equal
deleted
inserted
replaced
307 qed "insert_map_upd_same"; |
307 qed "insert_map_upd_same"; |
308 |
308 |
309 Goal "(insert_map j t f)(i := s) = \ |
309 Goal "(insert_map j t f)(i := s) = \ |
310 \ (if i=j then insert_map i s f \ |
310 \ (if i=j then insert_map i s f \ |
311 \ else if i<j then insert_map j t (f(i:=s)) \ |
311 \ else if i<j then insert_map j t (f(i:=s)) \ |
312 \ else insert_map j t (f(i-1' := s)))"; |
312 \ else insert_map j t (f(i - Suc 0 := s)))"; |
313 by (rtac ext 1); |
313 by (rtac ext 1); |
314 by (auto_tac (claset(), simpset() addsplits [nat_diff_split])); |
314 by (auto_tac (claset(), simpset() addsplits [nat_diff_split])); |
315 by (ALLGOALS arith_tac); |
315 by (ALLGOALS arith_tac); |
316 qed "insert_map_upd"; |
316 qed "insert_map_upd"; |
317 |
317 |