
theorem Th8:
  for a1,a2,a3,a4,a5,b1,b2,b3,b4,b5 being Real holds (for x
  being Real holds Polynom(a1,a2,a3,a4,a5,x)=Polynom(b1,b2,b3,b4,b5,x))
  implies a1-b1=b3-a3 & a2-b2=b4-a4
proof
  let a1,a2,a3,a4,a5,b1,b2,b3,b4,b5 be Real;
  assume for x being Real holds Polynom(a1,a2,a3,a4,a5,x)=Polynom(b1,
  b2,b3,b4,b5,x);
  then a1-a2+a3-a4=b1-b2+b3-b4 & a1+a2+a3+a4=b1+b2+b3+b4 by Th7;
  hence thesis;
end;
