doc-src/TutorialI/ToyList2/ToyList2

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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