reserve i, j, m, n for Nat,
  z, B0 for set,
  f, x0 for real-valued FinSequence;

theorem
  <* z *> * <* 1 *> = <* z *>
proof
A1: dom <* z *>=Seg 1 by FINSEQ_1:38;
  rng <* 1 *>= {1} by FINSEQ_1:38;
  then
A2: dom (<* z *>*<* 1 *>)=dom <* 1 *> by A1,FINSEQ_1:2,RELAT_1:27;
A3: dom <* 1 *> = Seg 1 by FINSEQ_1:38;
  then 1 in dom <* 1 *> by FINSEQ_1:2,TARSKI:def 1;
  then (<* z *>*<* 1 *>).1 =<* z *>.((<* 1 *>).1) by FUNCT_1:13
    .=<* z *>.1
    .= z;
  hence thesis by A3,A2,FINSEQ_1:def 8;
end;
