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

theorem Th209:
  (for a being Real st 0 < a & a < 1 holds c <= b/a) implies c <= b
proof
  assume
A1: for a st a > 0 & a < 1 holds b/a >= c;
  now
    let d;
    assume d > 1;
    then
A2: b/(d") >= c by A1,Lm36;
    d" = 1/d by XCMPLX_1:215;
    then b*d/1 >= c by A2,XCMPLX_1:77;
    hence b*d >= c;
  end;
  hence thesis by Th167;
end;
