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
  a>b & b>c implies b/(a-b)>c/(a-c)
proof
  assume that
A1: a>b and
A2: b>c;
A3: a-b>0 by A1,XREAL_1:50;
  b*(-1)<c*(-1) by A2,XREAL_1:69;
  then -b+a<-c+a by XREAL_1:8;
  then
A4: c/(a-b)>c/(a-c) by A3,XREAL_1:76;
  b/(a-b)>c/(a-b) by A2,A3,XREAL_1:74;
  hence thesis by A4,XXREAL_0:2;
end;
