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 Th18
.= ((lim s) *') - ((lim s9) *') by COMPLEX1:34 ; :: thesis: verum