theorem
  for K,E,e,M,F st E.e = 1 & Polish-ext-head F = e
      ex G st F = Polish-unOp(K,M,e).G
proof
  let K,E,e,M,F;
  assume that A1: E.e = 1 and A2: Polish-ext-head F = e;
  set G = K-tail F;
  A5: M is E-compatible;
  A6: F is K-headed & K-head F = e by A2, Th10;
  then G in M^^(E.e) by A5;
  then reconsider G as Element of M by A1;
  take G;
  thus F = e^G by A6 .= Polish-unOp(K,M,e).G by A1, Def15r;
  thus thesis;
end;
