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 Th100:
  (u + t + z) is even implies u*t*z is even
  proof
    assume
    A1: u + t + z is even;
    per cases;
    suppose u is even;
      hence thesis;
    end;
    suppose
      B1: u is odd;
      per cases;
      suppose t is even;
        hence thesis;
      end;
      suppose
        t is odd; then
        z is even by A1,B1;
        hence thesis;
      end;
    end;
  end;
