let s, s' be Complex_Sequence; :: thesis: ( s is convergent & s' is convergent implies lim ((s - s') *' ) = ((lim s) *' ) - ((lim s') *' ) )
assume A1: ( s is convergent & s' is convergent ) ; :: thesis: lim ((s - s') *' ) = ((lim s) *' ) - ((lim s') *' )
then s - s' is convergent by Th25;
hence lim ((s - s') *' ) = (lim (s - s')) *' by Th12
.= ((lim s) - (lim s')) *' by A1, Th26
.= ((lim s) *' ) - ((lim s') *' ) by COMPLEX1:120 ;
:: thesis: verum