theorem Th79:
  for L, E for t being Element of L for F being Polish-WFF of L, E holds
    Polish-WFF-head F = t
      iff ex u being Element of Polish-WFF-set(L, E)^^(E.t)
        st F = Polish-operation(L, E, t).u
proof
 let L, E;
 let t be Element of L;
 let F be Polish-WFF of L, E;
 set W = Polish-WFF-set(L, E);
 set H = Polish-operation(L, E, t);
 A2: dom H = W^^(E.t) by FUNCT_2:def 1;
 thus Polish-WFF-head F = t implies ex u being Element of W^^(E.t) st F = H.u
 proof
   assume A3: Polish-WFF-head F = t;
   set u = (L, E)-tail F;
   reconsider u as Element of W^^(E.t) by A3;
   take u;
   thus F = t^u by A3 .= H.u by A2, Def12;
 end;
 given u being Element of W^^(E.t) such that A20: F = H.u;
 reconsider u as FinSequence;
 thus Polish-WFF-head F = t by A20;
end;
