author | paulson |
Wed, 28 Jun 2000 10:54:21 +0200 | |
changeset 9169 | 85a47aa21f74 |
parent 8161 | bde1391fd0a5 |
child 9245 | 428385c4bc50 |
permissions | -rw-r--r-- |
9169 | 1 |
(* Title: HOLCF/Ssum3.ML |
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ID: $Id$ |
1461 | 3 |
Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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9169 | 6 |
Class instance of ++ for class pcpo |
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*) |
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(* for compatibility with old HOLCF-Version *) |
9169 | 10 |
Goal "UU = Isinl UU"; |
11 |
by (simp_tac (HOL_ss addsimps [UU_def,UU_ssum_def]) 1); |
|
12 |
qed "inst_ssum_pcpo"; |
|
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|
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(* ------------------------------------------------------------------------ *) |
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(* continuity for Isinl and Isinr *) |
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(* ------------------------------------------------------------------------ *) |
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9169 | 18 |
Goal "contlub(Isinl)"; |
19 |
by (rtac contlubI 1); |
|
20 |
by (strip_tac 1); |
|
21 |
by (rtac trans 1); |
|
22 |
by (rtac (thelub_ssum1a RS sym) 2); |
|
23 |
by (rtac allI 3); |
|
24 |
by (rtac exI 3); |
|
25 |
by (rtac refl 3); |
|
26 |
by (etac (monofun_Isinl RS ch2ch_monofun) 2); |
|
27 |
by (case_tac "lub(range(Y))=UU" 1); |
|
28 |
by (res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1); |
|
29 |
by (atac 1); |
|
30 |
by (res_inst_tac [("f","Isinl")] arg_cong 1); |
|
31 |
by (rtac (chain_UU_I_inverse RS sym) 1); |
|
32 |
by (rtac allI 1); |
|
33 |
by (res_inst_tac [("s","UU"),("t","Y(i)")] ssubst 1); |
|
34 |
by (etac (chain_UU_I RS spec ) 1); |
|
35 |
by (atac 1); |
|
36 |
by (rtac Iwhen1 1); |
|
37 |
by (res_inst_tac [("f","Isinl")] arg_cong 1); |
|
38 |
by (rtac lub_equal 1); |
|
39 |
by (atac 1); |
|
40 |
by (rtac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
41 |
by (etac (monofun_Isinl RS ch2ch_monofun) 1); |
|
42 |
by (rtac allI 1); |
|
43 |
by (case_tac "Y(k)=UU" 1); |
|
44 |
by (asm_simp_tac Ssum0_ss 1); |
|
45 |
by (asm_simp_tac Ssum0_ss 1); |
|
46 |
qed "contlub_Isinl"; |
|
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9169 | 48 |
Goal "contlub(Isinr)"; |
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by (rtac contlubI 1); |
|
50 |
by (strip_tac 1); |
|
51 |
by (rtac trans 1); |
|
52 |
by (rtac (thelub_ssum1b RS sym) 2); |
|
53 |
by (rtac allI 3); |
|
54 |
by (rtac exI 3); |
|
55 |
by (rtac refl 3); |
|
56 |
by (etac (monofun_Isinr RS ch2ch_monofun) 2); |
|
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by (case_tac "lub(range(Y))=UU" 1); |
|
58 |
by (res_inst_tac [("s","UU"),("t","lub(range(Y))")] ssubst 1); |
|
59 |
by (atac 1); |
|
60 |
by ((rtac arg_cong 1) THEN (rtac (chain_UU_I_inverse RS sym) 1)); |
|
61 |
by (rtac allI 1); |
|
62 |
by (res_inst_tac [("s","UU"),("t","Y(i)")] ssubst 1); |
|
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by (etac (chain_UU_I RS spec ) 1); |
|
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by (atac 1); |
|
65 |
by (rtac (strict_IsinlIsinr RS subst) 1); |
|
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by (rtac Iwhen1 1); |
|
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by ((rtac arg_cong 1) THEN (rtac lub_equal 1)); |
|
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by (atac 1); |
|
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by (rtac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
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by (etac (monofun_Isinr RS ch2ch_monofun) 1); |
|
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by (rtac allI 1); |
|
72 |
by (case_tac "Y(k)=UU" 1); |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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qed "contlub_Isinr"; |
|
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Goal "cont(Isinl)"; |
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by (rtac monocontlub2cont 1); |
|
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by (rtac monofun_Isinl 1); |
|
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by (rtac contlub_Isinl 1); |
|
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qed "cont_Isinl"; |
|
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9169 | 83 |
Goal "cont(Isinr)"; |
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by (rtac monocontlub2cont 1); |
|
85 |
by (rtac monofun_Isinr 1); |
|
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by (rtac contlub_Isinr 1); |
|
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qed "cont_Isinr"; |
|
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|
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|
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(* ------------------------------------------------------------------------ *) |
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(* continuity for Iwhen in the firts two arguments *) |
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(* ------------------------------------------------------------------------ *) |
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9169 | 94 |
Goal "contlub(Iwhen)"; |
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by (rtac contlubI 1); |
|
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by (strip_tac 1); |
|
97 |
by (rtac trans 1); |
|
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by (rtac (thelub_fun RS sym) 2); |
|
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by (etac (monofun_Iwhen1 RS ch2ch_monofun) 2); |
|
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by (rtac (expand_fun_eq RS iffD2) 1); |
|
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by (strip_tac 1); |
|
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by (rtac trans 1); |
|
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by (rtac (thelub_fun RS sym) 2); |
|
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by (rtac ch2ch_fun 2); |
|
105 |
by (etac (monofun_Iwhen1 RS ch2ch_monofun) 2); |
|
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by (rtac (expand_fun_eq RS iffD2) 1); |
|
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by (strip_tac 1); |
|
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by (res_inst_tac [("p","xa")] IssumE 1); |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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by (rtac (lub_const RS thelubI RS sym) 1); |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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by (etac contlub_cfun_fun 1); |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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by (rtac (lub_const RS thelubI RS sym) 1); |
|
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qed "contlub_Iwhen1"; |
|
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9169 | 117 |
Goal "contlub(Iwhen(f))"; |
118 |
by (rtac contlubI 1); |
|
119 |
by (strip_tac 1); |
|
120 |
by (rtac trans 1); |
|
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by (rtac (thelub_fun RS sym) 2); |
|
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by (etac (monofun_Iwhen2 RS ch2ch_monofun) 2); |
|
123 |
by (rtac (expand_fun_eq RS iffD2) 1); |
|
124 |
by (strip_tac 1); |
|
125 |
by (res_inst_tac [("p","x")] IssumE 1); |
|
126 |
by (asm_simp_tac Ssum0_ss 1); |
|
127 |
by (rtac (lub_const RS thelubI RS sym) 1); |
|
128 |
by (asm_simp_tac Ssum0_ss 1); |
|
129 |
by (rtac (lub_const RS thelubI RS sym) 1); |
|
130 |
by (asm_simp_tac Ssum0_ss 1); |
|
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by (etac contlub_cfun_fun 1); |
|
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qed "contlub_Iwhen2"; |
|
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(* ------------------------------------------------------------------------ *) |
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(* continuity for Iwhen in its third argument *) |
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(* ------------------------------------------------------------------------ *) |
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|
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(* ------------------------------------------------------------------------ *) |
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(* first 5 ugly lemmas *) |
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(* ------------------------------------------------------------------------ *) |
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9169 | 142 |
Goal "[| chain(Y); lub(range(Y)) = Isinl(x)|] ==> !i.? x. Y(i)=Isinl(x)"; |
143 |
by (strip_tac 1); |
|
144 |
by (res_inst_tac [("p","Y(i)")] IssumE 1); |
|
145 |
by (etac exI 1); |
|
146 |
by (etac exI 1); |
|
147 |
by (res_inst_tac [("P","y=UU")] notE 1); |
|
148 |
by (atac 1); |
|
149 |
by (rtac (less_ssum3d RS iffD1) 1); |
|
150 |
by (etac subst 1); |
|
151 |
by (etac subst 1); |
|
152 |
by (etac is_ub_thelub 1); |
|
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qed "ssum_lemma9"; |
|
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9169 | 156 |
Goal "[| chain(Y); lub(range(Y)) = Isinr(x)|] ==> !i.? x. Y(i)=Isinr(x)"; |
157 |
by (strip_tac 1); |
|
158 |
by (res_inst_tac [("p","Y(i)")] IssumE 1); |
|
159 |
by (rtac exI 1); |
|
160 |
by (etac trans 1); |
|
161 |
by (rtac strict_IsinlIsinr 1); |
|
162 |
by (etac exI 2); |
|
163 |
by (res_inst_tac [("P","xa=UU")] notE 1); |
|
164 |
by (atac 1); |
|
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by (rtac (less_ssum3c RS iffD1) 1); |
|
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by (etac subst 1); |
|
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by (etac subst 1); |
|
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by (etac is_ub_thelub 1); |
|
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qed "ssum_lemma10"; |
|
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|
9169 | 171 |
Goal "[| chain(Y); lub(range(Y)) = Isinl(UU) |] ==>\ |
8161 | 172 |
\ Iwhen f g (lub(range Y)) = lub(range(%i. Iwhen f g (Y i)))"; |
173 |
by (asm_simp_tac Ssum0_ss 1); |
|
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by (rtac (chain_UU_I_inverse RS sym) 1); |
|
175 |
by (rtac allI 1); |
|
176 |
by (res_inst_tac [("s","Isinl(UU)"),("t","Y(i)")] subst 1); |
|
177 |
by (rtac (inst_ssum_pcpo RS subst) 1); |
|
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by (rtac (chain_UU_I RS spec RS sym) 1); |
|
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by (atac 1); |
|
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by (etac (inst_ssum_pcpo RS ssubst) 1); |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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qed "ssum_lemma11"; |
|
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9169 | 184 |
Goal "[| chain(Y); lub(range(Y)) = Isinl(x); x ~= UU |] ==>\ |
185 |
\ Iwhen f g (lub(range Y)) = lub(range(%i. Iwhen f g (Y i)))"; |
|
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by (asm_simp_tac Ssum0_ss 1); |
|
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by (res_inst_tac [("t","x")] subst 1); |
|
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by (rtac inject_Isinl 1); |
|
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by (rtac trans 1); |
|
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by (atac 2); |
|
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by (rtac (thelub_ssum1a RS sym) 1); |
|
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by (atac 1); |
|
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by (etac ssum_lemma9 1); |
|
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by (atac 1); |
|
195 |
by (rtac trans 1); |
|
196 |
by (rtac contlub_cfun_arg 1); |
|
197 |
by (rtac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
198 |
by (atac 1); |
|
199 |
by (rtac lub_equal2 1); |
|
200 |
by (rtac (chain_mono2 RS exE) 1); |
|
201 |
by (atac 2); |
|
202 |
by (rtac chain_UU_I_inverse2 1); |
|
203 |
by (stac inst_ssum_pcpo 1); |
|
204 |
by (etac swap 1); |
|
205 |
by (rtac inject_Isinl 1); |
|
206 |
by (rtac trans 1); |
|
207 |
by (etac sym 1); |
|
208 |
by (etac notnotD 1); |
|
209 |
by (rtac exI 1); |
|
210 |
by (strip_tac 1); |
|
211 |
by (rtac (ssum_lemma9 RS spec RS exE) 1); |
|
212 |
by (atac 1); |
|
213 |
by (atac 1); |
|
214 |
by (res_inst_tac [("t","Y(i)")] ssubst 1); |
|
215 |
by (atac 1); |
|
216 |
by (rtac trans 1); |
|
217 |
by (rtac cfun_arg_cong 1); |
|
218 |
by (rtac Iwhen2 1); |
|
219 |
by (res_inst_tac [("Pa","Y(i)=UU")] swap 1); |
|
220 |
by (fast_tac HOL_cs 1); |
|
221 |
by (stac inst_ssum_pcpo 1); |
|
222 |
by (res_inst_tac [("t","Y(i)")] ssubst 1); |
|
223 |
by (atac 1); |
|
224 |
by (fast_tac HOL_cs 1); |
|
225 |
by (stac Iwhen2 1); |
|
226 |
by (res_inst_tac [("Pa","Y(i)=UU")] swap 1); |
|
227 |
by (fast_tac HOL_cs 1); |
|
228 |
by (stac inst_ssum_pcpo 1); |
|
229 |
by (res_inst_tac [("t","Y(i)")] ssubst 1); |
|
230 |
by (atac 1); |
|
231 |
by (fast_tac HOL_cs 1); |
|
232 |
by (simp_tac (simpset_of Cfun3.thy) 1); |
|
233 |
by (rtac (monofun_Rep_CFun2 RS ch2ch_monofun) 1); |
|
234 |
by (etac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
235 |
by (etac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
236 |
qed "ssum_lemma12"; |
|
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9169 | 239 |
Goal "[| chain(Y); lub(range(Y)) = Isinr(x); x ~= UU |] ==>\ |
240 |
\ Iwhen f g (lub(range Y)) = lub(range(%i. Iwhen f g (Y i)))"; |
|
241 |
by (asm_simp_tac Ssum0_ss 1); |
|
242 |
by (res_inst_tac [("t","x")] subst 1); |
|
243 |
by (rtac inject_Isinr 1); |
|
244 |
by (rtac trans 1); |
|
245 |
by (atac 2); |
|
246 |
by (rtac (thelub_ssum1b RS sym) 1); |
|
247 |
by (atac 1); |
|
248 |
by (etac ssum_lemma10 1); |
|
249 |
by (atac 1); |
|
250 |
by (rtac trans 1); |
|
251 |
by (rtac contlub_cfun_arg 1); |
|
252 |
by (rtac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
253 |
by (atac 1); |
|
254 |
by (rtac lub_equal2 1); |
|
255 |
by (rtac (chain_mono2 RS exE) 1); |
|
256 |
by (atac 2); |
|
257 |
by (rtac chain_UU_I_inverse2 1); |
|
258 |
by (stac inst_ssum_pcpo 1); |
|
259 |
by (etac swap 1); |
|
260 |
by (rtac inject_Isinr 1); |
|
261 |
by (rtac trans 1); |
|
262 |
by (etac sym 1); |
|
263 |
by (rtac (strict_IsinlIsinr RS subst) 1); |
|
264 |
by (etac notnotD 1); |
|
265 |
by (rtac exI 1); |
|
266 |
by (strip_tac 1); |
|
267 |
by (rtac (ssum_lemma10 RS spec RS exE) 1); |
|
268 |
by (atac 1); |
|
269 |
by (atac 1); |
|
270 |
by (res_inst_tac [("t","Y(i)")] ssubst 1); |
|
271 |
by (atac 1); |
|
272 |
by (rtac trans 1); |
|
273 |
by (rtac cfun_arg_cong 1); |
|
274 |
by (rtac Iwhen3 1); |
|
275 |
by (res_inst_tac [("Pa","Y(i)=UU")] swap 1); |
|
276 |
by (fast_tac HOL_cs 1); |
|
277 |
by (dtac notnotD 1); |
|
278 |
by (stac inst_ssum_pcpo 1); |
|
279 |
by (stac strict_IsinlIsinr 1); |
|
280 |
by (res_inst_tac [("t","Y(i)")] ssubst 1); |
|
281 |
by (atac 1); |
|
282 |
by (fast_tac HOL_cs 1); |
|
283 |
by (stac Iwhen3 1); |
|
284 |
by (res_inst_tac [("Pa","Y(i)=UU")] swap 1); |
|
285 |
by (fast_tac HOL_cs 1); |
|
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by (dtac notnotD 1); |
|
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by (stac inst_ssum_pcpo 1); |
|
288 |
by (stac strict_IsinlIsinr 1); |
|
289 |
by (res_inst_tac [("t","Y(i)")] ssubst 1); |
|
290 |
by (atac 1); |
|
291 |
by (fast_tac HOL_cs 1); |
|
292 |
by (simp_tac (simpset_of Cfun3.thy) 1); |
|
293 |
by (rtac (monofun_Rep_CFun2 RS ch2ch_monofun) 1); |
|
294 |
by (etac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
295 |
by (etac (monofun_Iwhen3 RS ch2ch_monofun) 1); |
|
296 |
qed "ssum_lemma13"; |
|
243
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297 |
|
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298 |
|
9169 | 299 |
Goal "contlub(Iwhen(f)(g))"; |
300 |
by (rtac contlubI 1); |
|
301 |
by (strip_tac 1); |
|
302 |
by (res_inst_tac [("p","lub(range(Y))")] IssumE 1); |
|
303 |
by (etac ssum_lemma11 1); |
|
304 |
by (atac 1); |
|
305 |
by (etac ssum_lemma12 1); |
|
306 |
by (atac 1); |
|
307 |
by (atac 1); |
|
308 |
by (etac ssum_lemma13 1); |
|
309 |
by (atac 1); |
|
310 |
by (atac 1); |
|
311 |
qed "contlub_Iwhen3"; |
|
243
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312 |
|
9169 | 313 |
Goal "cont(Iwhen)"; |
314 |
by (rtac monocontlub2cont 1); |
|
315 |
by (rtac monofun_Iwhen1 1); |
|
316 |
by (rtac contlub_Iwhen1 1); |
|
317 |
qed "cont_Iwhen1"; |
|
243
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318 |
|
9169 | 319 |
Goal "cont(Iwhen(f))"; |
320 |
by (rtac monocontlub2cont 1); |
|
321 |
by (rtac monofun_Iwhen2 1); |
|
322 |
by (rtac contlub_Iwhen2 1); |
|
323 |
qed "cont_Iwhen2"; |
|
243
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324 |
|
9169 | 325 |
Goal "cont(Iwhen(f)(g))"; |
326 |
by (rtac monocontlub2cont 1); |
|
327 |
by (rtac monofun_Iwhen3 1); |
|
328 |
by (rtac contlub_Iwhen3 1); |
|
329 |
qed "cont_Iwhen3"; |
|
243
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330 |
|
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|
331 |
(* ------------------------------------------------------------------------ *) |
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332 |
(* continuous versions of lemmas for 'a ++ 'b *) |
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333 |
(* ------------------------------------------------------------------------ *) |
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334 |
|
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335 |
qed_goalw "strict_sinl" Ssum3.thy [sinl_def] "sinl`UU =UU" |
243
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336 |
(fn prems => |
1461 | 337 |
[ |
338 |
(simp_tac (Ssum0_ss addsimps [cont_Isinl]) 1), |
|
339 |
(rtac (inst_ssum_pcpo RS sym) 1) |
|
340 |
]); |
|
243
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|
341 |
|
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342 |
qed_goalw "strict_sinr" Ssum3.thy [sinr_def] "sinr`UU=UU" |
243
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343 |
(fn prems => |
1461 | 344 |
[ |
345 |
(simp_tac (Ssum0_ss addsimps [cont_Isinr]) 1), |
|
346 |
(rtac (inst_ssum_pcpo RS sym) 1) |
|
347 |
]); |
|
243
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|
348 |
|
892 | 349 |
qed_goalw "noteq_sinlsinr" Ssum3.thy [sinl_def,sinr_def] |
1461 | 350 |
"sinl`a=sinr`b ==> a=UU & b=UU" |
243
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|
351 |
(fn prems => |
1461 | 352 |
[ |
353 |
(cut_facts_tac prems 1), |
|
354 |
(rtac noteq_IsinlIsinr 1), |
|
355 |
(etac box_equals 1), |
|
356 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1), |
|
357 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1) |
|
358 |
]); |
|
243
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|
359 |
|
892 | 360 |
qed_goalw "inject_sinl" Ssum3.thy [sinl_def,sinr_def] |
1461 | 361 |
"sinl`a1=sinl`a2==> a1=a2" |
243
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|
362 |
(fn prems => |
1461 | 363 |
[ |
364 |
(cut_facts_tac prems 1), |
|
365 |
(rtac inject_Isinl 1), |
|
366 |
(etac box_equals 1), |
|
367 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1), |
|
368 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1) |
|
369 |
]); |
|
243
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|
370 |
|
892 | 371 |
qed_goalw "inject_sinr" Ssum3.thy [sinl_def,sinr_def] |
1461 | 372 |
"sinr`a1=sinr`a2==> a1=a2" |
243
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|
373 |
(fn prems => |
1461 | 374 |
[ |
375 |
(cut_facts_tac prems 1), |
|
376 |
(rtac inject_Isinr 1), |
|
377 |
(etac box_equals 1), |
|
378 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1), |
|
379 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1) |
|
380 |
]); |
|
243
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|
381 |
|
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|
382 |
|
9169 | 383 |
Goal "x~=UU ==> sinl`x ~= UU"; |
384 |
by (etac swap 1); |
|
385 |
by (rtac inject_sinl 1); |
|
386 |
by (stac strict_sinl 1); |
|
387 |
by (etac notnotD 1); |
|
388 |
qed "defined_sinl"; |
|
243
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|
389 |
|
9169 | 390 |
Goal "x~=UU ==> sinr`x ~= UU"; |
391 |
by (etac swap 1); |
|
392 |
by (rtac inject_sinr 1); |
|
393 |
by (stac strict_sinr 1); |
|
394 |
by (etac notnotD 1); |
|
395 |
qed "defined_sinr"; |
|
243
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|
396 |
|
892 | 397 |
qed_goalw "Exh_Ssum1" Ssum3.thy [sinl_def,sinr_def] |
1461 | 398 |
"z=UU | (? a. z=sinl`a & a~=UU) | (? b. z=sinr`b & b~=UU)" |
243
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|
399 |
(fn prems => |
1461 | 400 |
[ |
401 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1), |
|
2033 | 402 |
(stac inst_ssum_pcpo 1), |
1461 | 403 |
(rtac Exh_Ssum 1) |
404 |
]); |
|
243
c22b85994e17
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|
405 |
|
c22b85994e17
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parents:
diff
changeset
|
406 |
|
892 | 407 |
qed_goalw "ssumE" Ssum3.thy [sinl_def,sinr_def] |
1461 | 408 |
"[|p=UU ==> Q ;\ |
409 |
\ !!x.[|p=sinl`x; x~=UU |] ==> Q;\ |
|
410 |
\ !!y.[|p=sinr`y; y~=UU |] ==> Q|] ==> Q" |
|
243
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|
411 |
(fn prems => |
1461 | 412 |
[ |
413 |
(rtac IssumE 1), |
|
414 |
(resolve_tac prems 1), |
|
2033 | 415 |
(stac inst_ssum_pcpo 1), |
1461 | 416 |
(atac 1), |
417 |
(resolve_tac prems 1), |
|
418 |
(atac 2), |
|
419 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1), |
|
420 |
(resolve_tac prems 1), |
|
421 |
(atac 2), |
|
422 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1) |
|
423 |
]); |
|
243
c22b85994e17
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|
424 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
425 |
|
892 | 426 |
qed_goalw "ssumE2" Ssum3.thy [sinl_def,sinr_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
427 |
"[|!!x.[|p=sinl`x|] ==> Q;\ |
1461 | 428 |
\ !!y.[|p=sinr`y|] ==> Q|] ==> Q" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
429 |
(fn prems => |
1461 | 430 |
[ |
431 |
(rtac IssumE2 1), |
|
432 |
(resolve_tac prems 1), |
|
2033 | 433 |
(stac beta_cfun 1), |
1461 | 434 |
(rtac cont_Isinl 1), |
435 |
(atac 1), |
|
436 |
(resolve_tac prems 1), |
|
2033 | 437 |
(stac beta_cfun 1), |
1461 | 438 |
(rtac cont_Isinr 1), |
439 |
(atac 1) |
|
440 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
441 |
|
5439 | 442 |
qed_goalw "sscase1" Ssum3.thy [sscase_def,sinl_def,sinr_def] |
443 |
"sscase`f`g`UU = UU" (fn _ => let |
|
2566 | 444 |
val tac = (REPEAT (resolve_tac (cont_lemmas1 @ [cont_Iwhen1,cont_Iwhen2, |
445 |
cont_Iwhen3,cont2cont_CF1L]) 1)) in |
|
446 |
[ |
|
2033 | 447 |
(stac inst_ssum_pcpo 1), |
448 |
(stac beta_cfun 1), |
|
2566 | 449 |
tac, |
450 |
(stac beta_cfun 1), |
|
451 |
tac, |
|
2033 | 452 |
(stac beta_cfun 1), |
2566 | 453 |
tac, |
1461 | 454 |
(simp_tac Ssum0_ss 1) |
2566 | 455 |
] end); |
456 |
||
457 |
||
458 |
val tac = (REPEAT (resolve_tac (cont_lemmas1 @ [cont_Iwhen1,cont_Iwhen2, |
|
459 |
cont_Iwhen3,cont_Isinl,cont_Isinr,cont2cont_CF1L]) 1)); |
|
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
460 |
|
5439 | 461 |
qed_goalw "sscase2" Ssum3.thy [sscase_def,sinl_def,sinr_def] |
462 |
"x~=UU==> sscase`f`g`(sinl`x) = f`x" (fn prems => [ |
|
1461 | 463 |
(cut_facts_tac prems 1), |
2033 | 464 |
(stac beta_cfun 1), |
2566 | 465 |
tac, |
2033 | 466 |
(stac beta_cfun 1), |
2566 | 467 |
tac, |
2033 | 468 |
(stac beta_cfun 1), |
2566 | 469 |
tac, |
2033 | 470 |
(stac beta_cfun 1), |
2566 | 471 |
tac, |
1461 | 472 |
(asm_simp_tac Ssum0_ss 1) |
473 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
474 |
|
5439 | 475 |
qed_goalw "sscase3" Ssum3.thy [sscase_def,sinl_def,sinr_def] |
476 |
"x~=UU==> sscase`f`g`(sinr`x) = g`x" (fn prems => [ |
|
1461 | 477 |
(cut_facts_tac prems 1), |
2033 | 478 |
(stac beta_cfun 1), |
2566 | 479 |
tac, |
2033 | 480 |
(stac beta_cfun 1), |
2566 | 481 |
tac, |
2033 | 482 |
(stac beta_cfun 1), |
2566 | 483 |
tac, |
2033 | 484 |
(stac beta_cfun 1), |
2566 | 485 |
tac, |
1461 | 486 |
(asm_simp_tac Ssum0_ss 1) |
487 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
488 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
489 |
|
892 | 490 |
qed_goalw "less_ssum4a" Ssum3.thy [sinl_def,sinr_def] |
2566 | 491 |
"(sinl`x << sinl`y) = (x << y)" (fn prems => [ |
2033 | 492 |
(stac beta_cfun 1), |
2566 | 493 |
tac, |
2033 | 494 |
(stac beta_cfun 1), |
2566 | 495 |
tac, |
1461 | 496 |
(rtac less_ssum3a 1) |
497 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
498 |
|
892 | 499 |
qed_goalw "less_ssum4b" Ssum3.thy [sinl_def,sinr_def] |
2566 | 500 |
"(sinr`x << sinr`y) = (x << y)" (fn prems => [ |
2033 | 501 |
(stac beta_cfun 1), |
2566 | 502 |
tac, |
2033 | 503 |
(stac beta_cfun 1), |
2566 | 504 |
tac, |
1461 | 505 |
(rtac less_ssum3b 1) |
506 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
507 |
|
892 | 508 |
qed_goalw "less_ssum4c" Ssum3.thy [sinl_def,sinr_def] |
2566 | 509 |
"(sinl`x << sinr`y) = (x = UU)" (fn prems => |
1461 | 510 |
[ |
2033 | 511 |
(stac beta_cfun 1), |
2566 | 512 |
tac, |
2033 | 513 |
(stac beta_cfun 1), |
2566 | 514 |
tac, |
1461 | 515 |
(rtac less_ssum3c 1) |
516 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
517 |
|
892 | 518 |
qed_goalw "less_ssum4d" Ssum3.thy [sinl_def,sinr_def] |
1461 | 519 |
"(sinr`x << sinl`y) = (x = UU)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
520 |
(fn prems => |
1461 | 521 |
[ |
2033 | 522 |
(stac beta_cfun 1), |
2566 | 523 |
tac, |
2033 | 524 |
(stac beta_cfun 1), |
2566 | 525 |
tac, |
1461 | 526 |
(rtac less_ssum3d 1) |
527 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
528 |
|
892 | 529 |
qed_goalw "ssum_chainE" Ssum3.thy [sinl_def,sinr_def] |
4721
c8a8482a8124
renamed is_chain to chain, is_tord to tord, replaced chain_finite by chfin
oheimb
parents:
4098
diff
changeset
|
530 |
"chain(Y) ==> (!i.? x.(Y i)=sinl`x)|(!i.? y.(Y i)=sinr`y)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
531 |
(fn prems => |
1461 | 532 |
[ |
533 |
(cut_facts_tac prems 1), |
|
534 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinr,cont_Isinl]) 1), |
|
535 |
(etac ssum_lemma4 1) |
|
536 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
537 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
538 |
|
5439 | 539 |
qed_goalw "thelub_ssum2a" Ssum3.thy [sinl_def,sinr_def,sscase_def] |
4721
c8a8482a8124
renamed is_chain to chain, is_tord to tord, replaced chain_finite by chfin
oheimb
parents:
4098
diff
changeset
|
540 |
"[| chain(Y); !i.? x. Y(i) = sinl`x |] ==>\ |
5439 | 541 |
\ lub(range(Y)) = sinl`(lub(range(%i. sscase`(LAM x. x)`(LAM y. UU)`(Y i))))" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
542 |
(fn prems => |
1461 | 543 |
[ |
544 |
(cut_facts_tac prems 1), |
|
2033 | 545 |
(stac beta_cfun 1), |
2566 | 546 |
tac, |
2033 | 547 |
(stac beta_cfun 1), |
2566 | 548 |
tac, |
2033 | 549 |
(stac beta_cfun 1), |
2566 | 550 |
tac, |
2033 | 551 |
(stac (beta_cfun RS ext) 1), |
2566 | 552 |
tac, |
1461 | 553 |
(rtac thelub_ssum1a 1), |
554 |
(atac 1), |
|
555 |
(rtac allI 1), |
|
556 |
(etac allE 1), |
|
557 |
(etac exE 1), |
|
558 |
(rtac exI 1), |
|
559 |
(etac box_equals 1), |
|
560 |
(rtac refl 1), |
|
561 |
(asm_simp_tac (Ssum0_ss addsimps [cont_Isinl]) 1) |
|
562 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
563 |
|
5439 | 564 |
qed_goalw "thelub_ssum2b" Ssum3.thy [sinl_def,sinr_def,sscase_def] |
4721
c8a8482a8124
renamed is_chain to chain, is_tord to tord, replaced chain_finite by chfin
oheimb
parents:
4098
diff
changeset
|
565 |
"[| chain(Y); !i.? x. Y(i) = sinr`x |] ==>\ |
5439 | 566 |
\ lub(range(Y)) = sinr`(lub(range(%i. sscase`(LAM y. UU)`(LAM x. x)`(Y i))))" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
567 |
(fn prems => |
1461 | 568 |
[ |
569 |
(cut_facts_tac prems 1), |
|
2033 | 570 |
(stac beta_cfun 1), |
2566 | 571 |
tac, |
2033 | 572 |
(stac beta_cfun 1), |
2566 | 573 |
tac, |
2033 | 574 |
(stac beta_cfun 1), |
2566 | 575 |
tac, |
2033 | 576 |
(stac (beta_cfun RS ext) 1), |
2566 | 577 |
tac, |
1461 | 578 |
(rtac thelub_ssum1b 1), |
579 |
(atac 1), |
|
580 |
(rtac allI 1), |
|
581 |
(etac allE 1), |
|
582 |
(etac exE 1), |
|
583 |
(rtac exI 1), |
|
584 |
(etac box_equals 1), |
|
585 |
(rtac refl 1), |
|
586 |
(asm_simp_tac (Ssum0_ss addsimps |
|
587 |
[cont_Isinr,cont_Isinl,cont_Iwhen1,cont_Iwhen2, |
|
588 |
cont_Iwhen3]) 1) |
|
589 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
590 |
|
892 | 591 |
qed_goalw "thelub_ssum2a_rev" Ssum3.thy [sinl_def,sinr_def] |
4721
c8a8482a8124
renamed is_chain to chain, is_tord to tord, replaced chain_finite by chfin
oheimb
parents:
4098
diff
changeset
|
592 |
"[| chain(Y); lub(range(Y)) = sinl`x|] ==> !i.? x. Y(i)=sinl`x" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
593 |
(fn prems => |
1461 | 594 |
[ |
595 |
(cut_facts_tac prems 1), |
|
596 |
(asm_simp_tac (Ssum0_ss addsimps |
|
597 |
[cont_Isinr,cont_Isinl,cont_Iwhen1,cont_Iwhen2, |
|
598 |
cont_Iwhen3]) 1), |
|
599 |
(etac ssum_lemma9 1), |
|
600 |
(asm_simp_tac (Ssum0_ss addsimps |
|
601 |
[cont_Isinr,cont_Isinl,cont_Iwhen1,cont_Iwhen2, |
|
602 |
cont_Iwhen3]) 1) |
|
603 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
604 |
|
892 | 605 |
qed_goalw "thelub_ssum2b_rev" Ssum3.thy [sinl_def,sinr_def] |
4721
c8a8482a8124
renamed is_chain to chain, is_tord to tord, replaced chain_finite by chfin
oheimb
parents:
4098
diff
changeset
|
606 |
"[| chain(Y); lub(range(Y)) = sinr`x|] ==> !i.? x. Y(i)=sinr`x" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
607 |
(fn prems => |
1461 | 608 |
[ |
609 |
(cut_facts_tac prems 1), |
|
610 |
(asm_simp_tac (Ssum0_ss addsimps |
|
611 |
[cont_Isinr,cont_Isinl,cont_Iwhen1,cont_Iwhen2, |
|
612 |
cont_Iwhen3]) 1), |
|
613 |
(etac ssum_lemma10 1), |
|
614 |
(asm_simp_tac (Ssum0_ss addsimps |
|
615 |
[cont_Isinr,cont_Isinl,cont_Iwhen1,cont_Iwhen2, |
|
616 |
cont_Iwhen3]) 1) |
|
617 |
]); |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
618 |
|
9169 | 619 |
Goal "chain(Y) ==>\ |
5439 | 620 |
\ lub(range(Y)) = sinl`(lub(range(%i. sscase`(LAM x. x)`(LAM y. UU)`(Y i))))\ |
9169 | 621 |
\ | lub(range(Y)) = sinr`(lub(range(%i. sscase`(LAM y. UU)`(LAM x. x)`(Y i))))"; |
622 |
by (rtac (ssum_chainE RS disjE) 1); |
|
623 |
by (atac 1); |
|
624 |
by (rtac disjI1 1); |
|
625 |
by (etac thelub_ssum2a 1); |
|
626 |
by (atac 1); |
|
627 |
by (rtac disjI2 1); |
|
628 |
by (etac thelub_ssum2b 1); |
|
629 |
by (atac 1); |
|
630 |
qed "thelub_ssum3"; |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
631 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
632 |
|
9169 | 633 |
Goal "sscase`sinl`sinr`z=z"; |
634 |
by (res_inst_tac [("p","z")] ssumE 1); |
|
635 |
by (asm_simp_tac ((simpset_of Cfun3.thy) addsimps [sscase1,sscase2,sscase3]) 1); |
|
636 |
by (asm_simp_tac ((simpset_of Cfun3.thy) addsimps [sscase1,sscase2,sscase3]) 1); |
|
637 |
by (asm_simp_tac ((simpset_of Cfun3.thy) addsimps [sscase1,sscase2,sscase3]) 1); |
|
638 |
qed "sscase4"; |
|
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
639 |
|
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 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
642 |
(* install simplifier for Ssum *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
643 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
644 |
|
1274 | 645 |
val Ssum_rews = [strict_sinl,strict_sinr,defined_sinl,defined_sinr, |
5439 | 646 |
sscase1,sscase2,sscase3]; |
1274 | 647 |
|
648 |
Addsimps [strict_sinl,strict_sinr,defined_sinl,defined_sinr, |
|
5439 | 649 |
sscase1,sscase2,sscase3]; |