Commit 530b9800 authored by Robbert Krebbers's avatar Robbert Krebbers

Fix some identation.

parent 92a48e1b
......@@ -248,22 +248,21 @@ Lemma map_singleton_update i (x y : A) : x ~~> y → {[ i ↦ x ]} ~~> {[ i ↦
Proof. apply map_insert_update. Qed.
Lemma map_singleton_updateP_empty `{Empty A, !CMRAIdentity A}
(P : A Prop) (Q : gmap K A Prop) i :
(P : A Prop) (Q : gmap K A Prop) i :
~~>: P ( y, P y Q {[ i y ]}) ~~>: Q.
Proof.
intros Hx HQ gf n Hg.
destruct (Hx (default (gf !! i) id) n) as (y&?&Hy).
{ move:(Hg i). rewrite !left_id. case _: (gf !! i); first done.
intros. apply cmra_empty_valid. }
exists {[ i y]}. split; first by apply HQ.
intros i'. rewrite lookup_op.
destruct (decide (i' = i)).
- subst i'. rewrite lookup_singleton. move:Hy.
case _: (gf !! i); first done.
by rewrite right_id.
- move:(Hg i'). rewrite lookup_singleton_ne // !left_id. done.
Proof.
intros Hx HQ gf n Hg.
destruct (Hx (from_option (gf !! i)) n) as (y&?&Hy).
{ move:(Hg i). rewrite !left_id.
case _: (gf !! i); simpl; auto using cmra_empty_valid. }
exists {[ i y ]}; split; first by auto.
intros i'; destruct (decide (i' = i)) as [->|].
- rewrite lookup_op lookup_singleton.
move:Hy; case _: (gf !! i); first done.
by rewrite right_id.
- move:(Hg i'). by rewrite !lookup_op lookup_singleton_ne // !left_id.
Qed.
Lemma map_singleton_updateP_empty' `{Empty A, !CMRAIdentity A} (P : A Prop) i :
Lemma map_singleton_updateP_empty' `{Empty A, !CMRAIdentity A} (P: A Prop) i :
~~>: P ~~>: λ m, y, m = {[ i y ]} P y.
Proof. eauto using map_singleton_updateP_empty. Qed.
......
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