 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 Th10:
  for S,T,p st S-head p in T holds p is T-headed & S-head p = T-head p
proof
  let S,T,p;
  set q = S-head p;
  set r = S-tail p;
  assume A1: q in T;
  p = q^r;
  hence thesis by A1, POLNOT_1:52;
end;
