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Add two library lemmas

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Adam Chlipala 2017-03-21 21:39:37 -04:00
parent c5600db874
commit e9e8e6b92b
1 changed files with 16 additions and 0 deletions
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FrapWithoutSets.v
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@ -371,3 +371,19 @@ Ltac simplify_map :=
Require Import Classical. Require Import Classical.
Ltac excluded_middle P := destruct (classic P). Ltac excluded_middle P := destruct (classic P).
Lemma join_idempotent: forall (A B : Type) (m : fmap A B), (m $++ m) = m.
Proof.
simplify; apply fmap_ext; simplify.
cases (m $? k).
- rewrite lookup_join1; auto.
eauto using lookup_Some_dom.
- rewrite lookup_join2; auto.
eauto using lookup_None_dom.
Qed.
Lemma includes_refl: forall (A B : Type) (m : fmap A B), m $<= m.
Proof.
simplify.
apply includes_intro; auto.
Qed.