reserve a,b,c,d for positive Real,
  m,u,w,x,y,z for Real,
  n,k for Nat,
  s,s1 for Real_Sequence;

theorem
  b>a & c>d implies c/(c+a)>d/(d+b)
proof
  assume that
A1: b>a and
A2: c>d;
  b*c>a*d by A1,A2,XREAL_1:96;
  then b*c+c*d>a*d+c*d by XREAL_1:8;
  then c*(b+d)>d*(a+c);
  hence thesis by XREAL_1:106;
end;
