refactor(Data/Rat/NNRat): move BigOperator lemmas to a new file (#9917)

`NNRat` has far too many dependencies at the moment. This only removes 20 from its transitive closure (1609 -> 1589 according to `lake exe graph` and `| wc -l`), but it's a start.

Author: eric-wieser

Mathlib.lean

@@ -1919,6 +1919,7 @@ import Mathlib.Data.Rat.Floor
 import Mathlib.Data.Rat.Init
 import Mathlib.Data.Rat.Lemmas
 import Mathlib.Data.Rat.NNRat
+import Mathlib.Data.Rat.NNRat.BigOperators
 import Mathlib.Data.Rat.Order
 import Mathlib.Data.Rat.Sqrt
 import Mathlib.Data.Rat.Star

Mathlib/Data/Rat/NNRat.lean

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 -/
 import Mathlib.Algebra.Algebra.Basic
-import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor
 
@@ -248,49 +247,6 @@ theorem coe_indicator (s : Set α) (f : α → ℚ≥0) (a : α) :
 theorem coe_pow (q : ℚ≥0) (n : ℕ) : (↑(q ^ n) : ℚ) = (q : ℚ) ^ n :=
   coeHom.map_pow _ _
 #align nnrat.coe_pow NNRat.coe_pow
-
-@[norm_cast]
-theorem coe_list_sum (l : List ℚ≥0) : (l.sum : ℚ) = (l.map (↑)).sum :=
-  coeHom.map_list_sum _
-#align nnrat.coe_list_sum NNRat.coe_list_sum
-
-@[norm_cast]
-theorem coe_list_prod (l : List ℚ≥0) : (l.prod : ℚ) = (l.map (↑)).prod :=
-  coeHom.map_list_prod _
-#align nnrat.coe_list_prod NNRat.coe_list_prod
-
-@[norm_cast]
-theorem coe_multiset_sum (s : Multiset ℚ≥0) : (s.sum : ℚ) = (s.map (↑)).sum :=
-  coeHom.map_multiset_sum _
-#align nnrat.coe_multiset_sum NNRat.coe_multiset_sum
-
-@[norm_cast]
-theorem coe_multiset_prod (s : Multiset ℚ≥0) : (s.prod : ℚ) = (s.map (↑)).prod :=
-  coeHom.map_multiset_prod _
-#align nnrat.coe_multiset_prod NNRat.coe_multiset_prod
-
-@[norm_cast]
-theorem coe_sum {s : Finset α} {f : α → ℚ≥0} : ↑(∑ a in s, f a) = ∑ a in s, (f a : ℚ) :=
-  coeHom.map_sum _ _
-#align nnrat.coe_sum NNRat.coe_sum
-
-theorem toNNRat_sum_of_nonneg {s : Finset α} {f : α → ℚ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
-    (∑ a in s, f a).toNNRat = ∑ a in s, (f a).toNNRat := by
-  rw [← coe_inj, coe_sum, Rat.coe_toNNRat _ (Finset.sum_nonneg hf)]
-  exact Finset.sum_congr rfl fun x hxs ↦ by rw [Rat.coe_toNNRat _ (hf x hxs)]
-#align nnrat.to_nnrat_sum_of_nonneg NNRat.toNNRat_sum_of_nonneg
-
-@[norm_cast]
-theorem coe_prod {s : Finset α} {f : α → ℚ≥0} : ↑(∏ a in s, f a) = ∏ a in s, (f a : ℚ) :=
-  coeHom.map_prod _ _
-#align nnrat.coe_prod NNRat.coe_prod
-
-theorem toNNRat_prod_of_nonneg {s : Finset α} {f : α → ℚ} (hf : ∀ a ∈ s, 0 ≤ f a) :
-    (∏ a in s, f a).toNNRat = ∏ a in s, (f a).toNNRat := by
-  rw [← coe_inj, coe_prod, Rat.coe_toNNRat _ (Finset.prod_nonneg hf)]
-  exact Finset.prod_congr rfl fun x hxs ↦ by rw [Rat.coe_toNNRat _ (hf x hxs)]
-#align nnrat.to_nnrat_prod_of_nonneg NNRat.toNNRat_prod_of_nonneg
-
 @[norm_cast]
 theorem nsmul_coe (q : ℚ≥0) (n : ℕ) : ↑(n • q) = n • (q : ℚ) :=
   coeHom.toAddMonoidHom.map_nsmul _ _

Mathlib/Data/Rat/NNRat/BigOperators.lean

@@ -0,0 +1,61 @@
+/-
+Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Yaël Dillies, Bhavik Mehta
+-/
+import Mathlib.Algebra.BigOperators.Order
+import Mathlib.Data.Rat.BigOperators
+import Mathlib.Data.Rat.NNRat
+
+/-! # Casting lemmas for non-negative rational numbers involving sums and products
+-/
+
+open BigOperators
+
+variable {ι α : Type*}
+
+namespace NNRat
+
+@[norm_cast]
+theorem coe_list_sum (l : List ℚ≥0) : (l.sum : ℚ) = (l.map (↑)).sum :=
+  coeHom.map_list_sum _
+#align nnrat.coe_list_sum NNRat.coe_list_sum
+
+@[norm_cast]
+theorem coe_list_prod (l : List ℚ≥0) : (l.prod : ℚ) = (l.map (↑)).prod :=
+  coeHom.map_list_prod _
+#align nnrat.coe_list_prod NNRat.coe_list_prod
+
+@[norm_cast]
+theorem coe_multiset_sum (s : Multiset ℚ≥0) : (s.sum : ℚ) = (s.map (↑)).sum :=
+  coeHom.map_multiset_sum _
+#align nnrat.coe_multiset_sum NNRat.coe_multiset_sum
+
+@[norm_cast]
+theorem coe_multiset_prod (s : Multiset ℚ≥0) : (s.prod : ℚ) = (s.map (↑)).prod :=
+  coeHom.map_multiset_prod _
+#align nnrat.coe_multiset_prod NNRat.coe_multiset_prod
+
+@[norm_cast]
+theorem coe_sum {s : Finset α} {f : α → ℚ≥0} : ↑(∑ a in s, f a) = ∑ a in s, (f a : ℚ) :=
+  coeHom.map_sum _ _
+#align nnrat.coe_sum NNRat.coe_sum
+
+theorem toNNRat_sum_of_nonneg {s : Finset α} {f : α → ℚ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
+    (∑ a in s, f a).toNNRat = ∑ a in s, (f a).toNNRat := by
+  rw [← coe_inj, coe_sum, Rat.coe_toNNRat _ (Finset.sum_nonneg hf)]
+  exact Finset.sum_congr rfl fun x hxs ↦ by rw [Rat.coe_toNNRat _ (hf x hxs)]
+#align nnrat.to_nnrat_sum_of_nonneg NNRat.toNNRat_sum_of_nonneg
+
+@[norm_cast]
+theorem coe_prod {s : Finset α} {f : α → ℚ≥0} : ↑(∏ a in s, f a) = ∏ a in s, (f a : ℚ) :=
+  coeHom.map_prod _ _
+#align nnrat.coe_prod NNRat.coe_prod
+
+theorem toNNRat_prod_of_nonneg {s : Finset α} {f : α → ℚ} (hf : ∀ a ∈ s, 0 ≤ f a) :
+    (∏ a in s, f a).toNNRat = ∏ a in s, (f a).toNNRat := by
+  rw [← coe_inj, coe_prod, Rat.coe_toNNRat _ (Finset.prod_nonneg hf)]
+  exact Finset.prod_congr rfl fun x hxs ↦ by rw [Rat.coe_toNNRat _ (hf x hxs)]
+#align nnrat.to_nnrat_prod_of_nonneg NNRat.toNNRat_prod_of_nonneg
+
+end NNRat