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Commit a70caa4b authored by Robbert Krebbers's avatar Robbert Krebbers
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All multiset elements are cancelable.

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theories/algebra/gmultiset.v
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...@@ -50,6 +50,11 @@ Section gmultiset. ...@@ -50,6 +50,11 @@ Section gmultiset.
Proof. split. done. intros X. by rewrite gmultiset_op_union left_id_L. done. Qed. Proof. split. done. intros X. by rewrite gmultiset_op_union left_id_L. done. Qed.
Canonical Structure gmultisetUR := UcmraT (gmultiset K) gmultiset_ucmra_mixin. Canonical Structure gmultisetUR := UcmraT (gmultiset K) gmultiset_ucmra_mixin.
Global Instance gmultiset_cancelable X : Cancelable X.
Proof.
apply: discrete_cancelable=> Y Z _ ?. fold_leibniz. by apply (inj (X ∪)).
Qed.
Lemma gmultiset_opM X mY : X ⋅? mY = X ∪ from_option id ∅ mY. Lemma gmultiset_opM X mY : X ⋅? mY = X ∪ from_option id ∅ mY.
Proof. destruct mY; by rewrite /= ?right_id_L. Qed. Proof. destruct mY; by rewrite /= ?right_id_L. Qed.
...@@ -71,7 +76,6 @@ Section gmultiset. ...@@ -71,7 +76,6 @@ Section gmultiset.
repeat (rewrite multiplicity_difference || rewrite multiplicity_union). repeat (rewrite multiplicity_difference || rewrite multiplicity_union).
omega. omega.
Qed. Qed.
End gmultiset. End gmultiset.
Arguments gmultisetC _ {_ _}. Arguments gmultisetC _ {_ _}.
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