reserve m,n for Nat;
reserve r for Real;
reserve c for Element of F_Complex;

theorem Th22:
  for f being REAL-valued Polynomial of F_Complex holds
  f is Polynomial of F_Real
  proof
    let f be REAL-valued Polynomial of FC;
    rng f c= REAL;
    then reconsider f1 = f as sequence of FR by FUNCT_2:6;
    f1 is finite-Support by Lm1,ALGSEQ_1:def 1;
    hence thesis;
  end;
