From 794ce99ac2d17cdd50dd90b323d299ccbe0fe456 Mon Sep 17 00:00:00 2001 From: Ralf Jung <jung@mpi-sws.org> Date: Mon, 11 Jan 2021 18:50:32 +0100 Subject: [PATCH] add seqZ_S --- theories/list_numbers.v | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/theories/list_numbers.v b/theories/list_numbers.v index b976599c..1caa8ede 100644 --- a/theories/list_numbers.v +++ b/theories/list_numbers.v @@ -156,6 +156,15 @@ Section seqZ. intros. simpl. lia. Qed. + Lemma seqZ_S m i : seqZ m (S i) = seqZ m i ++ [m + i]. + Proof. + intros. + replace (Z.of_nat (S i)) with (Z.of_nat i + 1)%Z by lia. + rewrite seqZ_app; [|lia..]. + unfold seqZ; simpl. + replace (0%nat + (m+i))%Z with (m + i)%Z by lia. done. + Qed. + Lemma elem_of_seqZ m n k : k ∈ seqZ m n ↔ m ≤ k < m + n. Proof. -- GitLab