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264 lemma vimage_parametric [transfer_rule]: |
264 lemma vimage_parametric [transfer_rule]: |
265 assumes [transfer_rule]: "bi_total A" "bi_unique B" |
265 assumes [transfer_rule]: "bi_total A" "bi_unique B" |
266 shows "((A ===> B) ===> rel_set B ===> rel_set A) vimage vimage" |
266 shows "((A ===> B) ===> rel_set B ===> rel_set A) vimage vimage" |
267 unfolding vimage_def[abs_def] by transfer_prover |
267 unfolding vimage_def[abs_def] by transfer_prover |
268 |
268 |
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269 lemma Image_parametric [transfer_rule]: |
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270 assumes "bi_unique A" |
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271 shows "(rel_set (rel_prod A B) ===> rel_set A ===> rel_set B) op `` op ``" |
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272 by(intro rel_funI rel_setI) |
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273 (force dest: rel_setD1 bi_uniqueDr[OF assms], force dest: rel_setD2 bi_uniqueDl[OF assms]) |
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274 |
269 end |
275 end |
270 |
276 |
271 lemma (in comm_monoid_set) F_parametric [transfer_rule]: |
277 lemma (in comm_monoid_set) F_parametric [transfer_rule]: |
272 fixes A :: "'b \<Rightarrow> 'c \<Rightarrow> bool" |
278 fixes A :: "'b \<Rightarrow> 'c \<Rightarrow> bool" |
273 assumes "bi_unique A" |
279 assumes "bi_unique A" |