let s, s1 be Complex_Sequence; :: thesis: ( s is convergent & s1 is bounded & lim s = 0c implies lim ((s (#) s1) *') = 0c )
assume A1: ( s is convergent & s1 is bounded & lim s = 0c ) ; :: thesis: lim ((s (#) s1) *') = 0c
then s (#) s1 is convergent by Th29;
hence lim ((s (#) s1) *') = (lim (s (#) s1)) *' by Th11
.= 0c by A1, Th30, COMPLEX1:28 ;
:: thesis: verum