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 Th51:
  3 divides (a+b)*(a-b)+a*b iff 3 divides a & 3 divides b
  proof
    3 divides a & 3 divides b implies 3 divides (a+b) by WSIERP_1:4;
    hence thesis by Lm33,Lm34,WSIERP_1:5;
  end;
