Commit 8b4d7a8d authored by Ralf Jung's avatar Ralf Jung
Browse files

derive sts_op_frag from a generic DRA property

parent e1589fea
...@@ -131,10 +131,24 @@ Proof. ...@@ -131,10 +131,24 @@ Proof.
intuition eauto 10 using dra_disjoint_minus, dra_op_minus. intuition eauto 10 using dra_disjoint_minus, dra_op_minus.
Qed. Qed.
Definition validityRA : cmraT := discreteRA validity_ra. Definition validityRA : cmraT := discreteRA validity_ra.
Definition validity_update (x y : validityRA) : Lemma validity_update (x y : validityRA) :
( z, x z validity_car x z y validity_car y z) x ~~> y. ( z, x z validity_car x z y validity_car y z) x ~~> y.
Proof. Proof.
intros Hxy. apply discrete_update. intros Hxy. apply discrete_update.
intros z (?&?&?); split_ands'; try eapply Hxy; eauto. intros z (?&?&?); split_ands'; try eapply Hxy; eauto.
Qed. Qed.
Lemma to_validity_valid (x : A) :
to_validity x x.
Proof. intros. done. Qed.
Lemma to_validity_op (x y : A) :
x y ( (x y) x y)
to_validity (x y) to_validity x to_validity y.
Proof.
intros Hvalx Hvaly Hdisj. split; [split | done].
- simpl. auto.
- simpl. intros (_ & _ & ?).
auto using dra_op_valid, to_validity_valid.
Qed.
End dra. End dra.
...@@ -336,19 +336,10 @@ Lemma sts_op_frag S1 S2 T1 T2 : ...@@ -336,19 +336,10 @@ Lemma sts_op_frag S1 S2 T1 T2 :
T1 T2 sts.closed S1 T1 sts.closed S2 T2 T1 T2 sts.closed S1 T1 sts.closed S2 T2
sts_frag (S1 S2) (T1 T2) sts_frag S1 T1 sts_frag S2 T2. sts_frag (S1 S2) (T1 T2) sts_frag S1 T1 sts_frag S2 T2.
Proof. Proof.
(* Somehow I feel like a very similar proof muts have happened above, when intros HT HS1 HS2. rewrite /sts_frag.
proving the DRA axioms. After all, we are just reflecting the operation here. *) (* FIXME why does rewrite not work?? *)
intros HT HS1 HS2; split; [split|constructor; solve_elem_of]; simpl. etransitivity; last eapply to_validity_op; try done; [].
- intros; split_ands; try done; []. constructor; last solve_elem_of. intros Hval. constructor; last solve_elem_of. eapply closed_ne, Hval.
by eapply closed_ne.
- intros (_ & _ & H). inversion_clear H. constructor; first done.
+ move=>s /elem_of_intersection
[/(closed_disjoint _ _ HS1) Hs1 /(closed_disjoint _ _ HS2) Hs2].
solve_elem_of +Hs1 Hs2.
+ move=> s1 s2 /elem_of_intersection [Hs1 Hs2] Hstep.
apply elem_of_intersection.
split; eapply closed_step; eauto; [|]; eapply framestep_mono, Hstep;
done || solve_elem_of.
Qed. Qed.
(** Frame preserving updates *) (** Frame preserving updates *)
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