equal
deleted
inserted
replaced
381 Goal "A Un B - (A - B) = B"; |
381 Goal "A Un B - (A - B) = B"; |
382 by (Blast_tac 1); |
382 by (Blast_tac 1); |
383 qed "Un_Diff_Diff"; |
383 qed "Un_Diff_Diff"; |
384 Addsimps [Un_Diff_Diff]; |
384 Addsimps [Un_Diff_Diff]; |
385 |
385 |
386 Goal "Union(B) Int A = Union((%C. C Int A)``B)"; |
386 Goal "Union(B) Int A = Union((%C. C Int A)`B)"; |
387 by (Blast_tac 1); |
387 by (Blast_tac 1); |
388 qed "Int_Union_Union"; |
388 qed "Int_Union_Union"; |
389 |
389 |
390 (** Needed for WF reasoning in WFair.ML **) |
390 (** Needed for WF reasoning in WFair.ML **) |
391 |
391 |
392 Goal "less_than ``` {k} = greaterThan k"; |
392 Goal "less_than `` {k} = greaterThan k"; |
393 by (Blast_tac 1); |
393 by (Blast_tac 1); |
394 qed "Image_less_than"; |
394 qed "Image_less_than"; |
395 |
395 |
396 Goal "less_than^-1 ``` {k} = lessThan k"; |
396 Goal "less_than^-1 `` {k} = lessThan k"; |
397 by (Blast_tac 1); |
397 by (Blast_tac 1); |
398 qed "Image_inverse_less_than"; |
398 qed "Image_inverse_less_than"; |
399 |
399 |
400 Addsimps [Image_less_than, Image_inverse_less_than]; |
400 Addsimps [Image_less_than, Image_inverse_less_than]; |