let n be Nat; :: thesis: ( 61 divides n iff 61 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (6 * ((digits (n,10)) . 0)) )
reconsider p = 61 as Prime by Th29;
A1: (10 * 6) + 1 = p * 1 ;
p,10 are_coprime by EULER_1:2;
hence ( 61 divides n iff 61 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (6 * ((digits (n,10)) . 0)) ) by Th37, A1; :: thesis: verum