let n be Nat; :: thesis: ( 7 divides n iff 7 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (2 * ((digits (n,10)) . 0)) )
reconsider p = 7 as Prime by NAT_4:26;
(10 * 2) + 1 = p * 3 ;
hence ( 7 divides n iff 7 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (2 * ((digits (n,10)) . 0)) ) by Th37, Th22; :: thesis: verum