reserve n,k,b for Nat, i for Integer;

theorem Th64:
  53 divides n iff 53 divides
  value(mid(digits(n,10),2,len(digits(n,10))),10) + 16*digits(n,10).0
  proof
    reconsider p=53 as Prime by Th27;
    A1: 10*16 - 1 = p*3;
    p,10 are_coprime by EULER_1:2;
    hence thesis by Th38,A1;
  end;
