Commit ef7ea67f authored by Robbert Krebbers's avatar Robbert Krebbers

Some cleanup in upred.

parent f402c1cc
......@@ -812,9 +812,7 @@ Proof. move => x n Hv [a' ?]; cofe_subst; eauto using cmra_validN_op_l. Qed.
Lemma valid_intro {A : cmraT} (a : A) : a True ( a).
Proof. by intros ? x n ? _; simpl; apply cmra_valid_validN. Qed.
Lemma valid_elim {A : cmraT} (a : A) : ¬ {1} a ( a) False.
Proof.
intros Ha x [|n] ??; [|apply Ha, cmra_validN_le with (S n)]; auto with lia.
Qed.
Proof. intros Ha x [|n] ??; [|apply Ha, cmra_validN_le with (S n)]; auto. Qed.
Lemma valid_mono {A B : cmraT} (a : A) (b : B) :
( n, {n} a {n} b) ( a) ( b).
Proof. by intros ? x n ?; simpl; auto. Qed.
......@@ -832,26 +830,20 @@ Global Instance uPred_big_and_perm : Proper ((≡ₚ) ==> (≡)) (@uPred_big_and
Proof.
induction 1 as [|P Ps Qs ? IH|P Q Ps|]; simpl; auto.
* by rewrite IH.
* by rewrite !(associative _) (commutative _ P).
* by rewrite !associative (commutative _ P).
* etransitivity; eauto.
Qed.
Global Instance uPred_big_sep_perm : Proper (() ==> ()) (@uPred_big_sep M).
Proof.
induction 1 as [|P Ps Qs ? IH|P Q Ps|]; simpl; auto.
* by rewrite IH.
* by rewrite !(associative _) (commutative _ P).
* by rewrite !associative (commutative _ P).
* etransitivity; eauto.
Qed.
Lemma uPred_big_and_app Ps Qs : (Π (Ps ++ Qs))%I (Π Ps Π Qs)%I.
Proof.
by induction Ps as [|P Ps IH];
rewrite /= ?(left_id _ _) -?(associative _) ?IH.
Qed.
Proof. by induction Ps as [|?? IH]; rewrite /= ?left_id -?associative ?IH. Qed.
Lemma uPred_big_sep_app Ps Qs : (Π★ (Ps ++ Qs))%I (Π★ Ps Π★ Qs)%I.
Proof.
by induction Ps as [|P Ps IH];
rewrite /= ?(left_id _ _) -?(associative _) ?IH.
Qed.
Proof. by induction Ps as [|?? IH]; rewrite /= ?left_id -?associative ?IH. Qed.
Lemma uPred_big_sep_and Ps : (Π★ Ps) (Π Ps).
Proof. by induction Ps as [|P Ps IH]; simpl; auto. Qed.
Lemma uPred_big_and_elem_of Ps P : P Ps (Π Ps) P.
......
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