339 |
339 |
340 lemma "FUNION (FUNION x xa) xb = FUNION x (FUNION xa xb)" |
340 lemma "FUNION (FUNION x xa) xb = FUNION x (FUNION xa xb)" |
341 apply (tactic {* lift_tac_fset @{context} @{thm append_assoc} 1 *}) |
341 apply (tactic {* lift_tac_fset @{context} @{thm append_assoc} 1 *}) |
342 done |
342 done |
343 |
343 |
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344 ML {* fun r_mk_comb_tac_fset lthy = r_mk_comb_tac' lthy rty [quot] [rel_refl] [trans2] rsp_thms *} |
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345 |
344 lemma cheat: "P" sorry |
346 lemma cheat: "P" sorry |
345 |
347 |
346 lemma "\<lbrakk>P EMPTY; \<And>a x. P x \<Longrightarrow> P (INSERT a x)\<rbrakk> \<Longrightarrow> P l" |
348 lemma "\<lbrakk>P EMPTY; \<And>a x. P x \<Longrightarrow> P (INSERT a x)\<rbrakk> \<Longrightarrow> P l" |
347 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *}) |
349 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *}) |
348 apply(tactic {* regularize_tac @{context} [rel_eqv] [rel_refl] 1 *}) |
350 apply(tactic {* regularize_tac @{context} [rel_eqv] [rel_refl] 1 *}) |
349 prefer 2 |
351 prefer 2 |
350 apply (tactic {* clean_tac @{context} [quot] defs |
352 apply(rule cheat) |
351 [(@{typ "('a list \<Rightarrow> bool)"},@{typ "('a fset \<Rightarrow> bool)"})] 1 *}) |
353 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *) |
352 apply(tactic {* r_mk_comb_tac' @{context} rty [quot] rel_refl trans2 rsp_thms 1*}) |
354 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
353 done |
355 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) |
354 |
356 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *) |
355 |
357 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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358 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) |
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359 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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360 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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361 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *) |
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362 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *) |
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363 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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364 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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365 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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366 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* D *) (* reflexivity of basic relations *) |
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367 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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368 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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369 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *) |
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370 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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371 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *) |
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372 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* C *) (* = and extensionality *) |
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373 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *) |
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374 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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375 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) |
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376 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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377 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* B *) (* Cong *) |
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378 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *) |
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379 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *) |
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380 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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381 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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382 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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383 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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384 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *) |
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385 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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386 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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387 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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388 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *) |
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389 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *) |
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390 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 7 *) (* respectfulness *) |
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391 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *) |
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392 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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393 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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394 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *) |
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395 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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396 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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397 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *) |
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398 apply(tactic {* r_mk_comb_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *) |
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399 done |
356 |
400 |
357 |
401 |
358 quotient_def |
402 quotient_def |
359 fset_rec::"'a \<Rightarrow> ('b \<Rightarrow> 'b fset \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> 'b fset \<Rightarrow> 'a" |
403 fset_rec::"'a \<Rightarrow> ('b \<Rightarrow> 'b fset \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> 'b fset \<Rightarrow> 'a" |
360 where |
404 where |