Commit 87957de9 authored by Robbert Krebbers's avatar Robbert Krebbers

Stronger version of auth_update w.r.t. step indexes.

parent efd82c63
......@@ -148,11 +148,11 @@ Lemma auth_frag_op a b : ◯ (a ⋅ b) ≡ ◯ a ⋅ ◯ b.
Proof. done. Qed.
Lemma auth_update a a' b b' :
( n af, {n} a a ={n}= a' af b ={n}= b' af {n} b)
( n af, {S n} a a ={S n}= a' af b ={S n}= b' af {S n} b)
a a' ~~> b b'.
Proof.
move=> Hab [[] bf1] n // =>-[[bf2 Ha] ?]; do 2 red; simpl in *.
destruct (Hab (S n) (bf1 bf2)) as [Ha' ?]; auto.
move=> Hab [[?| |] bf1] n // =>-[[bf2 Ha] ?]; do 2 red; simpl in *.
destruct (Hab n (bf1 bf2)) as [Ha' ?]; auto.
{ by rewrite Ha left_id associative. }
split; [by rewrite Ha' left_id associative; apply cmra_includedN_l|done].
Qed.
......
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