let h be non-zero 0 -convergent Complex_Sequence; :: thesis:
A1: (h ") (#) ((a (#) R) /* h) = (h ") (#) (a (#) (R /* h)) by CFCONT_1:15
.= a (#) ((h ") (#) (R /* h)) by COMSEQ_1:13 ;
A2: (h ") (#) (R /* h) is convergent by Def3;
hence (h ") (#) ((a (#) R) /* h) is convergent by A1; :: thesis:
lim ((h ") (#) (R /* h)) = 0c by Def3;
hence lim ((h ") (#) ((a (#) R) /* h)) = a * 0c by A2, A1, COMSEQ_2:18
.= 0c ;
:: thesis:

end;