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