equal
deleted
inserted
replaced
488 |
488 |
489 goal ZF.thy "r-``(A Int B) <= (r-``A) Int (r-``B)"; |
489 goal ZF.thy "r-``(A Int B) <= (r-``A) Int (r-``B)"; |
490 by (Blast_tac 1); |
490 by (Blast_tac 1); |
491 qed "vimage_Int_subset"; |
491 qed "vimage_Int_subset"; |
492 |
492 |
493 goalw thy [function_def] |
493 Goalw [function_def] |
494 "!!f. function(f) ==> f-``(A Int B) = (f-``A) Int (f-``B)"; |
494 "!!f. function(f) ==> f-``(A Int B) = (f-``A) Int (f-``B)"; |
495 by (Blast_tac 1); |
495 by (Blast_tac 1); |
496 qed "function_vimage_Int"; |
496 qed "function_vimage_Int"; |
497 |
497 |
498 goalw thy [function_def] |
498 Goalw [function_def] |
499 "!!f. function(f) ==> f-``(A-B) = (f-``A) - (f-``B)"; |
499 "!!f. function(f) ==> f-``(A-B) = (f-``A) - (f-``B)"; |
500 by (Blast_tac 1); |
500 by (Blast_tac 1); |
501 qed "function_vimage_Diff"; |
501 qed "function_vimage_Diff"; |
502 |
502 |
503 goal ZF.thy "(r Int A*A)-``B <= (r-``B) Int A"; |
503 goal ZF.thy "(r Int A*A)-``B <= (r-``B) Int A"; |