theorem
  for T, A for t being Element of T for u st u in Polish-WFF-set(T, A)^^(A.t)
      holds T-head(Polish-operation(T,A,t).u) = t
          & T-tail (Polish-operation(T, A, t).u) = u
proof
  let T, A;
  let t be Element of T;
  let u;
  set W = Polish-WFF-set(T, A);
  set f = Polish-operation(T, A, t);
  assume u in W^^(A.t);
  then u in dom f by FUNCT_2:def 1;
  then f.u = t^u by Def12;
  hence thesis;
end;
