reserve a,b,c,d,x,j,k,l,m,n for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  p+q divides p*(t*(p+q)+z) + q*z
  proof
    A1: z = q*t*0+z;
    p*(t*(p+q)) + q*(t*0) = p*t*(p+q) + q*t*0;
    hence thesis by A1,INT_1:def 3,Th29;
  end;
