theorem
  for L, E for t being Element of L
      for a st a in dom Polish-operation(L, E, t) ex p st
    p = Polish-operation(L, E, t).a & L-head p = t
proof
  let L, E;
  let t be Element of L;
  let a;
  assume A1: a in dom Polish-operation(L, E, t);
  then a in Polish-WFF-set(L, E)^^E.t by FUNCT_2:def 1;
  then reconsider q = a as FinSequence;
  take t^q;
  thus Polish-operation(L, E, t).a = t^q by A1, Def12;
  thus thesis;
end;
