theorem Th12:
  for B, J for F being Formula of J st F is (dom B)-headed
    holds Polish-ext-head F = (dom B)-head F
proof
  let B, J;
  set T = dom B;
  let F be Formula of J;
  assume A1: F is T-headed;
  T c= Polish-ext-domain(B,J) by Def9;
  hence thesis by A1, POLNOT_1:55;
end;
