let s1, s2 be sequence of NAT; :: thesis: ( ( for n being Element of NAT holds s1 . n = IFGT (n,n1,(n + n2),n) ) & ( for n being Element of NAT holds s2 . n = IFGT (n,n1,(n + n2),n) ) implies s1 = s2 )
assume that
A1: for n being Element of NAT holds s1 . n = IFGT (n,n1,(n + n2),n) and
A2: for n being Element of NAT holds s2 . n = IFGT (n,n1,(n + n2),n) ; :: thesis: s1 = s2
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: s1 . n = s2 . n
( s1 . n = IFGT (n,n1,(n + n2),n) & s2 . n = IFGT (n,n1,(n + n2),n) ) by A1, A2;
hence s1 . n = s2 . n ; :: thesis: verum