theorem Th5:
  |- f1^<*p*> & |- f1^<*q*> implies |- f1^<*p '&' q*>
proof
  set g = f1^<*p*>;
  set g1 = f1^<*q*>;
  assume that
A1: |- g and
A2: |- g1;
A3: Ant(g) = f1 by CALCUL_1:5;
A4: Suc(g) = p by CALCUL_1:5;
A5: Suc(g1) = q by CALCUL_1:5;
  Ant(g) = Ant(g1) by A3,CALCUL_1:5;
  hence thesis by A1,A2,A3,A4,A5,CALCUL_1:39;
end;
