theorem Th124:
  for x1,x2,x3 being real-valued FinSequence st len x1=len x2 & len x2
  =len x3 holds |(x1-x2, x3)| = |(x1, x3)| - |(x2, x3)|
proof
  let x1,x2,x3 be real-valued FinSequence;
  assume that
A1: len x1=len x2 and
A2: len x2=len x3;
  len (-x2)=len x2 by Th114;
  then |(x1 - x2, x3)| = |(x1, x3)| + |(-x2, x3)| by A1,A2,Th120
    .= |(x1, x3)| + - |(x2, x3)| by A2,Th122;
  hence thesis;
end;
