let k1, k2 be Tuple of n,(k -SD ); :: thesis: ( ( for i being Nat st i in Seg n holds
DigA k1,i = SDMinDigit m,k,i ) & ( for i being Nat st i in Seg n holds
DigA k2,i = SDMinDigit m,k,i ) implies k1 = k2 )
assume that
A5: for i being Nat st i in Seg n holds
DigA k1,i = SDMinDigit m,k,i and
A6: for i being Nat st i in Seg n holds
DigA k2,i = SDMinDigit m,k,i ; :: thesis: k1 = k2
A7: ( len k1 = n & len k2 = n ) by FINSEQ_1:def 18;
X: dom k1 = Seg n by A7, FINSEQ_1:def 3;

now

let j be Nat; :: thesis: ( j in dom k1 implies k1 . j = k2 . j )
assume A8: j in dom k1 ; :: thesis: k1 . j = k2 . j
then k1 . j = DigA k1,j by X, RADIX_1:def 3
.= SDMinDigit m,k,j by A5, A8, X
.= DigA k2,j by A6, A8, X
.= k2 . j by A8, X, RADIX_1:def 3 ;
hence k1 . j = k2 . j ; :: thesis: verum

end;

hence k1 = k2 by A7, FINSEQ_2:10; :: thesis: verum