reserve x for object,
  a,b for Real,
  k,k1,i1,j1,w for Nat,
  m,m1,n,n1 for Integer;
reserve p,q for Rational;

theorem Th26:
  not ex w st 1 < w & ex m,k st numerator(p) = m*w & denominator(p) = k*w
proof
  assume not thesis;
  then consider w such that
A1: 1<w and
A2: ex m,k st numerator(p)=m*w & denominator(p)=k*w;
  consider m,k such that
A3: numerator(p)=m*w and
A4: denominator(p)=k*w by A2;
A5: p=(m*w)/(k*w) by A3,A4,Th12
    .=(m/k)*(w/w) by XCMPLX_1:76
    .=m/k*1 by A1,XCMPLX_1:60
    .=m/k;
A6: k<>0 by A4;
  then k*1<k*w by A1,XREAL_1:68;
  hence contradiction by A4,A6,A5,Def3;
end;
