theorem
  for K being right_complementable add-associative right_zeroed
    non empty doubleLoopStr
  for a,b being Element of K holds <*a*> "*" <*b*>= a * b
proof
  let K be right_complementable add-associative right_zeroed
    non empty doubleLoopStr;
  let a,b be Element of K;
  set p = <*a*>, q = <*b*>;
  set m = mlt(p,q);
  m = <* (a * b) *> by FINSEQ_2:74;
  hence thesis by RLVECT_1:44;
end;
