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;
reserve t, u, v, w for GRZ-formula;

theorem
  for t holds t is negative iff ex u st t = 'not' u
proof
  let t;
  thus t is negative implies ex u st t = 'not' u
    proof
    assume t is negative;
    then consider u such that
        A3: t = Polish-unOp(GRZ-symbols, GRZ-arity, 'not').u
      by Th4, POLNOT_1:80;
    take u;
    thus thesis by A3;
    end;
  thus thesis by Th4, POLNOT_1:81;
end;
