let f, f1 be Complex_Sequence; :: thesis: ( ( for n being Nat holds f . n = (Polynom (a,b,n)) / (Polynom (c,d,n)) ) & ( for n being Nat holds f1 . n = (Polynom (a,b,n)) / (Polynom (c,d,n)) ) implies f = f1 )
assume that
A1: for n being Nat holds f . n = H₁(n) and
A2: for n being Nat holds f1 . n = H₁(n) ; :: thesis: f = f1
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f . n = f1 . n
thus f . n = H₁(n) by A1
.= f1 . n by A2 ; :: thesis: verum