Hint Resolve meet_hom.

(* Barnabei Brini Rota p136 *)
Lemma join_meet_swap n k1 k2 k3 (x y z : vect n) :
hom n k1 x -> hom n k2 y ->  hom n k3 z -> (k1 + k2 + k3 = n)%nat ->
x ∧ (y ∨ z) = (x ∨ y) ∧ z.