Commit 397250e0 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Improve and document split_and tactics.

parent 1fb156c3
......@@ -72,7 +72,7 @@ Lemma wsat_init k E σ mm : ✓{S k} mm → wsat (S k) E σ (Res ∅ (Excl σ) m
intros Hv. exists ; constructor; auto.
- rewrite big_opM_empty right_id.
split_ands'; try (apply cmra_valid_validN, ra_empty_valid);
split_and!; try (apply cmra_valid_validN, ra_empty_valid);
constructor || apply Hv.
- by intros i; rewrite lookup_empty=>-[??].
- intros i P ?; rewrite /= left_id lookup_empty; inversion_clear 1.
......@@ -123,7 +123,7 @@ Proof.
apply (inj Excl).
by rewrite -Hpst_r -Hpst -assoc Hpst' right_id. }
split; [done|exists rs].
by constructor; split_ands'; try (rewrite /= -assoc Hpst').
by constructor; first split_and!; try rewrite /= -assoc Hpst'.
Lemma wsat_update_gst n E σ r rf mm1 (P : iGst Λ Σ Prop) :
mm1 {S n} gst r mm1 ~~>: (λ mm2, default False mm2 P)
......@@ -132,7 +132,8 @@ Proof.
intros [mf Hr] Hup [rs [(?&?&?) Hσ HE Hwld]].
destruct (Hup (S n) (mf gst (rf big_opM rs))) as ([m2|]&?&Hval'); try done.
{ by rewrite /= (assoc _ mm1) -Hr assoc. }
exists m2; split; [exists rs; split; split_ands'; auto|done].
exists m2; split; [exists rs|done].
by constructor; first split_and!; auto.
Lemma wsat_alloc n E1 E2 σ r P rP :
¬set_finite E1 P n rP wsat (S n) (E1 E2) σ (rP r)
......@@ -153,9 +154,9 @@ Proof.
rewrite /= !lookup_op !op_is_Some -!not_eq_None_Some; tauto. }
assert (r big_opM (<[i:=rP]> rs) rP r big_opM rs) as Hr.
{ by rewrite (comm _ rP) -assoc big_opM_insert. }
exists i; split_ands; [exists (<[i:=rP]>rs); constructor| |]; auto.
exists i; split_and?; [exists (<[i:=rP]>rs); constructor| |]; auto.
- destruct Hval as (?&?&?); rewrite -assoc Hr.
split_ands'; rewrite /= ?left_id; [|eauto|eauto].
split_and!; rewrite /= ?left_id; [|eauto|eauto].
intros j; destruct (decide (j = i)) as [->|].
+ by rewrite !lookup_op Hri HrPi Hrsi !right_id lookup_singleton.
+ by rewrite lookup_op lookup_singleton_ne // left_id.
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