let f, g be Function of NATPLUS,[:INT,INT,INT:]; :: thesis: ( ( for n being non zero Nat holds f . n = [(- 1),((- (5 * (n ^2))) - (2 * n)),((- (5 * n)) - 1)] ) & ( for n being non zero Nat holds g . n = [(- 1),((- (5 * (n ^2))) - (2 * n)),((- (5 * n)) - 1)] ) implies f = g )
assume that
A2: for n being non zero Nat holds f . n = H₄(n) and
A3: for n being non zero Nat holds g . n = H₄(n) ; :: thesis: f = g
let n be Element of NATPLUS ; :: according to FUNCT_2:def 8 :: thesis: f . n = g . n
thus f . n = H₄(n) by A2
.= g . n by A3 ; :: thesis: verum