A1: dom f = Seg (len f) by FINSEQ_1:def 3;
let f1, f2 be FinSequence; :: thesis: ( len f1 = len f & ( for i being Nat st i in dom f1 holds
f1 . i = f . (((len f) - i) + 1) ) & len f2 = len f & ( for i being Nat st i in dom f2 holds
f2 . i = f . (((len f) - i) + 1) ) implies f1 = f2 )
assume that
A2: len f1 = len f and
A3: for i being Nat st i in dom f1 holds
f1 . i = f . (((len f) - i) + 1) and
A4: len f2 = len f and
A5: for i being Nat st i in dom f2 holds
f2 . i = f . (((len f) - i) + 1) ; :: thesis: f1 = f2
A6: dom f1 = Seg (len f1) by FINSEQ_1:def 3;
A7: dom f2 = Seg (len f2) by FINSEQ_1:def 3;

now :: thesis: for i being Nat st i in dom f holds
f1 . i = f2 . i

let i be Nat; :: thesis: ( i in dom f implies f1 . i = f2 . i )
assume A8: i in dom f ; :: thesis: f1 . i = f2 . i
then f1 . i = f . (((len f) - i) + 1) by A2, A3, A6, A1;
hence f1 . i = f2 . i by A4, A5, A7, A1, A8; :: thesis: verum

end;

hence f1 = f2 by A2, A4, A6, A1, FINSEQ_2:9; :: thesis: verum