let n be Nat; :: thesis: ( 31 divides n iff 31 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (3 * ((digits (n,10)) . 0)) )
reconsider p = 31 as Prime by Th24;
A1: (10 * 3) + 1 = p * 1 ;
p,10 are_coprime by EULER_1:2;
hence ( 31 divides n iff 31 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (3 * ((digits (n,10)) . 0)) ) by Th37, A1; :: thesis: verum