equal
deleted
inserted
replaced
310 lemma map_of_append[simp]: "map_of (xs @ ys) = map_of ys ++ map_of xs" |
310 lemma map_of_append[simp]: "map_of (xs @ ys) = map_of ys ++ map_of xs" |
311 unfolding map_add_def |
311 unfolding map_add_def |
312 apply (induct xs) |
312 apply (induct xs) |
313 apply simp |
313 apply simp |
314 apply (rule ext) |
314 apply (rule ext) |
315 apply (simp split add: option.split) |
315 apply (simp split: option.split) |
316 done |
316 done |
317 |
317 |
318 lemma finite_range_map_of_map_add: |
318 lemma finite_range_map_of_map_add: |
319 "finite (range f) \<Longrightarrow> finite (range (f ++ map_of l))" |
319 "finite (range f) \<Longrightarrow> finite (range (f ++ map_of l))" |
320 apply (induct l) |
320 apply (induct l) |