let n be Nat; :: thesis: ( 59 divides n iff 59 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) + (6 * ((digits (n,10)) . 0)) )
reconsider p = 59 as prime Nat by Th28;
A1: (10 * 6) - 1 = p * 1 ;
p,10 are_coprime by EULER_1:2;
hence ( 59 divides n iff 59 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) + (6 * ((digits (n,10)) . 0)) ) by Th38, A1; :: thesis: verum