Section test.
Context {A:Type}`{Aid:Integral_domain A}.

Lemma example5 : forall x y z u v,
x+y+z+u+v==0 ->
x*y+x*z+x*u+x*v+y*z+y*u+y*v+z*u+z*v+u*v==0->
x*y*z+x*y*u+x*y*v+x*z*u+x*z*v+x*u*v+y*z*u+y*z*v+y*u*v+z*u*v==0->
x*y*z*u+y*z*u*v+z*u*v*x+u*v*x*y+v*x*y*z==0 ->
x*y*z*u*v==0 -> x^5%Z==0.