let n be Nat; ( 83 divides n iff 83 divides (value (((digits (n,10)) /^ 1),10)) + (25 * ((digits (n,10)) . 0)) )
(digits (n,10)) /^ 1 = mid ((digits (n,10)),2,(len (digits (n,10))))
by Th3;
hence
( 83 divides n iff 83 divides (value (((digits (n,10)) /^ 1),10)) + (25 * ((digits (n,10)) . 0)) )
by Th78; verum