theorem Th25:
  for f,g being FinSequence of CQC-WFF(Al) st 0 < len f & |- f^<*p*> holds
  |- Ant(f)^g^<*Suc(f)*>^<*p*>
proof
  let f,g be FinSequence of CQC-WFF(Al) such that
A1: 0 < len f and
A2: |- f^<*p*>;
  f is_Subsequence_of Ant(f)^g^<*Suc(f)*> by A1,CALCUL_1:13;
  then Ant(f^<*p*>) is_Subsequence_of Ant(f)^g^<*Suc(f)*> by CALCUL_1:5;
  then
A3: Ant(f^<*p*>) is_Subsequence_of Ant(Ant(f)^g^<*Suc(f)*>^<*p*>)
  by CALCUL_1:5;
  Suc(f^<*p*>) = p by CALCUL_1:5;
  then Suc(f^<*p*>) = Suc(Ant(f)^g^<*Suc(f)*>^<*p*>) by CALCUL_1:5;
  hence thesis by A2,A3,CALCUL_1:36;
end;
