let n be Nat; ( 37 divides n iff 37 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (11 * ((digits (n,10)) . 0)) )
reconsider p = 37 as prime Nat by NAT_4:31;
A1:
(10 * 11) + 1 = p * 3
;
p,10 are_coprime
by EULER_1:2;
hence
( 37 divides n iff 37 divides (value ((mid ((digits (n,10)),2,(len (digits (n,10))))),10)) - (11 * ((digits (n,10)) . 0)) )
by Th37, A1; verum