doc-src/TutorialI/ToyList2/ToyList2
changeset 8846 c7d945398677
parent 8751 9ed0548177fb
child 9458 c613cd06d5cf
equal deleted inserted replaced
8845:03a2ae3059da 8846:c7d945398677
     1 lemma app_Nil2 [simp]: "xs @ [] = xs";
     1 lemma app_Nil2 [simp]: "xs @ [] = xs";
     2 apply(induct_tac xs);
     2 apply(induct_tac xs);
     3 apply(auto).;
     3 apply(auto);.;
     4 
     4 
     5 lemma app_assoc [simp]: "(xs @ ys) @ zs = xs @ (ys @ zs)";
     5 lemma app_assoc [simp]: "(xs @ ys) @ zs = xs @ (ys @ zs)";
     6 apply(induct_tac xs);
     6 apply(induct_tac xs);
     7 apply(auto).;
     7 apply(auto);.;
     8 
     8 
     9 lemma rev_app [simp]: "rev(xs @ ys) = (rev ys) @ (rev xs)";
     9 lemma rev_app [simp]: "rev(xs @ ys) = (rev ys) @ (rev xs)";
    10 apply(induct_tac xs);
    10 apply(induct_tac xs);
    11 apply(auto).;
    11 apply(auto);.;
    12 
    12 
    13 theorem rev_rev [simp]: "rev(rev xs) = xs";
    13 theorem rev_rev [simp]: "rev(rev xs) = xs";
    14 apply(induct_tac xs);
    14 apply(induct_tac xs);
    15 apply(auto).;
    15 apply(auto);.;
    16 
    16 
    17 end
    17 end;