let n be Nat; ( 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 Nat 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; verum