reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  0 < c & 0 < a & a < b implies c/b < c/a
proof
  assume that
A1: 0 < c and
A2: 0 < a and
A3: a < b;
  a*b" < b*b" by A2,A3,Lm13;
  then a*b" < 1 by A2,A3,XCMPLX_0:def 7;
  then a"*(a*b") < a"*1 by A2,Lm13;
  then a"*a*b" < a";
  then 1*b" < a" by A2,XCMPLX_0:def 7;
  then c*b"<c*a" by A1,Lm13;
  then c/b < c*a" by XCMPLX_0:def 9;
  hence thesis by XCMPLX_0:def 9;
end;
