let seq be Complex_Sequence; :: thesis: 1r (#) seq = seq

now :: thesis: for n being Element of NAT holds (1r (#) seq) . n = seq . n

let n be Element of NAT ; :: thesis: (1r (#) seq) . n = seq . n
thus (1r (#) seq) . n = 1r * (seq . n) by VALUED_1:6
.= seq . n ; :: thesis: verum

end;

hence 1r (#) seq = seq by FUNCT_2:63; :: thesis: verum