242 lemma reflp_word: |
242 lemma reflp_word: |
243 "reflp (\<lambda>x y. bintrunc (len_of TYPE('a::len0)) x = bintrunc (len_of TYPE('a)) y)" |
243 "reflp (\<lambda>x y. bintrunc (len_of TYPE('a::len0)) x = bintrunc (len_of TYPE('a)) y)" |
244 by (simp add: reflp_def) |
244 by (simp add: reflp_def) |
245 |
245 |
246 local_setup {* |
246 local_setup {* |
247 Lifting_Setup.setup_lifting_infr @{thm Quotient_word} @{thm reflp_word} |
247 Lifting_Setup.setup_by_quotient @{thm Quotient_word} (SOME @{thm reflp_word}) |
248 *} |
248 *} |
249 |
249 |
250 text {* TODO: The next several lemmas could be generated automatically. *} |
250 text {* TODO: The next lemma could be generated automatically. *} |
251 |
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252 lemma bi_total_cr_word [transfer_rule]: "bi_total cr_word" |
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253 using Quotient_word reflp_word by (rule Quotient_bi_total) |
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254 |
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255 lemma right_unique_cr_word [transfer_rule]: "right_unique cr_word" |
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256 using Quotient_word by (rule Quotient_right_unique) |
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257 |
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258 lemma word_eq_transfer [transfer_rule]: |
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259 "(fun_rel cr_word (fun_rel cr_word op =)) |
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260 (\<lambda>x y. bintrunc (len_of TYPE('a)) x = bintrunc (len_of TYPE('a)) y) |
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261 (op = :: 'a::len0 word \<Rightarrow> 'a word \<Rightarrow> bool)" |
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262 using Quotient_word by (rule Quotient_rel_eq_transfer) |
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263 |
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264 lemma word_of_int_transfer [transfer_rule]: |
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265 "(fun_rel op = cr_word) (\<lambda>x. x) word_of_int" |
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266 using Quotient_word reflp_word by (rule Quotient_id_abs_transfer) |
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267 |
251 |
268 lemma uint_transfer [transfer_rule]: |
252 lemma uint_transfer [transfer_rule]: |
269 "(fun_rel cr_word op =) (bintrunc (len_of TYPE('a))) |
253 "(fun_rel cr_word op =) (bintrunc (len_of TYPE('a))) |
270 (uint :: 'a::len0 word \<Rightarrow> int)" |
254 (uint :: 'a::len0 word \<Rightarrow> int)" |
271 unfolding fun_rel_def cr_word_def by (simp add: word_ubin.eq_norm) |
255 unfolding fun_rel_def cr_word_def by (simp add: word_ubin.eq_norm) |