Definition separable U W : bool :=
all (separable_element U) (vbasis W).
Definition purely_inseparable U W : bool :=
all (purely_inseparable_element U) (vbasis W).

Lemma inseparable_add K x y :
purely_inseparable_element K x -> purely_inseparable_element K y ->
purely_inseparable_element K (x + y).