let X1, X2 be Subset of (D ^omega); :: thesis: ( ( for x being object holds
( x in X1 iff x is n -element XFinSequence of D ) ) & ( for x being object holds
( x in X2 iff x is n -element XFinSequence of D ) ) implies X1 = X2 )
assume that
A1: for x being object holds
( x in X1 iff x is n -element XFinSequence of D ) and
A2: for x being object holds
( x in X2 iff x is n -element XFinSequence of D ) ; :: thesis: X1 = X2

now :: thesis: for x being object holds
( x in X1 iff x in X2 )

let x be object ; :: thesis: ( x in X1 iff x in X2 )
( x in X1 iff x is n -element XFinSequence of D ) by A1;
hence ( x in X1 iff x in X2 ) by A2; :: thesis: verum

end;

hence X1 = X2 by TARSKI:2; :: thesis: verum