let n be Nat; :: thesis: ( 67 divides n iff 67 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (20 * ((digits (n,10)) . 0)) )
reconsider p = 67 as Prime by Th30;
A1: (10 * 20) + 1 = p * 3 ;
p,10 are_coprime by EULER_1:2;
hence ( 67 divides n iff 67 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (20 * ((digits (n,10)) . 0)) ) by Th37, A1; :: thesis: verum