Commit cbf274c0 authored by Robbert Krebbers's avatar Robbert Krebbers

Existentials commute with disjunction.

parent 4ecb139a
......@@ -199,6 +199,13 @@ Lemma and_exist_r {A} P (Φ: A → uPred M) : (∃ a, Φ a) ∧ P ⊣⊢ ∃ a,
Proof.
rewrite -(comm _ P) and_exist_l. apply exist_proper=>a. by rewrite comm.
Qed.
Lemma or_exist {A} (Φ Ψ : A uPred M) :
( a, Φ a Ψ a) ( a, Φ a) ( a, Ψ a).
Proof.
apply (anti_symm ()).
- apply exist_elim=> a. by rewrite -!(exist_intro a).
- apply or_elim; apply exist_elim=> a; rewrite -(exist_intro a); auto.
Qed.
Lemma pure_mono φ1 φ2 : (φ1 φ2) φ1 φ2.
Proof. intros; apply pure_elim with φ1; eauto. Qed.
......
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