theorem Th26:
  f (#) <* v1,v2 *> = <* v1 * f.v1, v2 * f.v2 *>
proof
A1: len(f (#) <* v1,v2 *>) = len<* v1,v2 *> by Def6
    .= 2 by FINSEQ_1:44;
  then
A2: dom(f (#) <* v1,v2 *>) = {1,2} by FINSEQ_1:2,def 3;
  2 in {1,2} by TARSKI:def 2;
  then
A3: (f (#) <* v1,v2 *>).2 = (<* v1,v2 *>/.2) * f.(<* v1,v2 *>/.2) by A2,Def6
    .= v2 * f.(<* v1,v2 *>/.2) by FINSEQ_4:17
    .= v2 * f.v2 by FINSEQ_4:17;
  1 in {1,2} by TARSKI:def 2;
  then (f (#) <* v1,v2 *>).1 = (<* v1,v2 *>/.1) * f.(<* v1,v2 *>/.1) by A2,Def6
    .= v1 * f.(<* v1,v2 *>/.1) by FINSEQ_4:17
    .= v1 * f.v1 by FINSEQ_4:17;
  hence thesis by A1,A3,FINSEQ_1:44;
end;
