
theorem
  for f be non empty complex-valued XFinSequence holds XProduct (f|1) = f.0
  proof
    let f be non empty complex-valued XFinSequence;
    1 <= len f by NAT_1:14; then
    B2: len (f|1) = 1 by AFINSQ_1:54; then
    0 in Segm (len (f|1)) by NAT_1:44; then
    0 in dom f & 0 in 1 by RELAT_1:57; then
    B3: 0 in (dom f) /\ 1 by XBOOLE_0:def 4;
    XProduct (f|1) = XProduct <%(f|1).0%> by B2,AFINSQ_1:34
    .= f.0 by B3,FUNCT_1:48;
    hence thesis;
  end;
