Merge branch 'ci/robbert/seq_S' into 'master'

Rename `seq_S_snoc` into `seq_S` to be consistent with Coq's stdlib

See merge request !212

CHANGELOG.md

@@ -40,7 +40,8 @@ Coq 8.8 and 8.9 are no longer supported.
   returns `"0"` for `N`, `Z`, and `nat`.
 - Remove duplicate `map_fmap_empty` of `fmap_empty`, and rename
   `map_fmap_empty_inv` into `fmap_empty_inv` for consistency's sake.
-- Rename `seq_S_end_app` to `seq_S_snoc`.
+- Rename `seq_S_end_app` to `seq_S`. (The lemma `seq_S` is also in Coq's stdlib
+  since Coq 8.12.)
 
 The following `sed` script should perform most of the renaming
 (on macOS, replace `sed` by `gsed`, installed via e.g. `brew install gnu-sed`):
@@ -57,7 +58,7 @@ s/\bQp_mult_plus_distr_l\b/Qp_mul_add_distr_r/g
 s/\bQp_mult_plus_distr_r\b/Qp_mul_add_distr_l/g
 s/\bmap_fmap_empty\b/fmap_empty/g
 s/\bmap_fmap_empty_inv\b/fmap_empty_inv/g
-s/\bseq_S_end_app\b/seq_S_snoc/g
+s/\bseq_S_end_app\b/seq_S/g
 ' $(find theories -name "*.v")
 ```
 

theories/list_numbers.v

@@ -67,9 +67,10 @@ Section seq.
   Qed.
   Lemma NoDup_seq j n : NoDup (seq j n).
   Proof. apply NoDup_ListNoDup, seq_NoDup. Qed.
-  Lemma seq_S_snoc j n : seq j (S n) = seq j n ++ [j + n].
+  (* FIXME: This lemma is in the stdlib since Coq 8.12 *)
+  Lemma seq_S n j : seq j (S n) = seq j n ++ [j + n].
   Proof.
-    revert j. induction n as [|n IH]; intros j; simpl in *; f_equal; [done |].
+    revert j. induction n as [|n IH]; intros j; f_equal/=; [done |].
     by rewrite IH, Nat.add_succ_r.
   Qed.
 
@@ -147,7 +148,8 @@ Section seqZ.
   Proof.
     intros. unfold seqZ. rewrite Z2Nat.inj_add, seq_app, fmap_app by done.
     f_equal. rewrite Nat.add_comm, <-!fmap_add_seq, <-list_fmap_compose.
-    apply list_fmap_ext; naive_solver auto with lia.
+    apply list_fmap_ext; [|done]; intros j; simpl.
+    rewrite Nat2Z.inj_add, Z2Nat.id by done. lia.
   Qed.
 
   Lemma seqZ_S m i : seqZ m (S i) = seqZ m i ++ [m + i].
@@ -161,7 +163,7 @@ Section seqZ.
   Proof.
     rewrite elem_of_list_lookup.
     setoid_rewrite lookup_seqZ. split; [naive_solver lia|].
-    exists (Z.to_nat (k - m)). lia.
+    exists (Z.to_nat (k - m)). rewrite Z2Nat.id by lia. lia.
   Qed.
 
   Lemma Forall_seqZ (P : Z → Prop) m n :