
theorem
  for a,b,c,d be positive Real st
    (a*b > c*d & a/b >= c/d) or (a*b >= c*d & a/b > c/d) holds a > c
  proof
    let a,b,c,d be positive Real;
    A1: (a/b)*b = a & (c/d)*d = c by XCMPLX_1:87;
    assume (a*b > c*d & a/b >= c/d) or (a*b >= c*d & a/b > c/d); then
    (a*b)*(a/b) > (c*d)*(c/d) by XREAL_1:98; then
    a*a > c*c by A1;
    hence thesis by XREAL_1:66;
  end;
