let n be Nat; ( 11 divides n iff 11 divides (value (((digits (n,10)) /^ 1),10)) - ((digits (n,10)) . 0) )
(digits (n,10)) /^ 1 = mid ((digits (n,10)),2,(len (digits (n,10))))
by Th3;
hence
( 11 divides n iff 11 divides (value (((digits (n,10)) /^ 1),10)) - ((digits (n,10)) . 0) )
by Th41; verum