Commit e49c4aa0 authored by Robbert Krebbers's avatar Robbert Krebbers
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Commonly used variant of `singleton_included` when the element is exclusive.

parent 87afb294
......@@ -278,6 +278,13 @@ Proof.
+ by rewrite lookup_op lookup_singleton lookup_partial_alter Hi.
+ by rewrite lookup_op lookup_singleton_ne// lookup_partial_alter_ne// left_id.
Lemma singleton_included_exclusive m i x :
Exclusive x m
{[ i := x ]} m m !! i Some x.
intros ? Hm. rewrite singleton_included. split; last by eauto.
intros (y&?&->%(Some_included_exclusive _)); eauto using lookup_valid_Some.
Global Instance singleton_cancelable i x :
Cancelable (Some x) Cancelable {[ i := x ]}.
......@@ -121,10 +121,8 @@ Section to_proph_map.
Lemma proph_map_singleton_included R p v :
{[p := Excl v]} to_proph_map R R !! p = Some v.
rewrite singleton_included=> -[v' []].
rewrite /to_proph_map lookup_fmap fmap_Some_equiv=> -[v'' [Hp ->]].
intros [=->]%Some_included_exclusive%leibniz_equiv_iff; first done; last done.
apply excl_exclusive.
rewrite singleton_included_exclusive; last by apply to_proph_map_valid.
by rewrite leibniz_equiv_iff /to_proph_map lookup_fmap fmap_Some=> -[v' [-> [->]]].
End to_proph_map.
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