Definition lset_same_support {A} (lset1 lset2 : AMap.t A) :=
forall loc,
AMap.find loc lset1 = None <->
AMap.find loc lset2 = None.

(* Specifications: *)
Lemma sparsity_same_support {A} (lset1 lset2 : AMap.t A) :
lset_same_support lset1 lset2 ->
lock_sparsity lset1 ->
lock_sparsity lset2.
Lemma same_support_change_lock {A} (lset : AMap.t A) l x :
AMap.find l lset <> None ->
lset_same_support lset (AMap.add l x lset).
Lemma lset_same_support_map {A} m (f : A -> A) :
lset_same_support (AMap.map (option_map f) m) m.
Lemma lset_same_support_sym {A} (m1 m2 : AMap.t A) :
lset_same_support m1 m2 ->
lset_same_support m2 m1.
Lemma lset_same_support_trans {A} (m1 m2 m3 : AMap.t A) :
lset_same_support m1 m2 ->
lset_same_support m2 m3 ->
lset_same_support m1 m3.