End BaseField.
Notation baseFieldType L := (baseField_type (Phant L)).
(* Base of fieldOver, finally. *)
Section MoreFieldOver.
Variables (F0 : fieldType) (L : fieldExtType F0) (F : {subfield L}).

Lemma base_vspaceOver V : baseVspace (vspaceOver F V) =i (F * V)%VS.
Let nz_p0 : p0 != 0. Proof. by rewrite monic_neq0 // p0_mon. Qed.