let s1, s2 be sequence of NAT; ( ( for n being Nat holds s1 . n = IFGT (n,(n1 + 1),(n + n2),n) ) & ( for n being Nat holds s2 . n = IFGT (n,(n1 + 1),(n + n2),n) ) implies s1 = s2 )
assume that
A2:
for n being Nat holds s1 . n = IFGT (n,(n1 + 1),(n + n2),n)
and
A3:
for n being Nat holds s2 . n = IFGT (n,(n1 + 1),(n + n2),n)
; s1 = s2
let n be Element of NAT ; FUNCT_2:def 8 s1 . n = s2 . n
( s1 . n = IFGT (n,(n1 + 1),(n + n2),n) & s2 . n = IFGT (n,(n1 + 1),(n + n2),n) )
by A2, A3;
hence
s1 . n = s2 . n
; verum