Commit dcfe93aa authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

parents dcc164e3 b00233e4
......@@ -131,10 +131,24 @@ Proof.
intuition eauto 10 using dra_disjoint_minus, dra_op_minus.
Qed.
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.
Proof.
intros Hxy. apply discrete_update.
intros z (?&?&?); split_ands'; try eapply Hxy; eauto.
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.
......@@ -333,22 +333,13 @@ Lemma sts_op_auth_frag_up s T :
Proof. intros; apply sts_op_auth_frag; auto using elem_of_up, closed_up. Qed.
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.
Proof.
(* Somehow I feel like a very similar proof muts have happened above, when
proving the DRA axioms. After all, we are just reflecting the operation here. *)
intros HT HS1 HS2; split; [split|constructor; solve_elem_of]; simpl.
- intros; split_ands; try done; []. constructor; last solve_elem_of.
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.
intros HT HS1 HS2. rewrite /sts_frag.
(* FIXME why does rewrite not work?? *)
etransitivity; last eapply to_validity_op; try done; [].
intros Hval. constructor; last solve_elem_of. eapply closed_ne, Hval.
Qed.
(** Frame preserving updates *)
......
......@@ -53,18 +53,19 @@ Section sts.
(* The same rule as implication does *not* hold, as could be shown using
sts_frag_included. *)
Lemma sts_ownS_weaken E γ S1 S2 T :
S1 S2 sts.closed S2 T
sts_ownS γ S1 T pvs E E (sts_ownS γ S2 T).
Proof. intros. by apply own_update, sts_update_frag. Qed.
Lemma sts_ownS_weaken E γ S1 S2 T1 T2 :
T1 T2 S1 S2 sts.closed S2 T2
sts_ownS γ S1 T1 pvs E E (sts_ownS γ S2 T2).
Proof. intros -> ? ?. by apply own_update, sts_update_frag. Qed.
Lemma sts_own_weaken E γ s S T :
s S sts.closed S T
sts_own γ s T pvs E E (sts_ownS γ S T).
Proof. intros. by apply own_update, sts_update_frag_up. Qed.
Lemma sts_own_weaken E γ s S T1 T2 :
T1 T2 s S sts.closed S T2
sts_own γ s T1 pvs E E (sts_ownS γ S T2).
(* FIXME for some reason, using "->" instead of "<-" does not work? *)
Proof. intros <- ? ?. by apply own_update, sts_update_frag_up. Qed.
Lemma sts_ownS_op γ 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_ownS γ (S1 S2) (T1 T2) (sts_ownS γ S1 T1 sts_ownS γ S2 T2)%I.
Proof. intros. by rewrite /sts_ownS -own_op sts_op_frag. Qed.
......
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