Commit 7583028f by Ralf Jung

### show that monadic set operations respect the partial order

parent c2e4e322
 ... ... @@ -531,12 +531,21 @@ End fresh. Section collection_monad. Context `{CollectionMonad M}. Global Instance collection_fmap_mono {A B} : Proper (pointwise_relation _ (=) ==> (⊆) ==> (⊆)) (@fmap M _ A B). Proof. intros f g ? X Y ?; solve_elem_of. Qed. Global Instance collection_fmap_proper {A B} : Proper (pointwise_relation _ (=) ==> (≡) ==> (≡)) (@fmap M _ A B). Proof. intros f g ? X Y [??]; split; solve_elem_of. Qed. Global Instance collection_bind_mono {A B} : Proper (((=) ==> (⊆)) ==> (⊆) ==> (⊆)) (@mbind M _ A B). Proof. unfold respectful; intros f g Hfg X Y ?; solve_elem_of. Qed. Global Instance collection_bind_proper {A B} : Proper (((=) ==> (≡)) ==> (≡) ==> (≡)) (@mbind M _ A B). Proof. unfold respectful; intros f g Hfg X Y [??]; split; solve_elem_of. Qed. Global Instance collection_join_mono {A} : Proper ((⊆) ==> (⊆)) (@mjoin M _ A). Proof. intros X Y ?; solve_elem_of. Qed. Global Instance collection_join_proper {A} : Proper ((≡) ==> (≡)) (@mjoin M _ A). Proof. intros X Y [??]; split; solve_elem_of. Qed. ... ...
 ... ... @@ -28,4 +28,4 @@ Instance set_join : MJoin set := λ A (XX : set (set A)), Instance set_collection_monad : CollectionMonad set. Proof. by split; try apply _. Qed. Global Opaque set_union set_intersection. Global Opaque set_union set_intersection set_difference.
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