let f1, f2 be XFinSequence; :: thesis: ( len f1 = len f & ( for i being Element of NAT st i in dom f1 holds
f1 . i = f . ((len f) - (i + 1)) ) & len f2 = len f & ( for i being Element of NAT st i in dom f2 holds
f2 . i = f . ((len f) - (i + 1)) ) implies f1 = f2 )
assume that
A1: len f1 = len f and
A2: for i being Element of NAT st i in dom f1 holds
f1 . i = f . ((len f) - (i + 1)) and
A3: len f2 = len f and
A4: for i being Element of NAT st i in dom f2 holds
f2 . i = f . ((len f) - (i + 1)) ; :: thesis: f1 = f2

now

let i be Element of NAT ; :: thesis: ( i in dom f implies f1 . i = f2 . i )
assume A5: i in dom f ; :: thesis: f1 . i = f2 . i
then f1 . i = f . ((len f) - (i + 1)) by A1, A2;
hence f1 . i = f2 . i by A3, A4, A5; :: thesis: verum

end;

hence f1 = f2 by A1, A3, AFINSQ_1:10; :: thesis: verum