let f, g be sequence of F_Real; :: thesis: ( ( for n being Nat holds f . n = (p . (n + 1)) * (n + 1) ) & ( for n being Nat holds g . n = (p . (n + 1)) * (n + 1) ) implies f = g )
assume that
A3: for n being Nat holds f . n = (p . (n + 1)) * (n + 1) and
A4: for n being Nat holds g . n = (p . (n + 1)) * (n + 1) ; :: thesis: f = g
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f . n = g . n
thus f . n = (p . (n + 1)) * (n + 1) by A3
.= g . n by A4 ; :: thesis: verum