reserve x1,x2,y1,a,b,c for Real;

theorem Th8:
  for p be Real st 1 <= p holds NORMSTR (#
    the_set_of_RealSequences_l^p, Zero_(the_set_of_RealSequences_l^p,
    Linear_Space_of_RealSequences), Add_(the_set_of_RealSequences_l^p,
    Linear_Space_of_RealSequences), Mult_(the_set_of_RealSequences_l^p,
    Linear_Space_of_RealSequences), l_norm^p #) is RealLinearSpace
proof
  let p be Real;
  assume 1 <= p;
  then RLSStruct (# the_set_of_RealSequences_l^p, Zero_(
    the_set_of_RealSequences_l^p,Linear_Space_of_RealSequences), Add_(
    the_set_of_RealSequences_l^p,Linear_Space_of_RealSequences), Mult_(
    the_set_of_RealSequences_l^p,Linear_Space_of_RealSequences) #) is
  RealLinearSpace by Th5;
  hence thesis by RSSPACE3:2;
end;
