doc-src/TutorialI/ToyList2/ToyList2

apply. -> by

lemma app_Nil2 [simp]: "xs @ [] = xs";
apply(induct_tac xs);
apply(auto);
.;

lemma app_assoc [simp]: "(xs @ ys) @ zs = xs @ (ys @ zs)";
apply(induct_tac xs);
by(auto);

lemma rev_app [simp]: "rev(xs @ ys) = (rev ys) @ (rev xs)";
apply(induct_tac xs);
by(auto);

theorem rev_rev [simp]: "rev(rev xs) = xs";
apply(induct_tac xs);
by(auto);

end;