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Add two library lemmas
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@ -371,3 +371,19 @@ Ltac simplify_map :=
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Require Import Classical.
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Ltac excluded_middle P := destruct (classic P).
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Lemma join_idempotent: forall (A B : Type) (m : fmap A B), (m $++ m) = m.
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Proof.
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simplify; apply fmap_ext; simplify.
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cases (m $? k).
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- rewrite lookup_join1; auto.
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eauto using lookup_Some_dom.
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- rewrite lookup_join2; auto.
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eauto using lookup_None_dom.
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Qed.
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Lemma includes_refl: forall (A B : Type) (m : fmap A B), m $<= m.
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Proof.
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simplify.
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apply includes_intro; auto.
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Qed.
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