Hint Resolve meet_hom.

Lemma grade_dual n k x : k < n -> grade n k x -> grade n (n - k) '@x.
assert (dual_aux: forall n x l, hom n 1 x -> is_vector_space n l ->
(forall y, In y l -> '@x ∧ y = 0) -> '@x ∧ joinl n l = 0).