
theorem
  the carrier of Linear_Space_of_ComplexSequences = the_set_of_ComplexSequences
  &
  (for x be set holds x is VECTOR of Linear_Space_of_ComplexSequences iff
   x is Complex_Sequence) &
  (for u be VECTOR of Linear_Space_of_ComplexSequences holds u =seq_id(u)) &
  (for u,v be VECTOR of Linear_Space_of_ComplexSequences holds
   u+v =seq_id(u)+seq_id(v)) &
  for z be Complex for u be VECTOR of Linear_Space_of_ComplexSequences holds
   z*u =z(#)seq_id(u) by FUNCT_2:8,66,Th2,Th3;
