reserve x,y for object, X for set;

theorem Th27:
  for L be Field,f be Polynomial of L st 0 <= deg f holds Roots(f)
is finite set & ex m,n be Element of NAT st n=deg f & m=card(Roots(f)) & m <= n
proof
  let L be Field,f be Polynomial of L;
  assume
A1: 0 <=deg f;
  then reconsider n = deg f as Element of NAT by INT_1:3;
  reconsider f as non-zero Polynomial of L by A1,Th26;
  ex m be Element of NAT st m=card(Roots(f)) & m <= n by Lm13;
  hence thesis;
end;
