Commit 1530f15f authored by Robbert Krebbers's avatar Robbert Krebbers

More bigop properties.

parent 18841bdb
......@@ -125,6 +125,10 @@ Lemma ra_empty_least x : ∅ ≼ x.
Proof. by exists x; rewrite (left_id _ _). Qed.
(** * Big ops *)
Lemma big_op_nil : big_op (@nil A) = .
Proof. done. Qed.
Lemma big_op_cons x xs : big_op (x :: xs) = x big_op xs.
Proof. done. Qed.
Global Instance big_op_permutation : Proper (() ==> ()) big_op.
Proof.
induction 1 as [|x xs1 xs2 ? IH|x y xs|xs1 xs2 xs3]; simpl; auto.
......@@ -147,6 +151,9 @@ Proof.
* by transitivity (big_op ys); [|apply ra_included_r].
* by transitivity (big_op ys).
Qed.
Lemma big_op_delete xs i x :
xs !! i = Some x x big_op (delete i xs) big_op xs.
Proof. by intros; rewrite {2}(delete_Permutation xs i x). Qed.
Context `{FinMap K M}.
Lemma big_opM_empty : big_opM ( : M A) .
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment