theorem
  for C,e,M,G,H st C.e = 2 holds
      Polish-ext-head(Polish-binOp(C,M,e).(G,H)) = e
proof
  let C,e,M,G,H;
  set F = Polish-binOp(C,M,e).(G,H);
  set K = dom C;
  assume A1: C.e = 2;
  F = e^(G^H) by A1, Def16;
  then F is K-headed & K-head F = e;
  hence thesis by Th12;
end;
