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 purely_inseparableP {K E} :
reflect (forall y, y \in E -> purely_inseparable_element K y)
(purely_inseparable K E).