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...@@ -2,14 +2,14 @@ ...@@ -2,14 +2,14 @@
Although this implementation is slow, it is very useful as decidable equality Although this implementation is slow, it is very useful as decidable equality
is the only constraint on the carrier set. *) is the only constraint on the carrier set. *)
From stdpp Require Export sets list. From stdpp Require Export sets list.
Set Default Proof Using "Type". From stdpp Require Import options.
Record listset_nodup A := ListsetNoDup { Record listset_nodup A := ListsetNoDup {
listset_nodup_car : list A; listset_nodup_prf : NoDup listset_nodup_car listset_nodup_car : list A; listset_nodup_prf : NoDup listset_nodup_car
}. }.
Arguments ListsetNoDup {_} _ _ : assert. Global Arguments ListsetNoDup {_} _ _ : assert.
Arguments listset_nodup_car {_} _ : assert. Global Arguments listset_nodup_car {_} _ : assert.
Arguments listset_nodup_prf {_} _ : assert. Global Arguments listset_nodup_prf {_} _ : assert.
Section list_set. Section list_set.
Context `{EqDecision A}. Context `{EqDecision A}.
...@@ -29,7 +29,7 @@ Global Instance listset_nodup_difference: Difference C := ...@@ -29,7 +29,7 @@ Global Instance listset_nodup_difference: Difference C :=
λ '(ListsetNoDup l Hl) '(ListsetNoDup k Hk), λ '(ListsetNoDup l Hl) '(ListsetNoDup k Hk),
ListsetNoDup _ (NoDup_list_difference _ k Hl). ListsetNoDup _ (NoDup_list_difference _ k Hl).
Instance listset_nodup_set: Set_ A C. Local Instance listset_nodup_set: Set_ A C.
Proof. Proof.
split; [split | | ]. split; [split | | ].
- by apply not_elem_of_nil. - by apply not_elem_of_nil.
...@@ -41,5 +41,5 @@ Qed. ...@@ -41,5 +41,5 @@ Qed.
Global Instance listset_nodup_elems: Elements A C := listset_nodup_car. Global Instance listset_nodup_elems: Elements A C := listset_nodup_car.
Global Instance listset_nodup_fin_set: FinSet A C. Global Instance listset_nodup_fin_set: FinSet A C.
Proof. split. apply _. done. by intros [??]. Qed. Proof. split; [apply _|done|]. by intros [??]. Qed.
End list_set. End list_set.
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...@@ -12,3 +12,4 @@ From stdpp Require Export ...@@ -12,3 +12,4 @@ From stdpp Require Export
list list
list_numbers list_numbers
lexico. lexico.
From stdpp Require Import options.
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