let n be Nat; ( 67 divides n iff 67 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (20 * ((digits (n,10)) . 0)) )
reconsider p = 67 as prime Nat by Th30;
A1:
(10 * 20) + 1 = p * 3
;
p,10 are_coprime
by EULER_1:2;
hence
( 67 divides n iff 67 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (20 * ((digits (n,10)) . 0)) )
by Th37, A1; verum