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

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

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

end;

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