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

theorem
  (for a st 0 < a & a < 1 holds b*a <= c) implies b <= c
proof
  assume
A1: for a st 0<a & a<1 holds b*a<=c;
  now
    let d;
    assume
A2: d>1;
    then b*(d")<=c by A1,Lm36;
    then b/d<=c by XCMPLX_0:def 9;
    hence b<=c*d by A2,Th81;
  end;
  hence thesis by Th167;
end;
