(* Sep_alg: additional properties that makes a Permission Algebra into a Separation Algebra. *)
Class Sep_alg A {J: Join A} : Type :=
mkSep {
core: A -> A;
core_unit: forall t, unit_for (core t) t;
join_core: forall {a b c}, join a b c -> core a = core c
}.
Arguments Sep_alg _ [J].

Lemma core_uniq {t} {J: Join t}{PA: Perm_alg t}:
forall (SA1: @Sep_alg _ J)
(SA2: @Sep_alg _ J),
forall x, @core _ _ SA1 x = @core _ _ SA2 x.