theorem
  for L, E for t being Element of L st E.t = 2 for F being Polish-WFF of L, E
      st Polish-WFF-head F = t ex G, H being Polish-WFF of L, E
      st F = Polish-binOp(L, E, t).(G, H)
proof
  let L, E;
  let t be Element of L;
  assume A1: E.t = 2;
  let F be Polish-WFF of L, E;
  assume A2: Polish-WFF-head F = t;
  set W = Polish-WFF-set(L, E);
  consider u being Element of W^^2
        such that A3: F = Polish-operation(L, E, t).u by A1, A2, Th79;
  W^^2 = W^^(1+1)
      .= (W^^1)^W by Th6
      .= W^W;
  then consider G, H being FinSequence such that
    A5: u = G^H and
    A6: G in W and
    A7: H in W by Def2;
  reconsider G as Element of W by A6;
  reconsider H as Element of W by A7;
  take G, H;
  thus thesis by A1, A3, A5, Def28;
end;
