
theorem THJD:
  for r,s being Real st 0 < r & 0 < s holds 0 <= r / (r+s) <= 1
  proof
    let r,s be Real;
    assume that
A1: 0 < r and
A2: 0 < s;
    thus 0 <= r/(r+s) by A1,A2;
    0 + r <= s + r by A2,XREAL_1:6;
    then r / (r+s) <= (r+s) / (r+s) by A1,XREAL_1:72;
    hence r / (r+s) <= 1 by A1,A2,XCMPLX_1:60;
  end;
