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
  t,z are_coprime & t,u are_coprime & t is even implies
    u + z is even & u - z is even & u*z is odd
  proof
    assume t,z are_coprime & t,u are_coprime & t is even; then
    z is odd & u is odd by Lm20;
    hence thesis;
  end;
