let n be Nat; :: thesis: ( 11 divides n iff 11 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - ((digits (n,10)) . 0) )
reconsider p = 11 as Prime by NAT_4:27;
A1: (10 * 1) + 1 = p * 1 ;
p,10 are_coprime by EULER_1:2;
then ( 11 divides n iff 11 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (1 * ((digits (n,10)) . 0)) ) by Th37, A1;
hence ( 11 divides n iff 11 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - ((digits (n,10)) . 0) ) ; :: thesis: verum