147 ML {* fun lift_tac_intex lthy t = lift_tac lthy t [rel_eqv] *} |
147 ML {* fun lift_tac_intex lthy t = lift_tac lthy t [rel_eqv] *} |
148 |
148 |
149 ML {* fun inj_repabs_tac_intex lthy = inj_repabs_tac lthy [rel_refl] [trans2] *} |
149 ML {* fun inj_repabs_tac_intex lthy = inj_repabs_tac lthy [rel_refl] [trans2] *} |
150 ML {* fun all_inj_repabs_tac_intex lthy = all_inj_repabs_tac lthy [rel_refl] [trans2] *} |
150 ML {* fun all_inj_repabs_tac_intex lthy = all_inj_repabs_tac lthy [rel_refl] [trans2] *} |
151 |
151 |
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152 lemma cheat: "P" sorry |
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153 |
152 lemma test1: "my_plus a b = my_plus a b" |
154 lemma test1: "my_plus a b = my_plus a b" |
153 apply(rule refl) |
155 apply(rule refl) |
154 done |
156 done |
155 |
157 |
156 abbreviation |
158 abbreviation |
158 abbreviation |
160 abbreviation |
159 "Rep \<equiv> REP_my_int" |
161 "Rep \<equiv> REP_my_int" |
160 abbreviation |
162 abbreviation |
161 "Resp \<equiv> Respects" |
163 "Resp \<equiv> Respects" |
162 |
164 |
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165 |
163 lemma "PLUS a b = PLUS a b" |
166 lemma "PLUS a b = PLUS a b" |
164 apply(tactic {* procedure_tac @{context} @{thm test1} 1 *}) |
167 apply(tactic {* procedure_tac @{context} @{thm test1} 1 *}) |
165 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *}) |
168 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *}) |
166 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*}) |
169 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*}) |
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170 apply(tactic {* lambda_allex_prs_tac @{context} 1 *}) |
167 apply(tactic {* clean_tac @{context} 1 *}) |
171 apply(tactic {* clean_tac @{context} 1 *}) |
168 done |
172 done |
169 |
173 |
170 lemma test2: "my_plus a = my_plus a" |
174 lemma test2: "my_plus a = my_plus a" |
171 apply(rule refl) |
175 apply(rule refl) |
172 done |
176 done |
173 |
177 |
174 lemma "PLUS a = PLUS a" |
178 lemma "PLUS a = PLUS a" |
175 apply(tactic {* procedure_tac @{context} @{thm test2} 1 *}) |
179 apply(tactic {* procedure_tac @{context} @{thm test2} 1 *}) |
176 oops |
180 apply(rule cheat) |
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181 apply(rule cheat) |
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182 apply(tactic {* clean_tac @{context} 1 *}) |
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183 done |
177 |
184 |
178 lemma test3: "my_plus = my_plus" |
185 lemma test3: "my_plus = my_plus" |
179 apply(rule refl) |
186 apply(rule refl) |
180 done |
187 done |
181 |
188 |
182 lemma "PLUS = PLUS" |
189 lemma "PLUS = PLUS" |
183 apply(tactic {* procedure_tac @{context} @{thm test3} 1 *}) |
190 apply(tactic {* procedure_tac @{context} @{thm test3} 1 *}) |
184 oops |
191 apply(rule cheat) |
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192 apply(rule cheat) |
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193 apply(tactic {* clean_tac @{context} 1 *}) |
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194 done |
185 |
195 |
186 |
196 |
187 lemma "PLUS a b = PLUS b a" |
197 lemma "PLUS a b = PLUS b a" |
188 apply(tactic {* procedure_tac @{context} @{thm plus_sym_pre} 1 *}) |
198 apply(tactic {* procedure_tac @{context} @{thm plus_sym_pre} 1 *}) |
189 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *}) |
199 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *}) |
260 apply(simp only: fun_map.simps id_simps) |
270 apply(simp only: fun_map.simps id_simps) |
261 apply(simp only: Quotient_abs_rep[OF fun_quotient[OF Quotient_my_int fun_quotient[OF Quotient_my_int Quotient_my_int]]]) |
271 apply(simp only: Quotient_abs_rep[OF fun_quotient[OF Quotient_my_int fun_quotient[OF Quotient_my_int Quotient_my_int]]]) |
262 apply(simp only: Quotient_abs_rep[OF list_quotient[OF Quotient_my_int]]) |
272 apply(simp only: Quotient_abs_rep[OF list_quotient[OF Quotient_my_int]]) |
263 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int]) |
273 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int]) |
264 apply(tactic {* clean_tac @{context} 1 *}) |
274 apply(tactic {* clean_tac @{context} 1 *}) |
265 sorry |
275 apply(simp) (* FIXME: why is this needed *) |
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276 done |
266 |
277 |
267 lemma ho_tst2: "foldl my_plus x (h # t) \<approx> my_plus h (foldl my_plus x t)" |
278 lemma ho_tst2: "foldl my_plus x (h # t) \<approx> my_plus h (foldl my_plus x t)" |
268 sorry |
279 sorry |
269 |
280 |
270 lemma "foldl PLUS x (h # t) = PLUS h (foldl PLUS x t)" |
281 lemma "foldl PLUS x (h # t) = PLUS h (foldl PLUS x t)" |