theorem
  for L, E, D, g for K being Function of Polish-WFF-set(L, E), D
    for t being Element of L for F being Polish-WFF of L, E
        st K is g-recursive & E.t = 1 holds
    K.(Polish-unOp(L, E, t).F) = g.(t, <*K.F*>)
proof
  let L, E, D, g;
  set W = Polish-WFF-set(L, E);
  let K be Function of W, D;
  let t be Element of L;
  let F be Polish-WFF of L, E;
  assume that
    A1: K is g-recursive and
    A2: E.t = 1;
  set G = Polish-unOp(L, E, t).F;
  reconsider G1 = G as Element of W;
  A3: dom K = W by FUNCT_2:def 1;
  Polish-WFF-args G1 = <*F*> by A2, Th81;
  then A5: K * Polish-WFF-args G1 = <*K.F*> by A3, FINSEQ_2:34;
  thus K.G = g.[L-head G1, K * (Polish-WFF-args G1)] by A1
      .= g.[t, K * Polish-WFF-args G1] by A2, Th81
      .= g.(t, <*K.F*>) by A5, BINOP_1:def 1;
end;
