Qed.

Theorem SF2Prim_inj : forall x y, SF2Prim x = SF2Prim y -> valid_binary x = true -> valid_binary y = true -> x = y.
intros. rewrite <- Prim2SF_SF2Prim by assumption. symmetry. rewrite <- Prim2SF_SF2Prim by assumption. rewrite H. reflexivity.