta_cfun RS ssubst) 1), |
|
569 |
(rtac cont_Issnd 1), |
|
570 |
(rtac (beta_cfun RS ssubst) 1), |
|
571 |
(rtac cont_Isfst 1), |
|
572 |
(rtac (surjective_pairing_Sprod RS sym) 1) |
|
573 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
574 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
575 |
|
892 | 576 |
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
|
577 |
"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
|
578 |
(fn prems => |
1461 | 579 |
[ |
580 |
(cut_facts_tac prems 1), |
|
581 |
(rtac (beta_cfun RS ssubst) 1), |
|
582 |
(rtac cont_Issnd 1), |
|
583 |
(rtac (beta_cfun RS ssubst) 1), |
|
584 |
(rtac cont_Issnd 1), |
|
585 |
(rtac (beta_cfun RS ssubst) 1), |
|
586 |
(rtac cont_Isfst 1), |
|
587 |
(rtac (beta_cfun RS ssubst) 1), |
|
588 |
(rtac cont_Isfst 1), |
|
589 |
(rtac less_sprod3b 1), |
|
590 |
(rtac (inst_sprod_pcpo RS subst) 1), |
|
591 |
(atac 1) |
|
592 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
593 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
594 |
|
892 | 595 |
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
|
596 |
"[|(|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
|
597 |
(fn prems => |
1461 | 598 |
[ |
599 |
(cut_facts_tac prems 1), |
|
600 |
(rtac less_sprod4c 1), |
|
601 |
(REPEAT (atac 2)), |
|
602 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
603 |
(rtac (beta_cfun_sprod RS subst) 1), |
|
604 |
(atac 1) |
|
605 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
606 |
|
892 | 607 |
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
nipkow
parents:
diff
changeset
|
608 |
"[|is_chain(S)|] ==> range(S) <<| \ |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
609 |
\ (| 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
|
610 |
(fn prems => |
1461 | 611 |
[ |
612 |
(cut_facts_tac prems 1), |
|
613 |
(rtac (beta_cfun_sprod RS ssubst) 1), |
|
614 |
(rtac (beta_cfun RS ext RS ssubst) 1), |
|
615 |
(rtac cont_Issnd 1), |
|
616 |
(rtac (beta_cfun RS ext RS ssubst) 1), |
|
617 |
(rtac cont_Isfst 1), |
|
618 |
(rtac lub_sprod 1), |
|
619 |
(resolve_tac prems 1) |
|
620 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
621 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
622 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
623 |
val 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
|
624 |
(* |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
625 |
"is_chain ?S1 ==> |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
626 |
lub (range ?S1) = |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
627 |
(|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
|
628 |
*) |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
629 |
|
892 | 630 |
qed_goalw "ssplit1" Sprod3.thy [ssplit_def] |
1461 | 631 |
"ssplit`f`UU=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
632 |
(fn prems => |
1461 | 633 |
[ |
634 |
(rtac (beta_cfun RS ssubst) 1), |
|
635 |
(cont_tacR 1), |
|
636 |
(rtac (strictify1 RS ssubst) 1), |
|
637 |
(rtac refl 1) |
|
638 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
639 |
|
892 | 640 |
qed_goalw "ssplit2" Sprod3.thy [ssplit_def] |
1461 | 641 |
"[|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
|
642 |
(fn prems => |
1461 | 643 |
[ |
644 |
(rtac (beta_cfun RS ssubst) 1), |
|
645 |
(cont_tacR 1), |
|
646 |
(rtac (strictify2 RS ssubst) 1), |
|
647 |
(rtac defined_spair 1), |
|
648 |
(resolve_tac prems 1), |
|
649 |
(resolve_tac prems 1), |
|
650 |
(rtac (beta_cfun RS ssubst) 1), |
|
651 |
(cont_tacR 1), |
|
652 |
(rtac (sfst2 RS ssubst) 1), |
|
653 |
(resolve_tac prems 1), |
|
654 |
(rtac (ssnd2 RS ssubst) 1), |
|
655 |
(resolve_tac prems 1), |
|
656 |
(rtac refl 1) |
|
657 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
658 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
659 |
|
892 | 660 |
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
|
661 |
"ssplit`spair`z=z" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
662 |
(fn prems => |
1461 | 663 |
[ |
664 |
(rtac (beta_cfun RS ssubst) 1), |
|
665 |
(cont_tacR 1), |
|
666 |
(res_inst_tac [("Q","z=UU")] classical2 1), |
|
667 |
(hyp_subst_tac 1), |
|
668 |
(rtac strictify1 1), |
|
669 |
(rtac trans 1), |
|
670 |
(rtac strictify2 1), |
|
671 |
(atac 1), |
|
672 |
(rtac (beta_cfun RS ssubst) 1), |
|
673 |
(cont_tacR 1), |
|
674 |
(rtac surjective_pairing_Sprod2 1) |
|
675 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
676 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
677 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
678 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
679 |
(* install simplifier for Sprod *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
680 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
681 |
|
1274 | 682 |
val Sprod_rews = [strict_spair1,strict_spair2,strict_sfst1,strict_sfst2, |
1461 | 683 |
strict_ssnd1,strict_ssnd2,sfst2,ssnd2,defined_spair, |
684 |
ssplit1,ssplit2]; |
|
1274 | 685 |
|
1267 | 686 |
Addsimps [strict_spair1,strict_spair2,strict_sfst1,strict_sfst2, |
1461 | 687 |
strict_ssnd1,strict_ssnd2,sfst2,ssnd2,defined_spair, |
688 |
ssplit1,ssplit2]; |