let s, s9 be convergent Complex_Sequence; :: thesis: lim ((s + s9) *') = ((lim s) *') + ((lim s9) *')
thus lim ((s + s9) *') = (lim (s + s9)) *' by Th11
.= ((lim s) + (lim s9)) *' by Th12
.= ((lim s) *') + ((lim s9) *') by COMPLEX1:32 ; :: thesis: verum