move some lemmas/hints to ListUtil

2 files changed, 15 insertions, 13 deletions

diff --git a/src/Experiments/SimplyTypedArithmetic.v b/src/Experiments/SimplyTypedArithmetic.v
index c872360ba..b0855969a 100644
--- a/src/Experiments/SimplyTypedArithmetic.v
+++ b/src/Experiments/SimplyTypedArithmetic.v
@@ -962,14 +962,6 @@ Module Rows.
     Hint Rewrite Positional.eval_nil Positional.eval0 @Positional.eval_snoc
          Columns.eval_nil Columns.eval_snoc using (auto; solve [distr_length]) : push_eval.
 
-    (* TODO: move to ListUtil *)
-    Lemma sum_app x y : sum (x ++ y) = sum x + sum y.
-    Proof. induction x; rewrite ?app_nil_l, <-?app_comm_cons, ?sum_nil, ?sum_cons; omega. Qed.
-    (* TODO: move to listUtil or wherever push_map is defined *)
-    Hint Rewrite @map_app : push_map.
-    Hint Rewrite sum_nil sum_cons sum_app : push_sum.
-    Hint Rewrite @combine_nil_r @combine_cons : push_combine.
-
     Hint Resolve in_eq in_cons.
 
     Definition eval n (inp : rows) :=
@@ -1093,11 +1085,6 @@ Module Rows.
     Proof. apply eval_from_columns'_with_length. Qed.
     Hint Rewrite eval_from_columns' using (auto; solve [distr_length]) : push_eval.
 
-    (* TODO: move to ListUtil *)
-    Lemma length_tl {A} ls : length (@tl A ls) = (length ls - 1)%nat.
-    Proof. destruct ls; cbn [tl length]; lia. Qed.
-    Hint Rewrite @length_tl : distr_length.
-    
     Lemma max_column_size_extract_row inp :
       max_column_size (fst (extract_row inp)) = (max_column_size inp - 1)%nat.
     Proof.
diff --git a/src/Util/ListUtil.v b/src/Util/ListUtil.v
index 68cc6a41f..081ef54b5 100644
--- a/src/Util/ListUtil.v
+++ b/src/Util/ListUtil.v
@@ -30,6 +30,7 @@ Create HintDb simpl_skipn discriminated.
 Create HintDb simpl_fold_right discriminated.
 Create HintDb simpl_sum_firstn discriminated.
 Create HintDb push_map discriminated.
+Create HintDb push_combine discriminated.
 Create HintDb push_flat_map discriminated.
 Create HintDb push_fold_right discriminated.
 Create HintDb push_partition discriminated.
@@ -41,6 +42,7 @@ Create HintDb pull_firstn discriminated.
 Create HintDb push_firstn discriminated.
 Create HintDb pull_skipn discriminated.
 Create HintDb push_skipn discriminated.
+Create HintDb push_sum discriminated.
 Create HintDb pull_update_nth discriminated.
 Create HintDb push_update_nth discriminated.
 Create HintDb znonzero discriminated.
@@ -94,6 +96,7 @@ Module Export List.
     Proof. induction n; simpl List.repeat; simpl map; congruence. Qed.
   End Map.
   Hint Rewrite @map_cons @map_nil @map_repeat : push_map.
+  Hint Rewrite @map_app : push_map.
 
   Section FlatMap.
     Lemma flat_map_nil {A B} (f:A->list B) : List.flat_map f (@nil A) = nil.
@@ -923,6 +926,10 @@ Proof.
   induction xs; boring; discriminate.
 Qed.
 
+Lemma length_tl {A} ls : length (@tl A ls) = (length ls - 1)%nat.
+Proof. destruct ls; cbn [tl length]; omega. Qed.
+Hint Rewrite @length_tl : distr_length.
+
 Lemma length_snoc : forall {T} xs (x:T),
   length xs = pred (length (xs++x::nil)).
 Proof.
@@ -932,6 +939,7 @@ Qed.
 Lemma combine_cons : forall {A B} a b (xs:list A) (ys:list B),
   combine (a :: xs) (b :: ys) = (a,b) :: combine xs ys.
 Proof. reflexivity. Qed.
+Hint Rewrite @combine_cons : push_combine.
 
 Lemma firstn_combine : forall {A B} n (xs:list A) (ys:list B),
   firstn n (combine xs ys) = combine (firstn n xs) (firstn n ys).
@@ -947,6 +955,7 @@ Lemma combine_nil_r : forall {A B} (xs:list A),
 Proof.
   induction xs; boring.
 Qed.
+Hint Rewrite @combine_nil_r : push_combine.
 
 Lemma skipn_combine : forall {A B} n (xs:list A) (ys:list B),
   skipn n (combine xs ys) = combine (skipn n xs) (skipn n ys).
@@ -1458,9 +1467,15 @@ Hint Rewrite @sum_firstn_app_sum : simpl_sum_firstn.
 
 Lemma sum_cons xs x : sum (x :: xs) = (x + sum xs)%Z.
 Proof. reflexivity. Qed.
+Hint Rewrite sum_cons : push_sum.
 
 Lemma sum_nil : sum nil = 0%Z.
 Proof. reflexivity. Qed.
+Hint Rewrite sum_nil : push_sum.
+
+Lemma sum_app x y : sum (x ++ y) = (sum x + sum y)%Z.
+Proof. induction x; rewrite ?app_nil_l, <-?app_comm_cons; autorewrite with push_sum; omega. Qed.
+Hint Rewrite sum_app : push_sum.
 
 Lemma nth_error_skipn : forall {A} n (l : list A) m,
 nth_error (skipn n l) m = nth_error l (n + m).