let n be Nat; :: thesis: ( 7 divides n iff 7 divides (value (((digits (n,10)) /^ 1),10)) - (2 * ((digits (n,10)) . 0)) )
(digits (n,10)) /^ 1 = mid ((digits (n,10)),2,(len (digits (n,10)))) by Th3;
hence ( 7 divides n iff 7 divides (value (((digits (n,10)) /^ 1),10)) - (2 * ((digits (n,10)) . 0)) ) by Th39; :: thesis: verum