| author | kleing | 
| Wed, 21 Sep 2011 09:17:01 +1000 | |
| changeset 45017 | 07a0638c351a | 
| parent 10171 | 59d6633835fa | 
| permissions | -rw-r--r-- | 
| 9541 | 1 | lemma app_Nil2 [simp]: "xs @ [] = xs" | 
| 2 | apply(induct_tac xs) | |
| 3 | apply(auto) | |
| 10171 | 4 | done | 
| 8751 | 5 | |
| 9541 | 6 | lemma app_assoc [simp]: "(xs @ ys) @ zs = xs @ (ys @ zs)" | 
| 7 | apply(induct_tac xs) | |
| 10171 | 8 | apply(auto) | 
| 9 | done | |
| 8751 | 10 | |
| 9541 | 11 | lemma rev_app [simp]: "rev(xs @ ys) = (rev ys) @ (rev xs)" | 
| 12 | apply(induct_tac xs) | |
| 10171 | 13 | apply(auto) | 
| 14 | done | |
| 8751 | 15 | |
| 9541 | 16 | theorem rev_rev [simp]: "rev(rev xs) = xs" | 
| 17 | apply(induct_tac xs) | |
| 10171 | 18 | apply(auto) | 
| 19 | done | |
| 8751 | 20 | |
| 9541 | 21 | end |