Hypothesis sepKy : separable_element K y.

(* Specifications: *)
Lemma Primitive_Element_Theorem : exists z, (<< <<K; y>>; x>> = <<K; z>>)%VS.
Lemma adjoin_separable : separable_element <<K; y>> x -> separable_element K x.
End PrimitiveElementTheorem.
Lemma strong_Primitive_Element_Theorem K x y :
separable_element <<K; x>> y ->
exists2 z : L, (<< <<K; y>>; x>> = <<K; z>>)%VS
& separable_element K x -> separable_element K y.