 reserve a,b for object;
 reserve k,l,m,n for Nat;
 reserve p,q,r,s for FinSequence;
 reserve P for non empty FinSequence-membered set;
 reserve S,T for Polish-language;
 reserve V for Polish-language of T;
 reserve K for non trivial Polish-language;
 reserve E for Polish-arity-function of K;
 reserve B for Polish-arity-function;
 reserve A for Polish-arity-function of T;
 reserve C for Extension of B;
 reserve Z for B-closed Polish-language;
 reserve J for Polish-ext-set of B;
 reserve V for full Polish-language of T;
 reserve U for T-extending Polish-language;
 reserve W for full Polish-language of U;

theorem
  for B, J for F being Formula of J st Polish-ext-head F in dom B
    holds Polish-ext-head F = (dom B)-head F by Th10;
