let f, g be Complex_Sequence; :: thesis: ( ( for n being Nat holds f . n = 1 / (n + r) ) & ( for n being Nat holds g . n = 1 / (n + r) ) implies f = g )
assume that
A1: for n being Nat holds f . n = 1 / (n + r) and
A2: for n being Nat holds g . n = 1 / (n + r) ; :: thesis: f = g
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f . n = g . n
thus f . n = 1 / (n + r) by A1
.= g . n by A2 ; :: thesis: verum