Commit f402c1cc authored by Robbert Krebbers's avatar Robbert Krebbers

Define some flipped monotonicity Propers for binary uPred connectives.

No idea why these aren't resolved automatically, for unary predicates
they do not seem necesarry.
parent e4763d5e
......@@ -486,8 +486,14 @@ Global Instance const_mono' : Proper (impl ==> (⊑)) (@uPred_const M).
Proof. intros φ1 φ2; apply const_mono. Qed.
Global Instance and_mono' : Proper (() ==> () ==> ()) (@uPred_and M).
Proof. by intros P P' HP Q Q' HQ; apply and_mono. Qed.
Global Instance and_flip_mono' :
Proper (flip () ==> flip () ==> flip ()) (@uPred_and M).
Proof. by intros P P' HP Q Q' HQ; apply and_mono. Qed.
Global Instance or_mono' : Proper (() ==> () ==> ()) (@uPred_or M).
Proof. by intros P P' HP Q Q' HQ; apply or_mono. Qed.
Global Instance or_flip_mono' :
Proper (flip () ==> flip () ==> flip ()) (@uPred_or M).
Proof. by intros P P' HP Q Q' HQ; apply or_mono. Qed.
Global Instance impl_mono' :
Proper (flip () ==> () ==> ()) (@uPred_impl M).
Proof. by intros P P' HP Q Q' HQ; apply impl_mono. Qed.
......@@ -591,6 +597,9 @@ Proof. by intros x [|n] ?; [done|intros (x1&x2&?&?&[a ?]); exists a,x1,x2]. Qed.
Hint Resolve sep_mono.
Global Instance sep_mono' : Proper (() ==> () ==> ()) (@uPred_sep M).
Proof. by intros P P' HP Q Q' HQ; apply sep_mono. Qed.
Global Instance sep_flip_mono' :
Proper (flip () ==> flip () ==> flip ()) (@uPred_sep M).
Proof. by intros P P' HP Q Q' HQ; apply sep_mono. Qed.
Lemma wand_mono P P' Q Q' : Q P P' Q' (P - P') (Q - Q').
Proof. intros HP HQ; apply wand_intro_r; rewrite HP -HQ; apply wand_elim_l. Qed.
Global Instance wand_mono' : Proper (flip () ==> () ==> ()) (@uPred_wand M).
......
......@@ -74,9 +74,7 @@ Proof.
apply const_elim_l=>-[v2' [Hv ?]] /=.
rewrite -pvs_intro.
rewrite (forall_elim v2') (forall_elim σ2') (forall_elim ef) const_equiv //.
rewrite left_id wand_elim_r. apply sep_mono; last done.
(* FIXME RJ why can't I do this rewrite before doing sep_mono? *)
by rewrite -(wp_value' _ _ e2').
by rewrite left_id wand_elim_r -(wp_value' _ _ e2').
Qed.
Lemma wp_lift_atomic_det_step {E Q e1} σ1 v2 σ2 ef :
......
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