Commit 624f2010 authored by Robbert Krebbers's avatar Robbert Krebbers

Some more FSA lemmas.

parent 30a309d3
......@@ -217,6 +217,7 @@ Class FrameShiftAssertion {Λ Σ A} (fsaV : Prop) (fsa : FSA Λ Σ A) := {
Section fsa.
Context {Λ Σ A} (fsa : FSA Λ Σ A) `{!FrameShiftAssertion fsaV fsa}.
Implicit Types Φ Ψ : A iProp Λ Σ.
Import uPred.
Lemma fsa_mono E Φ Ψ : ( a, Φ a Ψ a) fsa E Φ fsa E Ψ.
Proof. apply fsa_mask_frame_mono; auto. Qed.
......@@ -231,8 +232,20 @@ Proof.
Qed.
Lemma fsa_pvs_fsa E Φ : (|={E}=> fsa E Φ) ⊣⊢ fsa E Φ.
Proof. apply (anti_symm ()); [by apply fsa_strip_pvs|apply pvs_intro]. Qed.
Lemma pvs_fsa_fsa E Φ : fsa E (λ a, |={E}=> Φ a) ⊣⊢ fsa E Φ.
Proof.
apply (anti_symm ()); [|apply fsa_mono=> a; apply pvs_intro].
by rewrite (pvs_intro E (fsa E _)) fsa_trans3.
Qed.
Lemma fsa_mono_pvs E Φ Ψ : ( a, Φ a (|={E}=> Ψ a)) fsa E Φ fsa E Ψ.
Proof. intros. rewrite -[fsa E Ψ]fsa_trans3 -pvs_intro. by apply fsa_mono. Qed.
Lemma fsa_wand_l E Φ Ψ : (( a, Φ a - Ψ a) fsa E Φ) (fsa E Ψ).
Proof.
rewrite fsa_frame_l. apply fsa_mono=> a.
by rewrite (forall_elim a) wand_elim_l.
Qed.
Lemma fsa_wand_r E Φ Ψ : (fsa E Φ a, Φ a - Ψ a) (fsa E Ψ).
Proof. by rewrite (comm _ (fsa _ _)) fsa_wand_l. Qed.
End fsa.
Definition pvs_fsa {Λ Σ} : FSA Λ Σ () := λ E Φ, (|={E}=> Φ ())%I.
......
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