Definition wk_split {A} {JA: Join A} :=
      forall a b c d e : A, join a b c -> join d e c -> joins a d -> join_sub d b.

(* Specifications: *)
Lemma crosssplit_wkSplit {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{DA: Disj_alg A}{CrA: Cross_alg A}{AG: ageable A}{XA: Age_alg A}: wk_split.
Lemma ewand_sepcon {A} {JA: Join A}{PA: Perm_alg A}{AG: ageable A}{XA: Age_alg A}: forall P Q R, (ewand (P * Q) R = ewand P (ewand Q R))%pred.
Lemma distrib_orp_sepcon {A : Type}{JA : Join A}{PA : Perm_alg A}{agA : ageable A} {AgeA : Age_alg A}: forall (P Q R : pred A), ((P || Q) * R = P * R || Q * R)%pred.
Lemma distrib_orp_sepcon2{A : Type}{JA : Join A}{PA : Perm_alg A}{agA : ageable A} {AgeA : Age_alg A}: forall (P Q R : pred A), (R * (P || Q) = R * P || R * Q)%pred.