Section PROD'.
Variable A : Type.
Variable J_A: Join A.
Variable saA : Perm_alg A.
Variable B: Type.
Variable J_B: Join B.
Variable saB : Perm_alg B.
Variable agB : ageable B.
Variable asb : Age_alg B.

Lemma nec_join4 {A} `{asaA : Age_alg A}: forall z x' y' z' : A,
join x' y' z' ->
necR z z' ->
exists x,
exists y,
join x y z /\ necR x x' /\ necR y y'.