reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  a,b are_coprime implies not 3 divides (a+b)*(a-b)+ a*b
  proof
    assume a,b are_coprime; then
    not 3 divides a or not 3 divides b by PYTHTRIP:def 1;
    hence thesis by Th51;
  end;
