reserve k,m,n for Element of NAT,
  i, j for Nat,
  a, b, c for object,
  X, Y, Z for set,
  D, D1, D2 for non empty set;
reserve p, q, r, s for FinSequence;

theorem Th5:
  Polish-atoms(GRZ-symbols, GRZ-arity) = VAR
proof
  set X = Polish-atoms(GRZ-symbols, GRZ-arity);
  thus X c= VAR
    proof
    let a;
    assume A11: a in X;
    then GRZ-arity.a = 0 by POLNOT_1:def 7;
    then A13: not a in GRZ-ops by Th4, ENUMSET1:def 1;
    a in GRZ-symbols by A11, POLNOT_1:def 7;
    hence thesis by A13, XBOOLE_0:def 3;
    end;
    let a;
    assume A2: a in VAR;
    then A3: a in GRZ-symbols by XBOOLE_0:def 3;
    not a in GRZ-ops by A2, Lm4;
    then GRZ-arity.a = 0 by A3, Def4;
    hence a in X by A3, POLNOT_1:def 7;
end;
