theorem
  for L, E, D, g for K being Function of Polish-WFF-set(L, E), D
    for t being Element of L for F1, F2 being Polish-WFF of L, E
        st K is g-recursive & E.t = 2 holds
    K.(Polish-binOp(L, E, t).(F1, F2)) = g.(t, <*K.F1, K.F2*>)
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 F1, F2 be Polish-WFF of L, E;
  assume that
    A1: K is g-recursive and
    A2: E.t = 2;
  set G = Polish-binOp(L, E, t).(F1, F2);
  reconsider G1 = G as Element of W;
  Polish-WFF-args G1 = <*F1,F2*> by A2, Th83;
  then A5: K * Polish-WFF-args G1 = <*K.F1, K.F2*> by FINSEQ_2:36;
  thus K.G = g.[L-head G1, K * (Polish-WFF-args G1)] by A1
      .= g.[t, K * Polish-WFF-args G1] by A2, Th83
      .= g.(t, <*K.F1, K.F2*>) by A5, BINOP_1:def 1;
end;
