let s be Complex_Sequence; :: thesis: ( s is non-zero implies s *' is non-zero )
assume A1: s is non-zero ; :: thesis: s *' is non-zero

now :: thesis: for n being Element of NAT holds (s *') . n <> 0c

let n be Element of NAT ; :: thesis: (s *') . n <> 0c
(s . n) *' <> 0c by A1, COMPLEX1:29;
hence (s *') . n <> 0c by Def2; :: thesis: verum

end;

hence s *' is non-zero by COMSEQ_1:4; :: thesis: verum