FSet.thy
changeset 481 7f97c52021c9
parent 480 7fbbb2690bc5
child 482 767baada01dc
equal deleted inserted replaced
480:7fbbb2690bc5 481:7f97c52021c9
   342 done
   342 done
   343 
   343 
   344 lemma cheat: "P" sorry
   344 lemma cheat: "P" sorry
   345 
   345 
   346 ML {* fun inj_repabs_tac_fset lthy = inj_repabs_tac lthy rty [quot] [rel_refl] [trans2] *}
   346 ML {* fun inj_repabs_tac_fset lthy = inj_repabs_tac lthy rty [quot] [rel_refl] [trans2] *}
   347 ML {* fun inj_repabs_tac_fset' lthy = inj_repabs_tac' lthy rty [quot] [rel_refl] [trans2] *}
       
   348 
   347 
   349 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"
   350 apply (tactic {* (ObjectLogic.full_atomize_tac THEN' gen_frees_tac @{context}) 1 *})
   349 apply (tactic {* (ObjectLogic.full_atomize_tac THEN' gen_frees_tac @{context}) 1 *})
   351 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *})
   350 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *})
   352 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *})
   351 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *})
   353 prefer 2
   352 prefer 2
   354 apply(tactic {* clean_tac @{context} [quot] defs 1 *})
   353 apply(tactic {* clean_tac @{context} [quot] defs 1 *})
   355 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 3 *) (* Ball-Ball *)
   354 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
   356 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   355 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   357 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *)
   356 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *)
   358 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 3 *) (* Ball-Ball *)
   357 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
   359 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   358 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   360 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *)
   359 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *)
   361 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   360 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   362 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   361 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   363 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   362 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   364 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* A *) (* application if type needs lifting *)
   363 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
   365 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   364 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   366 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* E *) (* R x y assumptions *)
   365 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
   367 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   366 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   368 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* D *) (* reflexivity of basic relations *)
   367 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* D *) (* reflexivity of basic relations *)
   369 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   368 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   370 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   369 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   371 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   370 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   372 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   371 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   373 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   372 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   374 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* C *) (* = and extensionality *)
   373 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* C *) (* = and extensionality *)
   375 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 3 *) (* Ball-Ball *)
   374 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
   376 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   375 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   377 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
   376 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
   378 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   377 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   379 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* B *) (* Cong *)
   378 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
   380 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   379 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   381 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* A *) (* application if type needs lifting *)
   380 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
   382 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   381 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   383 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* E *) (* R x y assumptions *)
   382 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
   384 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   383 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   385 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* E *) (* R x y assumptions *)
   384 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
   386 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* A *) (* application if type needs lifting *)
   385 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
   387 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   386 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   388 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* E *) (* R x y assumptions *)
   387 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
   389 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   388 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   390 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* A *) (* application if type needs lifting *)
   389 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
   391 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* A *) (* application if type needs lifting *)
   390 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
   392 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 7 *) (* respectfulness *)
   391 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 7 *) (* respectfulness *)
   393 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   392 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
   394 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   393 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   395 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* E *) (* R x y assumptions *)
   394 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
   396 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* A *) (* application if type needs lifting *)
   395 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
   397 apply(tactic {* inj_repabs_tac_fset' @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   396 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
   398 done
   397 done
   399 
   398 
   400 quotient_def
   399 quotient_def
   401   fset_rec::"'a \<Rightarrow> ('b \<Rightarrow> 'b fset \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> 'b fset \<Rightarrow> 'a"
   400   fset_rec::"'a \<Rightarrow> ('b \<Rightarrow> 'b fset \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> 'b fset \<Rightarrow> 'a"
   402 where
   401 where
   457 apply (rule FUN_QUOTIENT)
   456 apply (rule FUN_QUOTIENT)
   458 apply (rule QUOTIENT_fset)
   457 apply (rule QUOTIENT_fset)
   459 apply (rule IDENTITY_QUOTIENT)
   458 apply (rule IDENTITY_QUOTIENT)
   460 apply (rule IDENTITY_QUOTIENT)
   459 apply (rule IDENTITY_QUOTIENT)
   461 apply (rule IDENTITY_QUOTIENT)
   460 apply (rule IDENTITY_QUOTIENT)
       
   461 prefer 2 apply(tactic{* quot_true_tac @{context} (snd o dest_comb) 1*})
       
   462 prefer 2 apply(tactic{* quot_true_tac @{context} (fst o dest_comb) 1*})
       
   463 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   464 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   465 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   466 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   467 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   468 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   469 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   470 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   471 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   472 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   462 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   473 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   463 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   474 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   464 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   475 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   465 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   476 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   466 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   477 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   467 apply (tactic {* (APPLY_RSP_TAC rty @{context}) 1 *})
   478 apply (tactic {* (APPLY_RSP_TAC rty @{context}) 1 *})
   468 apply (rule IDENTITY_QUOTIENT)
   479 apply (rule IDENTITY_QUOTIENT)
   469 apply (rule IDENTITY_QUOTIENT)
       
   470 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   471 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   472 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   473 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   474 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   475 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   476 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   477 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   478 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   479 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   480 apply (tactic {* (APPLY_RSP_TAC rty @{context}) 1 *})
       
   481 apply (rule IDENTITY_QUOTIENT)
       
   482 apply (rule FUN_QUOTIENT)
   480 apply (rule FUN_QUOTIENT)
   483 apply (rule QUOTIENT_fset)
   481 apply (rule QUOTIENT_fset)
   484 apply (rule IDENTITY_QUOTIENT)
   482 apply (rule IDENTITY_QUOTIENT)
   485 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   483 prefer 2 apply(tactic{* quot_true_tac @{context} (snd o dest_comb) 1*})
   486 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   484 prefer 2 apply(tactic{* quot_true_tac @{context} (fst o dest_comb) 1*})
   487 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   485 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   488 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   486 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   489 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   487 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   490 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   488 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   491 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   489 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   492 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   490 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   493 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   491 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   494 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   492 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   495 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   493 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   496 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   494 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   497 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   495 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   498 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   496 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   499 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   497 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   500 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   498 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   501 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   499 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   502 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   500 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   503 apply (tactic {* instantiate_tac @{thm APPLY_RSP2} @{context} 1 *})
   501 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   504 apply (tactic {* (instantiate_tac @{thm REP_ABS_RSP} @{context} THEN' (RANGE [quotient_tac [quot]])) 1 *})
   502 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   503 apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
       
   504 apply (rule IDENTITY_QUOTIENT)
       
   505 apply (rule FUN_QUOTIENT)
       
   506 apply (rule QUOTIENT_fset)
       
   507 apply (rule IDENTITY_QUOTIENT)
       
   508 prefer 2 apply(tactic{* quot_true_tac @{context} (snd o dest_comb) 1*})
       
   509 prefer 2 apply(tactic{* quot_true_tac @{context} (fst o dest_comb) 1*})
       
   510 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   505 apply assumption
   511 apply assumption
   506 apply (rule refl)
   512 apply (rule refl)
   507 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   513 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   508 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   514 apply assumption
   509 apply (tactic {* instantiate_tac @{thm APPLY_RSP2} @{context} 1 *})
   515 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   510 apply (tactic {* instantiate_tac @{thm APPLY_RSP2} @{context} 1 *})
   516 apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
   511 apply (tactic {* (instantiate_tac @{thm REP_ABS_RSP} @{context} THEN' (RANGE [quotient_tac [quot]])) 1 *})
   517 apply (rule IDENTITY_QUOTIENT)
   512 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   518 apply (rule FUN_QUOTIENT)
   513 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   519 apply (rule QUOTIENT_fset)
       
   520 apply (rule IDENTITY_QUOTIENT)
       
   521 prefer 2 apply(tactic{* quot_true_tac @{context} (snd o dest_comb) 1*})
       
   522 prefer 2 apply(tactic{* quot_true_tac @{context} (fst o dest_comb) 1*})
       
   523 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
       
   524 apply assumption
       
   525 apply (rule refl)
   514 apply (tactic {* REPEAT_ALL_NEW (inj_repabs_tac_fset @{context}) 1 *})
   526 apply (tactic {* REPEAT_ALL_NEW (inj_repabs_tac_fset @{context}) 1 *})
   515 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   527 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   516 apply (tactic {* instantiate_tac @{thm APPLY_RSP2} @{context} 1 *})
   528 apply (tactic {* instantiate_tac @{thm APPLY_RSP} @{context} 1 *})
   517 apply (tactic {* (instantiate_tac @{thm REP_ABS_RSP} @{context} THEN' (RANGE [quotient_tac [quot]])) 1 *})
   529 apply (rule IDENTITY_QUOTIENT)
       
   530 apply (rule FUN_QUOTIENT)
       
   531 apply (rule QUOTIENT_fset)
       
   532 apply (rule IDENTITY_QUOTIENT)
       
   533 prefer 2 apply(tactic{* quot_true_tac @{context} (snd o dest_comb) 1*})
       
   534 prefer 2 apply(tactic{* quot_true_tac @{context} (fst o dest_comb) 1*})
       
   535 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   518 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   536 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   519 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   537 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   520 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   538 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   521 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   539 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
   522 done
   540 done