theorem
  for C,e,M,F st C.e = 1 & Polish-ext-head F = e
      ex G st F = Polish-unOp(C,M,e).G
proof
  let C,e,M,F;
  set K = dom C;
  assume that A1: C.e = 1 and A2: Polish-ext-head F = e;
  set G = K-tail F;
  A5: M is C-compatible;
  A6: F is K-headed & K-head F = e by A2, Th10;
  then consider n such that A8: n = C.e & G in M^^n by A5;
  reconsider G as Element of M by A1, A8;
  take G;
  thus F = e^G by A6 .= Polish-unOp(C,M,e).G by A1, Def15;
  thus thesis;
end;
