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

theorem
  0 < a & 0 <= c & a <= b implies c/b <= c/a
proof
  assume that
A1: 0<a and
A2: 0<=c and
A3: a<=b;
  a*b"<=b*b" by A1,A3,Lm12;
  then a*b"<=1 by A1,A3,XCMPLX_0:def 7;
  then a"*(a*b")<=a"*1 by A1,Lm12;
  then a"*a*b"<=a";
  then 1*b"<=a" by A1,XCMPLX_0:def 7;
  then c*b"<=c*a" by A2,Lm12;
  then c/b<=c*a" by XCMPLX_0:def 9;
  hence thesis by XCMPLX_0:def 9;
end;
