let f, g be Function of NAT,[:INT,INT,INT,INT:]; :: thesis: ( ( for n being Nat holds f . n = [(- 1),n,(1 - n),(- 1)] ) & ( for n being Nat holds g . n = [(- 1),n,(1 - n),(- 1)] ) implies f = g )
assume that
A2: for n being Nat holds f . n = H₅(n) and
A3: for n being Nat holds g . n = H₅(n) ; :: thesis: f = g
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f . n = g . n
thus f . n = H₅(n) by A2
.= g . n by A3 ; :: thesis: verum