let s, s9 be Complex_Sequence; :: thesis: ( s is convergent & s9 is convergent implies lim ((s + s9) *') = ((lim s) *') + ((lim s9) *') )
assume A1: ( s is convergent & s9 is convergent ) ; :: thesis: lim ((s + s9) *') = ((lim s) *') + ((lim s9) *')
hence lim ((s + s9) *') = (lim (s + s9)) *' by Th12
.= ((lim s) + (lim s9)) *' by A1, Th14
.= ((lim s) *') + ((lim s9) *') by COMPLEX1:32 ;
:: thesis: verum