Commit 87abb52a authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Lemmas about Big ops and contains.

parent 2407263c
......@@ -157,6 +157,9 @@ Section list.
Lemma big_opL_permutation (f : A M) l1 l2 :
l1 l2 ([ list] x l1, f x) ([ list] x l2, f x).
Proof. intros Hl. by rewrite /big_opL !imap_const Hl. Qed.
Lemma big_opL_contains (f : A M) l1 l2 :
l1 `contains` l2 ([ list] x l1, f x) ([ list] x l2, f x).
Proof. intros Hl. apply big_op_contains. rewrite !imap_const. by rewrite ->Hl. Qed.
Global Instance big_opL_ne l n :
Proper (pointwise_relation _ (pointwise_relation _ (dist n)) ==> (dist n))
......
......@@ -219,6 +219,9 @@ Section list.
( k y, l !! k = Some y Φ k y Ψ k y)
([ list] k y l, Φ k y) ([ list] k y l, Ψ k y).
Proof. apply big_opL_proper. Qed.
Lemma big_sepL_contains (Φ : A uPred M) l1 l2 :
l1 `contains` l2 ([ list] y l2, Φ y) [ list] y l1, Φ y.
Proof. intros ?. apply uPred_included. by apply: big_opL_contains. Qed.
Global Instance big_sepL_mono' l :
Proper (pointwise_relation _ (pointwise_relation _ ()) ==> ())
......
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