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author | Michalis Pardalos <m.pardalos@gmail.com> | 2021-08-22 00:41:55 +0100 |
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committer | Michalis Pardalos <m.pardalos@gmail.com> | 2021-08-22 00:41:55 +0100 |
commit | f2fc2ac70aeceec2f3f7137acba5c0bf7a342a17 (patch) | |
tree | 4fdfd1eb539e6a50d5ce2f66bd595a6a0112fe43 /src/common | |
parent | 1d52421edaec304a9a9e3c5a368af7af31e9ff3c (diff) | |
download | vericert-f2fc2ac70aeceec2f3f7137acba5c0bf7a342a17.tar.gz vericert-f2fc2ac70aeceec2f3f7137acba5c0bf7a342a17.zip |
Move list lemmas to own file
Diffstat (limited to 'src/common')
-rw-r--r-- | src/common/ListExtra.v | 27 |
1 files changed, 27 insertions, 0 deletions
diff --git a/src/common/ListExtra.v b/src/common/ListExtra.v new file mode 100644 index 0000000..6b14a50 --- /dev/null +++ b/src/common/ListExtra.v @@ -0,0 +1,27 @@ +Require Export Coq.Lists.List. + +Require Import Coq.micromega.Lia. +Require Import vericert.common.Vericertlib. + +From Hammer Require Import Tactics. + +Lemma nth_error_length : forall {A} (l : list A) n x, + nth_error l n = Some x -> (n < length l)%nat. +Proof. + induction l; intros; simpl in *. + - destruct n; crush. + - destruct n; crush. + edestruct IHl; eauto with arith. +Qed. + +Lemma length_nth_error : forall {A} (l : list A) n, + (n < length l)%nat -> exists x, nth_error l n = Some x. +Proof. + induction l; intros; simpl in *. + - lia. + - destruct n; crush; eauto with arith. +Qed. + +Lemma combine_split : forall {A B} (l : list (A * B)), + List.combine (fst (List.split l)) (snd (List.split l)) = l. +Proof. hfcrush use: split_combine unfold: fst, snd inv: prod. Qed. |