Definition MulF (x y : F) : F.Global Instance mulF_morphism : Proper (EqF ==> EqF ==> EqF) MulF.Definition SubF (x y : F) : F.Global Instance subF_morphism : Proper (EqF ==> EqF ==> EqF) SubF.Definition OppF (x : F) : F.Global Instance oppF_morphism : Proper (EqF ==> EqF) OppF.Definition InvF (x : F) : F.Global Instance invF_morphism : Proper (EqF ==> EqF) InvF.Definition DivF (x y : F) : F.Global Instance divF_morphism : Proper (EqF ==> EqF ==> EqF) DivF.Definition PythF (x y : F) : F.

Lemma ringF : (ring_theory OF OneF AddF MulF SubF OppF EqF).