mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -5,7 +5,7 @@ Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 -/
 import Analysis.Convex.Jensen
 import Analysis.Convex.SpecificFunctions.Basic
-import Analysis.SpecialFunctions.Pow.Nnreal
+import Analysis.SpecialFunctions.Pow.NNReal
 import Tactic.Positivity
 
 #align_import analysis.mean_inequalities_pow from "leanprover-community/mathlib"@"ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f"
@@ -83,7 +83,7 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
   · simp_rw [Finset.sum_empty, zero_pow _ (Nat.succ_ne_zero n), zero_div]
   · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
     suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
-      rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,
+      rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ (s.card : ℝ), ← div_div,
         div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this
     have :=
       @ConvexOn.map_sum_le ℝ ℝ ℝ ι _ _ _ _ _ _ (Set.Ici 0) (fun x => x ^ (n + 1)) s

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -84,7 +84,7 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
   · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
     suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
       rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,
-        div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this 
+        div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this
     have :=
       @ConvexOn.map_sum_le ℝ ℝ ℝ ι _ _ _ _ _ _ (Set.Ici 0) (fun x => x ^ (n + 1)) s
         (fun _ => 1 / s.card) (coe ∘ f) (convexOn_pow (n + 1)) _ _ fun i hi =>
@@ -212,10 +212,10 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
   have hp_pos : 0 < p := by positivity
   by_cases h_zero : a + b = 0
   · simp [add_eq_zero_iff.mp h_zero, hp_pos.ne']
-  have h_nonzero : ¬(a = 0 ∧ b = 0) := by rwa [add_eq_zero_iff] at h_zero 
+  have h_nonzero : ¬(a = 0 ∧ b = 0) := by rwa [add_eq_zero_iff] at h_zero
   have h_add : a / (a + b) + b / (a + b) = 1 := by rw [div_add_div_same, div_self h_zero]
   have h := add_rpow_le_one_of_add_le_one (a / (a + b)) (b / (a + b)) h_add.le hp1
-  rw [div_rpow a (a + b), div_rpow b (a + b)] at h 
+  rw [div_rpow a (a + b), div_rpow b (a + b)] at h
   have hab_0 : (a + b) ^ p ≠ 0 := by simp [hp_pos, h_nonzero]
   have hab_0' : 0 < (a + b) ^ p := zero_lt_iff.mpr hab_0
   have h_mul : (a + b) ^ p * (a ^ p / (a + b) ^ p + b ^ p / (a + b) ^ p) ≤ (a + b) ^ p :=
@@ -223,7 +223,7 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
     nth_rw 4 [← mul_one ((a + b) ^ p)]
     exact (mul_le_mul_left hab_0').mpr h
   rwa [div_eq_mul_inv, div_eq_mul_inv, mul_add, mul_comm (a ^ p), mul_comm (b ^ p), ← mul_assoc, ←
-    mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul 
+    mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul
 #align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_add
 -/
 
@@ -251,7 +251,7 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p 
     rwa [one_le_div hp_pos]
   rw [h_rpow a, h_rpow b, NNReal.le_rpow_one_div_iff hp_pos, ← NNReal.rpow_mul, mul_comm,
     mul_one_div]
-  rwa [one_div_div] at h_rpow_add_rpow_le_add 
+  rwa [one_div_div] at h_rpow_add_rpow_le_add
 #align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_le
 -/
 
@@ -262,8 +262,8 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p 
   rcases hp.eq_or_lt with (rfl | hp_pos)
   · simp
   have h := rpow_add_rpow_le a b hp_pos hp1
-  rw [one_div_one] at h 
-  repeat' rw [NNReal.rpow_one] at h 
+  rw [one_div_one] at h
+  repeat' rw [NNReal.rpow_one] at h
   exact (NNReal.le_rpow_one_div_iff hp_pos).mp h
 #align nnreal.rpow_add_le_add_rpow NNReal.rpow_add_le_add_rpow
 -/
@@ -288,7 +288,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑
   · -- first, prove `(∑ i in s, w i * z i) ^ p = ⊤ → ∑ i in s, (w i * z i ^ p) = ⊤`
     rw [rpow_eq_top_iff, sum_eq_top_iff, sum_eq_top_iff]
     intro h
-    simp only [and_false_iff, hp_not_neg, false_or_iff] at h 
+    simp only [and_false_iff, hp_not_neg, false_or_iff] at h
     rcases h.left with ⟨a, H, ha⟩
     use a, H
     rwa [← h_top_iff_rpow_top a H]
@@ -301,7 +301,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑
       haveI h_top_sum : ∑ i : ι in s, w i * z i ≠ ⊤ :=
         by
         intro h
-        rw [h, top_rpow_of_pos hp_pos] at h_top_rpow_sum 
+        rw [h, top_rpow_of_pos hp_pos] at h_top_rpow_sum
         exact h_top_rpow_sum rfl
       fun a ha => (lt_top_of_sum_ne_top h_top_sum ha).Ne
     have h_top_rpow : ∀ a : ι, a ∈ s → w a * z a ^ p ≠ ⊤ :=
@@ -362,7 +362,7 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^
   by
   have hp_pos : 0 < p := by positivity
   by_cases h_top : a + b = ⊤
-  · rw [← @ENNReal.rpow_eq_top_iff_of_pos (a + b) p hp_pos] at h_top 
+  · rw [← @ENNReal.rpow_eq_top_iff_of_pos (a + b) p hp_pos] at h_top
     rw [h_top]
     exact le_top
   obtain ⟨ha_top, hb_top⟩ := add_ne_top.mp h_top
@@ -396,7 +396,7 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq :
     rwa [one_le_div hp_pos]
   rw [h_rpow a, h_rpow b, ENNReal.le_rpow_one_div_iff hp_pos, ← ENNReal.rpow_mul, mul_comm,
     mul_one_div]
-  rwa [one_div_div] at h_rpow_add_rpow_le_add 
+  rwa [one_div_div] at h_rpow_add_rpow_le_add
 #align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_le
 -/
 
@@ -409,8 +409,8 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 :
     norm_cast
     norm_num
   have h := rpow_add_rpow_le a b hp_pos hp1
-  rw [one_div_one] at h 
-  repeat' rw [ENNReal.rpow_one] at h 
+  rw [one_div_one] at h
+  repeat' rw [ENNReal.rpow_one] at h
   exact (ENNReal.le_rpow_one_div_iff hp_pos).mp h
 #align ennreal.rpow_add_le_add_rpow ENNReal.rpow_add_le_add_rpow
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -80,7 +80,7 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | hs)
-  · simp_rw [Finset.sum_empty, zero_pow' _ (Nat.succ_ne_zero n), zero_div]
+  · simp_rw [Finset.sum_empty, zero_pow _ (Nat.succ_ne_zero n), zero_div]
   · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
     suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
       rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,10 +3,10 @@ Copyright (c) 2019 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 -/
-import Mathbin.Analysis.Convex.Jensen
-import Mathbin.Analysis.Convex.SpecificFunctions.Basic
-import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
-import Mathbin.Tactic.Positivity
+import Analysis.Convex.Jensen
+import Analysis.Convex.SpecificFunctions.Basic
+import Analysis.SpecialFunctions.Pow.Nnreal
+import Tactic.Positivity
 
 #align_import analysis.mean_inequalities_pow from "leanprover-community/mathlib"@"ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,17 +2,14 @@
 Copyright (c) 2019 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-
-! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Jensen
 import Mathbin.Analysis.Convex.SpecificFunctions.Basic
 import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
 import Mathbin.Tactic.Positivity
 
+#align_import analysis.mean_inequalities_pow from "leanprover-community/mathlib"@"ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f"
+
 /-!
 # Mean value inequalities
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -61,18 +61,23 @@ variable {ι : Type u} (s : Finset ι)
 
 namespace Real
 
+#print Real.pow_arith_mean_le_arith_mean_pow /-
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   (convexOn_pow n).map_sum_le hw hw' hz
 #align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_pow
+-/
 
+#print Real.pow_arith_mean_le_arith_mean_pow_of_even /-
 theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) {n : ℕ} (hn : Even n) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
+-/
 
+#print Real.pow_sum_div_card_le_sum_pow /-
 /-- Specific case of Jensen's inequality for sums of powers -/
 theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s, 0 ≤ f a) :
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) :=
@@ -91,19 +96,25 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
     · simp only [one_div, inv_nonneg, Nat.cast_nonneg, imp_true_iff]
     · simpa only [one_div, Finset.sum_const, nsmul_eq_mul] using mul_inv_cancel hs0.ne'
 #align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_pow
+-/
 
+#print Real.zpow_arith_mean_le_arith_mean_zpow /-
 theorem zpow_arith_mean_le_arith_mean_zpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
     (∑ i in s, w i * z i) ^ m ≤ ∑ i in s, w i * z i ^ m :=
   (convexOn_zpow m).map_sum_le hw hw' hz
 #align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpow
+-/
 
+#print Real.rpow_arith_mean_le_arith_mean_rpow /-
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   (convexOn_rpow hp).map_sum_le hw hw' hz
 #align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpow
+-/
 
+#print Real.arith_mean_le_rpow_mean /-
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : ∑ i in s, w i = 1)
     (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) :=
@@ -116,11 +127,13 @@ theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     intro i hi
     apply_rules [mul_nonneg, rpow_nonneg_of_nonneg, hw i hi, hz i hi]
 #align real.arith_mean_le_rpow_mean Real.arith_mean_le_rpow_mean
+-/
 
 end Real
 
 namespace NNReal
 
+#print NNReal.pow_arith_mean_le_arith_mean_pow /-
 /-- Weighted generalized mean inequality, version sums over finite sets, with `ℝ≥0`-valued
 functions and natural exponent. -/
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) (n : ℕ) :
@@ -129,13 +142,17 @@ theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : ∑ i in
     Real.pow_arith_mean_le_arith_mean_pow s _ _ (fun i _ => (w i).coe_nonneg)
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) n
 #align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_pow
+-/
 
+#print NNReal.pow_sum_div_card_le_sum_pow /-
 theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) := by
   simpa only [← NNReal.coe_le_coe, NNReal.coe_sum, Nonneg.coe_div, NNReal.coe_pow] using
     @Real.pow_sum_div_card_le_sum_pow ι s (coe ∘ f) n fun _ _ => NNReal.coe_nonneg _
 #align nnreal.pow_sum_div_card_le_sum_pow NNReal.pow_sum_div_card_le_sum_pow
+-/
 
+#print NNReal.rpow_arith_mean_le_arith_mean_rpow /-
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ}
@@ -144,7 +161,9 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : ∑ i i
     Real.rpow_arith_mean_le_arith_mean_rpow s _ _ (fun i _ => (w i).coe_nonneg)
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.rpow_arith_mean_le_arith_mean_rpow NNReal.rpow_arith_mean_le_arith_mean_rpow
+-/
 
+#print NNReal.rpow_arith_mean_le_arith_mean2_rpow /-
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw' : w₁ + w₂ = 1) {p : ℝ}
     (hp : 1 ≤ p) : (w₁ * z₁ + w₂ * z₂) ^ p ≤ w₁ * z₁ ^ p + w₂ * z₂ ^ p :=
@@ -153,7 +172,9 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw'
   · simpa [Fin.sum_univ_succ] using h
   · simp [hw', Fin.sum_univ_succ]
 #align nnreal.rpow_arith_mean_le_arith_mean2_rpow NNReal.rpow_arith_mean_le_arith_mean2_rpow
+-/
 
+#print NNReal.rpow_add_le_mul_rpow_add_rpow /-
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
@@ -167,7 +188,9 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
     simp only [mul_rpow, rpow_sub' _ A, div_eq_inv_mul, rpow_one, mul_one]
     ring
 #align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpow
+-/
 
+#print NNReal.arith_mean_le_rpow_mean /-
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ} (hp : 1 ≤ p) :
@@ -176,6 +199,7 @@ theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i =
     Real.arith_mean_le_rpow_mean s _ _ (fun i _ => (w i).coe_nonneg) (by exact_mod_cast hw')
       (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.arith_mean_le_rpow_mean NNReal.arith_mean_le_rpow_mean
+-/
 
 private theorem add_rpow_le_one_of_add_le_one {p : ℝ} (a b : ℝ≥0) (hab : a + b ≤ 1) (hp1 : 1 ≤ p) :
     a ^ p + b ^ p ≤ 1 :=
@@ -185,6 +209,7 @@ private theorem add_rpow_le_one_of_add_le_one {p : ℝ} (a b : ℝ≥0) (hab : a
   have hb : b ≤ 1 := (self_le_add_left b a).trans hab
   exact (add_le_add (h_le_one a ha) (h_le_one b hb)).trans hab
 
+#print NNReal.add_rpow_le_rpow_add /-
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
@@ -203,7 +228,9 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
   rwa [div_eq_mul_inv, div_eq_mul_inv, mul_add, mul_comm (a ^ p), mul_comm (b ^ p), ← mul_assoc, ←
     mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul 
 #align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_add
+-/
 
+#print NNReal.rpow_add_rpow_le_add /-
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
@@ -211,7 +238,9 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
   rw [one_div_one_div]
   exact add_rpow_le_rpow_add _ _ hp1
 #align nnreal.rpow_add_rpow_le_add NNReal.rpow_add_rpow_le_add
+-/
 
+#print NNReal.rpow_add_rpow_le /-
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
@@ -227,7 +256,9 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p 
     mul_one_div]
   rwa [one_div_div] at h_rpow_add_rpow_le_add 
 #align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_le
+-/
 
+#print NNReal.rpow_add_le_add_rpow /-
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
   by
@@ -238,11 +269,13 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p 
   repeat' rw [NNReal.rpow_one] at h 
   exact (NNReal.le_rpow_one_div_iff hp_pos).mp h
 #align nnreal.rpow_add_le_add_rpow NNReal.rpow_add_le_add_rpow
+-/
 
 end NNReal
 
 namespace ENNReal
 
+#print ENNReal.rpow_arith_mean_le_arith_mean_rpow /-
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0∞`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑ i in s, w i = 1) {p : ℝ}
@@ -295,7 +328,9 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑
       exact hw'.symm ▸ ENNReal.one_ne_top
     rwa [← coe_eq_coe, ← h_sum_nnreal]
 #align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpow
+-/
 
+#print ENNReal.rpow_arith_mean_le_arith_mean2_rpow /-
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0∞` and real
 exponents. -/
 theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (hw' : w₁ + w₂ = 1) {p : ℝ}
@@ -305,7 +340,9 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
   · simpa [Fin.sum_univ_succ] using h
   · simp [hw', Fin.sum_univ_succ]
 #align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpow
+-/
 
+#print ENNReal.rpow_add_le_mul_rpow_add_rpow /-
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0∞` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
@@ -321,7 +358,9 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
       ENNReal.div_eq_inv_mul, rpow_one, mul_one]
     ring
 #align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow
+-/
 
+#print ENNReal.add_rpow_le_rpow_add /-
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
@@ -335,7 +374,9 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^
   simpa [← ENNReal.coe_rpow_of_nonneg _ hp_pos.le] using
     ENNReal.coe_le_coe.2 (NNReal.add_rpow_le_rpow_add a b hp1)
 #align ennreal.add_rpow_le_rpow_add ENNReal.add_rpow_le_rpow_add
+-/
 
+#print ENNReal.rpow_add_rpow_le_add /-
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
@@ -343,7 +384,9 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
   rw [one_div_one_div]
   exact add_rpow_le_rpow_add _ _ hp1
 #align ennreal.rpow_add_rpow_le_add ENNReal.rpow_add_rpow_le_add
+-/
 
+#print ENNReal.rpow_add_rpow_le /-
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
@@ -358,7 +401,9 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq :
     mul_one_div]
   rwa [one_div_div] at h_rpow_add_rpow_le_add 
 #align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_le
+-/
 
+#print ENNReal.rpow_add_le_add_rpow /-
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
   by
@@ -371,6 +416,7 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 :
   repeat' rw [ENNReal.rpow_one] at h 
   exact (ENNReal.le_rpow_one_div_iff hp_pos).mp h
 #align ennreal.rpow_add_le_add_rpow ENNReal.rpow_add_le_add_rpow
+-/
 
 end ENNReal
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 
 ! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
+! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -318,7 +318,7 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
   · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
   · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
     simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero two_ne_top,
-      div_eq_inv_mul, rpow_one, mul_one]
+      ENNReal.div_eq_inv_mul, rpow_one, mul_one]
     ring
 #align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -62,13 +62,13 @@ variable {ι : Type u} (s : Finset ι)
 namespace Real
 
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   (convexOn_pow n).map_sum_le hw hw' hz
 #align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_pow
 
 theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) {n : ℕ} (hn : Even n) :
+    (hw' : ∑ i in s, w i = 1) {n : ℕ} (hn : Even n) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
@@ -93,20 +93,20 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
 #align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_pow
 
 theorem zpow_arith_mean_le_arith_mean_zpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
     (∑ i in s, w i * z i) ^ m ≤ ∑ i in s, w i * z i ^ m :=
   (convexOn_zpow m).map_sum_le hw hw' hz
 #align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpow
 
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   (convexOn_rpow hp).map_sum_le hw hw' hz
 #align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpow
 
-theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : (∑ i in s, w i) = 1)
+theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : ∑ i in s, w i = 1)
     (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
-    (∑ i in s, w i * z i) ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) :=
+    ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) :=
   by
   have : 0 < p := by positivity
   rw [← rpow_le_rpow_iff _ _ this, ← rpow_mul, one_div_mul_cancel (ne_of_gt this), rpow_one]
@@ -123,7 +123,7 @@ namespace NNReal
 
 /-- Weighted generalized mean inequality, version sums over finite sets, with `ℝ≥0`-valued
 functions and natural exponent. -/
-theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) (n : ℕ) :
+theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n := by
   exact_mod_cast
     Real.pow_arith_mean_le_arith_mean_pow s _ _ (fun i _ => (w i).coe_nonneg)
@@ -138,7 +138,7 @@ theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
-theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
+theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ}
     (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p := by
   exact_mod_cast
     Real.rpow_arith_mean_le_arith_mean_rpow s _ _ (fun i _ => (w i).coe_nonneg)
@@ -170,8 +170,8 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
-theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ} (hp : 1 ≤ p) :
-    (∑ i in s, w i * z i) ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
+theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ} (hp : 1 ≤ p) :
+    ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
   exact_mod_cast
     Real.arith_mean_le_rpow_mean s _ _ (fun i _ => (w i).coe_nonneg) (by exact_mod_cast hw')
       (fun i _ => (z i).coe_nonneg) hp
@@ -245,7 +245,7 @@ namespace ENNReal
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0∞`-valued
 functions and real exponents. -/
-theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
+theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑ i in s, w i = 1) {p : ℝ}
     (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   by
   have hp_pos : 0 < p; positivity
@@ -268,7 +268,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
     intro h_top_rpow_sum _
     -- show hypotheses needed to put the `.to_nnreal` inside the sums.
     have h_top : ∀ a : ι, a ∈ s → w a * z a ≠ ⊤ :=
-      haveI h_top_sum : (∑ i : ι in s, w i * z i) ≠ ⊤ :=
+      haveI h_top_sum : ∑ i : ι in s, w i * z i ≠ ⊤ :=
         by
         intro h
         rw [h, top_rpow_of_pos hp_pos] at h_top_rpow_sum 
@@ -287,7 +287,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
       NNReal.rpow_arith_mean_le_arith_mean_rpow s (fun i => (w i).toNNReal)
         (fun i => (z i).toNNReal) _ hp
     -- verify the hypothesis `∑ i in s, (w i).to_nnreal = 1`, using `∑ i in s, w i = 1` .
-    have h_sum_nnreal : (∑ i in s, w i) = ↑(∑ i in s, (w i).toNNReal) :=
+    have h_sum_nnreal : ∑ i in s, w i = ↑(∑ i in s, (w i).toNNReal) :=
       by
       rw [coe_finset_sum]
       refine' sum_congr rfl fun i hi => (coe_to_nnreal _).symm

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -312,8 +312,8 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
   by
   rcases eq_or_lt_of_le hp with (rfl | h'p)
   · simp only [rpow_one, sub_self, rpow_zero, one_mul, le_refl]
-  convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂)
-      (ENNReal.add_halves 1) hp
+  convert
+    rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂) (ENNReal.add_halves 1) hp
   · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
   · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
   · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -82,7 +82,7 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
   · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
     suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
       rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,
-        div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this
+        div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this 
     have :=
       @ConvexOn.map_sum_le ℝ ℝ ℝ ι _ _ _ _ _ _ (Set.Ici 0) (fun x => x ^ (n + 1)) s
         (fun _ => 1 / s.card) (coe ∘ f) (convexOn_pow (n + 1)) _ _ fun i hi =>
@@ -190,10 +190,10 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
   have hp_pos : 0 < p := by positivity
   by_cases h_zero : a + b = 0
   · simp [add_eq_zero_iff.mp h_zero, hp_pos.ne']
-  have h_nonzero : ¬(a = 0 ∧ b = 0) := by rwa [add_eq_zero_iff] at h_zero
+  have h_nonzero : ¬(a = 0 ∧ b = 0) := by rwa [add_eq_zero_iff] at h_zero 
   have h_add : a / (a + b) + b / (a + b) = 1 := by rw [div_add_div_same, div_self h_zero]
   have h := add_rpow_le_one_of_add_le_one (a / (a + b)) (b / (a + b)) h_add.le hp1
-  rw [div_rpow a (a + b), div_rpow b (a + b)] at h
+  rw [div_rpow a (a + b), div_rpow b (a + b)] at h 
   have hab_0 : (a + b) ^ p ≠ 0 := by simp [hp_pos, h_nonzero]
   have hab_0' : 0 < (a + b) ^ p := zero_lt_iff.mpr hab_0
   have h_mul : (a + b) ^ p * (a ^ p / (a + b) ^ p + b ^ p / (a + b) ^ p) ≤ (a + b) ^ p :=
@@ -201,7 +201,7 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
     nth_rw 4 [← mul_one ((a + b) ^ p)]
     exact (mul_le_mul_left hab_0').mpr h
   rwa [div_eq_mul_inv, div_eq_mul_inv, mul_add, mul_comm (a ^ p), mul_comm (b ^ p), ← mul_assoc, ←
-    mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul
+    mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul 
 #align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_add
 
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
@@ -225,7 +225,7 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p 
     rwa [one_le_div hp_pos]
   rw [h_rpow a, h_rpow b, NNReal.le_rpow_one_div_iff hp_pos, ← NNReal.rpow_mul, mul_comm,
     mul_one_div]
-  rwa [one_div_div] at h_rpow_add_rpow_le_add
+  rwa [one_div_div] at h_rpow_add_rpow_le_add 
 #align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_le
 
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
@@ -234,8 +234,8 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p 
   rcases hp.eq_or_lt with (rfl | hp_pos)
   · simp
   have h := rpow_add_rpow_le a b hp_pos hp1
-  rw [one_div_one] at h
-  repeat' rw [NNReal.rpow_one] at h
+  rw [one_div_one] at h 
+  repeat' rw [NNReal.rpow_one] at h 
   exact (NNReal.le_rpow_one_div_iff hp_pos).mp h
 #align nnreal.rpow_add_le_add_rpow NNReal.rpow_add_le_add_rpow
 
@@ -258,7 +258,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
   · -- first, prove `(∑ i in s, w i * z i) ^ p = ⊤ → ∑ i in s, (w i * z i ^ p) = ⊤`
     rw [rpow_eq_top_iff, sum_eq_top_iff, sum_eq_top_iff]
     intro h
-    simp only [and_false_iff, hp_not_neg, false_or_iff] at h
+    simp only [and_false_iff, hp_not_neg, false_or_iff] at h 
     rcases h.left with ⟨a, H, ha⟩
     use a, H
     rwa [← h_top_iff_rpow_top a H]
@@ -271,7 +271,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
       haveI h_top_sum : (∑ i : ι in s, w i * z i) ≠ ⊤ :=
         by
         intro h
-        rw [h, top_rpow_of_pos hp_pos] at h_top_rpow_sum
+        rw [h, top_rpow_of_pos hp_pos] at h_top_rpow_sum 
         exact h_top_rpow_sum rfl
       fun a ha => (lt_top_of_sum_ne_top h_top_sum ha).Ne
     have h_top_rpow : ∀ a : ι, a ∈ s → w a * z a ^ p ≠ ⊤ :=
@@ -326,7 +326,7 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^
   by
   have hp_pos : 0 < p := by positivity
   by_cases h_top : a + b = ⊤
-  · rw [← @ENNReal.rpow_eq_top_iff_of_pos (a + b) p hp_pos] at h_top
+  · rw [← @ENNReal.rpow_eq_top_iff_of_pos (a + b) p hp_pos] at h_top 
     rw [h_top]
     exact le_top
   obtain ⟨ha_top, hb_top⟩ := add_ne_top.mp h_top
@@ -356,7 +356,7 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq :
     rwa [one_le_div hp_pos]
   rw [h_rpow a, h_rpow b, ENNReal.le_rpow_one_div_iff hp_pos, ← ENNReal.rpow_mul, mul_comm,
     mul_one_div]
-  rwa [one_div_div] at h_rpow_add_rpow_le_add
+  rwa [one_div_div] at h_rpow_add_rpow_le_add 
 #align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_le
 
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
@@ -367,8 +367,8 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 :
     norm_cast
     norm_num
   have h := rpow_add_rpow_le a b hp_pos hp1
-  rw [one_div_one] at h
-  repeat' rw [ENNReal.rpow_one] at h
+  rw [one_div_one] at h 
+  repeat' rw [ENNReal.rpow_one] at h 
   exact (ENNReal.le_rpow_one_div_iff hp_pos).mp h
 #align ennreal.rpow_add_le_add_rpow ENNReal.rpow_add_le_add_rpow
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -53,7 +53,7 @@ universe u v
 
 open Finset
 
-open Classical BigOperators NNReal ENNReal
+open scoped Classical BigOperators NNReal ENNReal
 
 noncomputable section
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -61,36 +61,18 @@ variable {ι : Type u} (s : Finset ι)
 
 namespace Real
 
-/- warning: real.pow_arith_mean_le_arith_mean_pow -> Real.pow_arith_mean_le_arith_mean_pow is a dubious translation:
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (z i))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (z i))) n) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (z i) n))))
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-Case conversion may be inaccurate. Consider using '#align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_powₓ'. -/
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   (convexOn_pow n).map_sum_le hw hw' hz
 #align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_pow
 
-/- warning: real.pow_arith_mean_le_arith_mean_pow_of_even -> Real.pow_arith_mean_le_arith_mean_pow_of_even is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_evenₓ'. -/
 theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) {n : ℕ} (hn : Even n) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
 
-/- warning: real.pow_sum_div_card_le_sum_pow -> Real.pow_sum_div_card_le_sum_pow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_powₓ'. -/
 /-- Specific case of Jensen's inequality for sums of powers -/
 theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s, 0 ≤ f a) :
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) :=
@@ -110,36 +92,18 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
     · simpa only [one_div, Finset.sum_const, nsmul_eq_mul] using mul_inv_cancel hs0.ne'
 #align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_pow
 
-/- warning: real.zpow_arith_mean_le_arith_mean_zpow -> Real.zpow_arith_mean_le_arith_mean_zpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpowₓ'. -/
 theorem zpow_arith_mean_le_arith_mean_zpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
     (∑ i in s, w i * z i) ^ m ≤ ∑ i in s, w i * z i ^ m :=
   (convexOn_zpow m).map_sum_le hw hw' hz
 #align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpow
 
-/- warning: real.rpow_arith_mean_le_arith_mean_rpow -> Real.rpow_arith_mean_le_arith_mean_rpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpowₓ'. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   (convexOn_rpow hp).map_sum_le hw hw' hz
 #align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpow
 
-/- warning: real.arith_mean_le_rpow_mean -> Real.arith_mean_le_rpow_mean is a dubious translation:
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (z i))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} Real Real.instLEReal (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (z i))) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p))))
-Case conversion may be inaccurate. Consider using '#align real.arith_mean_le_rpow_mean Real.arith_mean_le_rpow_meanₓ'. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : (∑ i in s, w i) = 1)
     (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) :=
@@ -157,12 +121,6 @@ end Real
 
 namespace NNReal
 
-/- warning: nnreal.pow_arith_mean_le_arith_mean_pow -> NNReal.pow_arith_mean_le_arith_mean_pow is a dubious translation:
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (n : Nat), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (z i))) n) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (z i) n))))
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (forall (n : Nat), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (z i))) n) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (z i) n))))
-Case conversion may be inaccurate. Consider using '#align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_powₓ'. -/
 /-- Weighted generalized mean inequality, version sums over finite sets, with `ℝ≥0`-valued
 functions and natural exponent. -/
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) (n : ℕ) :
@@ -172,24 +130,12 @@ theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) n
 #align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_pow
 
-/- warning: nnreal.pow_sum_div_card_le_sum_pow -> NNReal.pow_sum_div_card_le_sum_pow is a dubious translation:
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (n : Nat), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (x : ι) => f x)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (Finset.card.{u1} ι s)) n)) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (x : ι) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (f x) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
-but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (n : Nat), LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (NNReal.toReal (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (x : ι) => f x)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Nat.cast.{0} Real Real.natCast (Finset.card.{u1} ι s)) n)) (NNReal.toReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (x : ι) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (f x) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
-Case conversion may be inaccurate. Consider using '#align nnreal.pow_sum_div_card_le_sum_pow NNReal.pow_sum_div_card_le_sum_powₓ'. -/
 theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) := by
   simpa only [← NNReal.coe_le_coe, NNReal.coe_sum, Nonneg.coe_div, NNReal.coe_pow] using
     @Real.pow_sum_div_card_le_sum_pow ι s (coe ∘ f) n fun _ _ => NNReal.coe_nonneg _
 #align nnreal.pow_sum_div_card_le_sum_pow NNReal.pow_sum_div_card_le_sum_pow
 
-/- warning: nnreal.rpow_arith_mean_le_arith_mean_rpow -> NNReal.rpow_arith_mean_le_arith_mean_rpow is a dubious translation:
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (z i))) p) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (z i) p)))))
-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_arith_mean_le_arith_mean_rpow NNReal.rpow_arith_mean_le_arith_mean_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
@@ -199,12 +145,6 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.rpow_arith_mean_le_arith_mean_rpow NNReal.rpow_arith_mean_le_arith_mean_rpow
 
-/- warning: nnreal.rpow_arith_mean_le_arith_mean2_rpow -> NNReal.rpow_arith_mean_le_arith_mean2_rpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_arith_mean_le_arith_mean2_rpow NNReal.rpow_arith_mean_le_arith_mean2_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw' : w₁ + w₂ = 1) {p : ℝ}
     (hp : 1 ≤ p) : (w₁ * z₁ + w₂ * z₂) ^ p ≤ w₁ * z₁ ^ p + w₂ * z₂ ^ p :=
@@ -214,12 +154,6 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw'
   · simp [hw', Fin.sum_univ_succ]
 #align nnreal.rpow_arith_mean_le_arith_mean2_rpow NNReal.rpow_arith_mean_le_arith_mean2_rpow
 
-/- warning: nnreal.rpow_add_le_mul_rpow_add_rpow -> NNReal.rpow_add_le_mul_rpow_add_rpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpowₓ'. -/
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
@@ -234,12 +168,6 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
     ring
 #align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpow
 
-/- warning: nnreal.arith_mean_le_rpow_mean -> NNReal.arith_mean_le_rpow_mean is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.arith_mean_le_rpow_mean NNReal.arith_mean_le_rpow_meanₓ'. -/
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ} (hp : 1 ≤ p) :
@@ -257,12 +185,6 @@ private theorem add_rpow_le_one_of_add_le_one {p : ℝ} (a b : ℝ≥0) (hab : a
   have hb : b ≤ 1 := (self_le_add_left b a).trans hab
   exact (add_le_add (h_le_one a ha) (h_le_one b hb)).trans hab
 
-/- warning: nnreal.add_rpow_le_rpow_add -> NNReal.add_rpow_le_rpow_add is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_addₓ'. -/
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
@@ -282,12 +204,6 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
     mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul
 #align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_add
 
-/- warning: nnreal.rpow_add_rpow_le_add -> NNReal.rpow_add_rpow_le_add is a dubious translation:
-lean 3 declaration is
-  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) a b))
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-  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) a b))
-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_rpow_le_add NNReal.rpow_add_rpow_le_addₓ'. -/
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
@@ -296,12 +212,6 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
   exact add_rpow_le_rpow_add _ _ hp1
 #align nnreal.rpow_add_rpow_le_add NNReal.rpow_add_rpow_le_add
 
-/- warning: nnreal.rpow_add_rpow_le -> NNReal.rpow_add_rpow_le is a dubious translation:
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-  forall {p : Real} {q : Real} (a : NNReal) (b : NNReal), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (LE.le.{0} Real Real.hasLe p q) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b q)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) q)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)))
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-  forall {p : Real} {q : Real} (a : NNReal) (b : NNReal), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (LE.le.{0} Real Real.instLEReal p q) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b q)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) q)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)))
-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_leₓ'. -/
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
@@ -318,12 +228,6 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p 
   rwa [one_div_div] at h_rpow_add_rpow_le_add
 #align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_le
 
-/- warning: nnreal.rpow_add_le_add_rpow -> NNReal.rpow_add_le_add_rpow is a dubious translation:
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-  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (LE.le.{0} Real Real.hasLe p (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) a b) p) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)))
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-  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (LE.le.{0} Real Real.instLEReal p (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) a b) p) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)))
-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_le_add_rpow NNReal.rpow_add_le_add_rpowₓ'. -/
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
   by
@@ -339,12 +243,6 @@ end NNReal
 
 namespace ENNReal
 
-/- warning: ennreal.rpow_arith_mean_le_arith_mean_rpow -> ENNReal.rpow_arith_mean_le_arith_mean_rpow is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> ENNReal) (z : ι -> ENNReal), (Eq.{1} ENNReal (Finset.sum.{0, u1} ENNReal ι (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (Finset.sum.{0, u1} ENNReal ι (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) (z i))) p) (Finset.sum.{0, u1} ENNReal ι (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (z i) p)))))
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0∞`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
@@ -398,12 +296,6 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
     rwa [← coe_eq_coe, ← h_sum_nnreal]
 #align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpow
 
-/- warning: ennreal.rpow_arith_mean_le_arith_mean2_rpow -> ENNReal.rpow_arith_mean_le_arith_mean2_rpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0∞` and real
 exponents. -/
 theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (hw' : w₁ + w₂ = 1) {p : ℝ}
@@ -414,12 +306,6 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
   · simp [hw', Fin.sum_univ_succ]
 #align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpow
 
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpowₓ'. -/
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0∞` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
@@ -436,12 +322,6 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
     ring
 #align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow
 
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-Case conversion may be inaccurate. Consider using '#align ennreal.add_rpow_le_rpow_add ENNReal.add_rpow_le_rpow_addₓ'. -/
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
@@ -456,12 +336,6 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^
     ENNReal.coe_le_coe.2 (NNReal.add_rpow_le_rpow_add a b hp1)
 #align ennreal.add_rpow_le_rpow_add ENNReal.add_rpow_le_rpow_add
 
-/- warning: ennreal.rpow_add_rpow_le_add -> ENNReal.rpow_add_rpow_le_add is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_rpow_le_add ENNReal.rpow_add_rpow_le_addₓ'. -/
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
@@ -470,12 +344,6 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
   exact add_rpow_le_rpow_add _ _ hp1
 #align ennreal.rpow_add_rpow_le_add ENNReal.rpow_add_rpow_le_add
 
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_leₓ'. -/
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
@@ -491,12 +359,6 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq :
   rwa [one_div_div] at h_rpow_add_rpow_le_add
 #align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_le
 
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_le_add_rpow ENNReal.rpow_add_le_add_rpowₓ'. -/
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -350,10 +350,8 @@ functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
     (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   by
-  have hp_pos : 0 < p
-  positivity
-  have hp_nonneg : 0 ≤ p
-  positivity
+  have hp_pos : 0 < p; positivity
+  have hp_nonneg : 0 ≤ p; positivity
   have hp_not_nonpos : ¬p ≤ 0 := by simp [hp_pos]
   have hp_not_neg : ¬p < 0 := by simp [hp_nonneg]
   have h_top_iff_rpow_top : ∀ (i : ι) (hi : i ∈ s), w i * z i = ⊤ ↔ w i * z i ^ p = ⊤ := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 
 ! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Tactic.Positivity
 /-!
 # Mean value inequalities
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove several mean inequalities for finite sums. Versions for integrals of some of
 these inequalities are available in `measure_theory.mean_inequalities`.
 
@@ -253,7 +256,6 @@ private theorem add_rpow_le_one_of_add_le_one {p : ℝ} (a b : ℝ≥0) (hab : a
   have ha : a ≤ 1 := (self_le_add_right a b).trans hab
   have hb : b ≤ 1 := (self_le_add_left b a).trans hab
   exact (add_le_add (h_le_one a ha) (h_le_one b hb)).trans hab
-#align nnreal.add_rpow_le_one_of_add_le_one nnreal.add_rpow_le_one_of_add_le_one
 
 /- warning: nnreal.add_rpow_le_rpow_add -> NNReal.add_rpow_le_rpow_add is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -58,18 +58,36 @@ variable {ι : Type u} (s : Finset ι)
 
 namespace Real
 
+/- warning: real.pow_arith_mean_le_arith_mean_pow -> Real.pow_arith_mean_le_arith_mean_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_powₓ'. -/
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   (convexOn_pow n).map_sum_le hw hw' hz
 #align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_pow
 
+/- warning: real.pow_arith_mean_le_arith_mean_pow_of_even -> Real.pow_arith_mean_le_arith_mean_pow_of_even is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall {n : Nat}, (Even.{0} Nat Nat.hasAdd n) -> (LE.le.{0} Real Real.hasLe (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (z i))) n) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (z i) n)))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall {n : Nat}, (Even.{0} Nat instAddNat n) -> (LE.le.{0} Real Real.instLEReal (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (z i))) n) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (z i) n)))))
+Case conversion may be inaccurate. Consider using '#align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_evenₓ'. -/
 theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) {n : ℕ} (hn : Even n) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
 
+/- warning: real.pow_sum_div_card_le_sum_pow -> Real.pow_sum_div_card_le_sum_pow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} (n : Nat), (forall (a : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (x : ι) => f x)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (Finset.card.{u1} ι s)) n)) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (x : ι) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (f x) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} (n : Nat), (forall (a : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (x : ι) => f x)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Nat.cast.{0} Real Real.natCast (Finset.card.{u1} ι s)) n)) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (x : ι) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (f x) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_powₓ'. -/
 /-- Specific case of Jensen's inequality for sums of powers -/
 theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s, 0 ≤ f a) :
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) :=
@@ -89,18 +107,36 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
     · simpa only [one_div, Finset.sum_const, nsmul_eq_mul] using mul_inv_cancel hs0.ne'
 #align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_pow
 
+/- warning: real.zpow_arith_mean_le_arith_mean_zpow -> Real.zpow_arith_mean_le_arith_mean_zpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (z i))) -> (forall (m : Int), LE.le.{0} Real Real.hasLe (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (z i))) m) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (z i) m))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (z i))) -> (forall (m : Int), LE.le.{0} Real Real.instLEReal (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.instDivisionRingReal))) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (z i))) m) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.instDivisionRingReal))) (z i) m))))
+Case conversion may be inaccurate. Consider using '#align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpowₓ'. -/
 theorem zpow_arith_mean_le_arith_mean_zpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
     (∑ i in s, w i * z i) ^ m ≤ ∑ i in s, w i * z i ^ m :=
   (convexOn_zpow m).map_sum_le hw hw' hz
 #align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpow
 
+/- warning: real.rpow_arith_mean_le_arith_mean_rpow -> Real.rpow_arith_mean_le_arith_mean_rpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (z i))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} Real Real.hasLe (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (z i))) p) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) p)))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (z i))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} Real Real.instLEReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (z i))) p) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) p)))))
+Case conversion may be inaccurate. Consider using '#align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpowₓ'. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   (convexOn_rpow hp).map_sum_le hw hw' hz
 #align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpow
 
+/- warning: real.arith_mean_le_rpow_mean -> Real.arith_mean_le_rpow_mean is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (z i))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} Real Real.hasLe (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (z i))) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (w i) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (w i))) -> (Eq.{1} Real (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => w i)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (z i))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} Real Real.instLEReal (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (z i))) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (w i) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p))))
+Case conversion may be inaccurate. Consider using '#align real.arith_mean_le_rpow_mean Real.arith_mean_le_rpow_meanₓ'. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : (∑ i in s, w i) = 1)
     (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) :=
@@ -118,6 +154,12 @@ end Real
 
 namespace NNReal
 
+/- warning: nnreal.pow_arith_mean_le_arith_mean_pow -> NNReal.pow_arith_mean_le_arith_mean_pow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (n : Nat), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (z i))) n) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (z i) n))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (forall (n : Nat), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (z i))) n) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (z i) n))))
+Case conversion may be inaccurate. Consider using '#align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_powₓ'. -/
 /-- Weighted generalized mean inequality, version sums over finite sets, with `ℝ≥0`-valued
 functions and natural exponent. -/
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) (n : ℕ) :
@@ -127,12 +169,24 @@ theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) n
 #align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_pow
 
+/- warning: nnreal.pow_sum_div_card_le_sum_pow -> NNReal.pow_sum_div_card_le_sum_pow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (n : Nat), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (x : ι) => f x)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (Finset.card.{u1} ι s)) n)) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (x : ι) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (f x) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (n : Nat), LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (NNReal.toReal (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (x : ι) => f x)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Nat.cast.{0} Real Real.natCast (Finset.card.{u1} ι s)) n)) (NNReal.toReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (x : ι) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (f x) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align nnreal.pow_sum_div_card_le_sum_pow NNReal.pow_sum_div_card_le_sum_powₓ'. -/
 theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
     (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) := by
   simpa only [← NNReal.coe_le_coe, NNReal.coe_sum, Nonneg.coe_div, NNReal.coe_pow] using
     @Real.pow_sum_div_card_le_sum_pow ι s (coe ∘ f) n fun _ _ => NNReal.coe_nonneg _
 #align nnreal.pow_sum_div_card_le_sum_pow NNReal.pow_sum_div_card_le_sum_pow
 
+/- warning: nnreal.rpow_arith_mean_le_arith_mean_rpow -> NNReal.rpow_arith_mean_le_arith_mean_rpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (z i))) p) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (z i) p)))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (z i))) p) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (z i) p)))))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_arith_mean_le_arith_mean_rpow NNReal.rpow_arith_mean_le_arith_mean_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
@@ -142,6 +196,12 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.rpow_arith_mean_le_arith_mean_rpow NNReal.rpow_arith_mean_le_arith_mean_rpow
 
+/- warning: nnreal.rpow_arith_mean_le_arith_mean2_rpow -> NNReal.rpow_arith_mean_le_arith_mean2_rpow is a dubious translation:
+lean 3 declaration is
+  forall (w₁ : NNReal) (w₂ : NNReal) (z₁ : NNReal) (z₂ : NNReal), (Eq.{1} NNReal (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) w₁ w₂) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) w₁ z₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) w₂ z₂)) p) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) w₁ (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) z₁ p)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) w₂ (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) z₂ p)))))
+but is expected to have type
+  forall (w₁ : NNReal) (w₂ : NNReal) (z₁ : NNReal) (z₂ : NNReal), (Eq.{1} NNReal (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) w₁ w₂) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₁ z₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ z₂)) p) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₁ (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) z₁ p)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) z₂ p)))))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_arith_mean_le_arith_mean2_rpow NNReal.rpow_arith_mean_le_arith_mean2_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw' : w₁ + w₂ = 1) {p : ℝ}
     (hp : 1 ≤ p) : (w₁ * z₁ + w₂ * z₂) ^ p ≤ w₁ * z₁ ^ p + w₂ * z₂ ^ p :=
@@ -151,6 +211,12 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw'
   · simp [hw', Fin.sum_univ_succ]
 #align nnreal.rpow_arith_mean_le_arith_mean2_rpow NNReal.rpow_arith_mean_le_arith_mean2_rpow
 
+/- warning: nnreal.rpow_add_le_mul_rpow_add_rpow -> NNReal.rpow_add_le_mul_rpow_add_rpow is a dubious translation:
+lean 3 declaration is
+  forall (z₁ : NNReal) (z₂ : NNReal) {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) z₁ z₂) p) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) p (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) z₁ p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) z₂ p))))
+but is expected to have type
+  forall (z₁ : NNReal) (z₂ : NNReal) {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) z₁ z₂) p) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) p (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) z₁ p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) z₂ p))))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpowₓ'. -/
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
@@ -165,6 +231,12 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
     ring
 #align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpow
 
+/- warning: nnreal.arith_mean_le_rpow_mean -> NNReal.arith_mean_le_rpow_mean is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (z i))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (w i) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (z i) p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> NNReal) (z : ι -> NNReal), (Eq.{1} NNReal (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (z i))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (w i) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (z i) p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p))))
+Case conversion may be inaccurate. Consider using '#align nnreal.arith_mean_le_rpow_mean NNReal.arith_mean_le_rpow_meanₓ'. -/
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ} (hp : 1 ≤ p) :
@@ -183,6 +255,12 @@ private theorem add_rpow_le_one_of_add_le_one {p : ℝ} (a b : ℝ≥0) (hab : a
   exact (add_le_add (h_le_one a ha) (h_le_one b hb)).trans hab
 #align nnreal.add_rpow_le_one_of_add_le_one nnreal.add_rpow_le_one_of_add_le_one
 
+/- warning: nnreal.add_rpow_le_rpow_add -> NNReal.add_rpow_le_rpow_add is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) a b) p))
+but is expected to have type
+  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) a b) p))
+Case conversion may be inaccurate. Consider using '#align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_addₓ'. -/
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
@@ -202,6 +280,12 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) : a ^ p +
     mul_assoc, mul_inv_cancel hab_0, one_mul, one_mul] at h_mul
 #align nnreal.add_rpow_le_rpow_add NNReal.add_rpow_le_rpow_add
 
+/- warning: nnreal.rpow_add_rpow_le_add -> NNReal.rpow_add_rpow_le_add is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) a b))
+but is expected to have type
+  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) a b))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_rpow_le_add NNReal.rpow_add_rpow_le_addₓ'. -/
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
@@ -210,6 +294,12 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
   exact add_rpow_le_rpow_add _ _ hp1
 #align nnreal.rpow_add_rpow_le_add NNReal.rpow_add_rpow_le_add
 
+/- warning: nnreal.rpow_add_rpow_le -> NNReal.rpow_add_rpow_le is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} {q : Real} (a : NNReal) (b : NNReal), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (LE.le.{0} Real Real.hasLe p q) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b q)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) q)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)))
+but is expected to have type
+  forall {p : Real} {q : Real} (a : NNReal) (b : NNReal), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (LE.le.{0} Real Real.instLEReal p q) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b q)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) q)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_leₓ'. -/
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
@@ -226,6 +316,12 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p 
   rwa [one_div_div] at h_rpow_add_rpow_le_add
 #align nnreal.rpow_add_rpow_le NNReal.rpow_add_rpow_le
 
+/- warning: nnreal.rpow_add_le_add_rpow -> NNReal.rpow_add_le_add_rpow is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (LE.le.{0} Real Real.hasLe p (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) a b) p) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b p)))
+but is expected to have type
+  forall {p : Real} (a : NNReal) (b : NNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (LE.le.{0} Real Real.instLEReal p (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) a b) p) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b p)))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_add_le_add_rpow NNReal.rpow_add_le_add_rpowₓ'. -/
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
   by
@@ -241,6 +337,12 @@ end NNReal
 
 namespace ENNReal
 
+/- warning: ennreal.rpow_arith_mean_le_arith_mean_rpow -> ENNReal.rpow_arith_mean_le_arith_mean_rpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> ENNReal) (z : ι -> ENNReal), (Eq.{1} ENNReal (Finset.sum.{0, u1} ENNReal ι (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (Finset.sum.{0, u1} ENNReal ι (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) (z i))) p) (Finset.sum.{0, u1} ENNReal ι (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (z i) p)))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> ENNReal) (z : ι -> ENNReal), (Eq.{1} ENNReal (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => w i)) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (w i) (z i))) p) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (w i) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (z i) p)))))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0∞`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
@@ -296,6 +398,12 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
     rwa [← coe_eq_coe, ← h_sum_nnreal]
 #align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpow
 
+/- warning: ennreal.rpow_arith_mean_le_arith_mean2_rpow -> ENNReal.rpow_arith_mean_le_arith_mean2_rpow is a dubious translation:
+lean 3 declaration is
+  forall (w₁ : ENNReal) (w₂ : ENNReal) (z₁ : ENNReal) (z₂ : ENNReal), (Eq.{1} ENNReal (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) w₁ w₂) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (forall {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) w₁ z₁) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) w₂ z₂)) p) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) w₁ (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) z₁ p)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) w₂ (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) z₂ p)))))
+but is expected to have type
+  forall (w₁ : ENNReal) (w₂ : ENNReal) (z₁ : ENNReal) (z₂ : ENNReal), (Eq.{1} ENNReal (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) w₁ w₂) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) -> (forall {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) w₁ z₁) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) w₂ z₂)) p) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) w₁ (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) z₁ p)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) w₂ (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) z₂ p)))))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpowₓ'. -/
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0∞` and real
 exponents. -/
 theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (hw' : w₁ + w₂ = 1) {p : ℝ}
@@ -306,6 +414,12 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
   · simp [hw', Fin.sum_univ_succ]
 #align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpow
 
+/- warning: ennreal.rpow_add_le_mul_rpow_add_rpow -> ENNReal.rpow_add_le_mul_rpow_add_rpow is a dubious translation:
+lean 3 declaration is
+  forall (z₁ : ENNReal) (z₂ : ENNReal) {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) z₁ z₂) p) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) p (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) z₁ p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) z₂ p))))
+but is expected to have type
+  forall (z₁ : ENNReal) (z₂ : ENNReal) {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) z₁ z₂) p) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) p (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) z₁ p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) z₂ p))))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpowₓ'. -/
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0∞` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
@@ -322,6 +436,12 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
     ring
 #align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow
 
+/- warning: ennreal.add_rpow_le_rpow_add -> ENNReal.add_rpow_le_rpow_add is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} (a : ENNReal) (b : ENNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b p)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) a b) p))
+but is expected to have type
+  forall {p : Real} (a : ENNReal) (b : ENNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b p)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) a b) p))
+Case conversion may be inaccurate. Consider using '#align ennreal.add_rpow_le_rpow_add ENNReal.add_rpow_le_rpow_addₓ'. -/
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
@@ -336,6 +456,12 @@ theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^
     ENNReal.coe_le_coe.2 (NNReal.add_rpow_le_rpow_add a b hp1)
 #align ennreal.add_rpow_le_rpow_add ENNReal.add_rpow_le_rpow_add
 
+/- warning: ennreal.rpow_add_rpow_le_add -> ENNReal.rpow_add_rpow_le_add is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} (a : ENNReal) (b : ENNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) a b))
+but is expected to have type
+  forall {p : Real} (a : ENNReal) (b : ENNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) a b))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_rpow_le_add ENNReal.rpow_add_rpow_le_addₓ'. -/
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
@@ -344,6 +470,12 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
   exact add_rpow_le_rpow_add _ _ hp1
 #align ennreal.rpow_add_rpow_le_add ENNReal.rpow_add_rpow_le_add
 
+/- warning: ennreal.rpow_add_rpow_le -> ENNReal.rpow_add_rpow_le is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} {q : Real} (a : ENNReal) (b : ENNReal), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (LE.le.{0} Real Real.hasLe p q) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a q) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b q)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) q)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)))
+but is expected to have type
+  forall {p : Real} {q : Real} (a : ENNReal) (b : ENNReal), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (LE.le.{0} Real Real.instLEReal p q) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a q) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b q)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) q)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b p)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_leₓ'. -/
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
@@ -359,6 +491,12 @@ theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq :
   rwa [one_div_div] at h_rpow_add_rpow_le_add
 #align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_le
 
+/- warning: ennreal.rpow_add_le_add_rpow -> ENNReal.rpow_add_le_add_rpow is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} (a : ENNReal) (b : ENNReal), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (LE.le.{0} Real Real.hasLe p (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) a b) p) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b p)))
+but is expected to have type
+  forall {p : Real} (a : ENNReal) (b : ENNReal), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (LE.le.{0} Real Real.instLEReal p (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) a b) p) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a p) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b p)))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_add_le_add_rpow ENNReal.rpow_add_le_add_rpowₓ'. -/
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -4,11 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 
 ! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit 13bf7613c96a9fd66a81b9020a82cad9a6ea1fcf
+! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.Convex.SpecificFunctions
+import Mathbin.Analysis.Convex.Jensen
+import Mathbin.Analysis.Convex.SpecificFunctions.Basic
+import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
 import Mathbin.Tactic.Positivity
 
 /-!
@@ -68,6 +70,25 @@ theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i
   hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
 
+/-- Specific case of Jensen's inequality for sums of powers -/
+theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s, 0 ≤ f a) :
+    (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) :=
+  by
+  rcases s.eq_empty_or_nonempty with (rfl | hs)
+  · simp_rw [Finset.sum_empty, zero_pow' _ (Nat.succ_ne_zero n), zero_div]
+  · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
+    suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
+      rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,
+        div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this
+    have :=
+      @ConvexOn.map_sum_le ℝ ℝ ℝ ι _ _ _ _ _ _ (Set.Ici 0) (fun x => x ^ (n + 1)) s
+        (fun _ => 1 / s.card) (coe ∘ f) (convexOn_pow (n + 1)) _ _ fun i hi =>
+        Set.mem_Ici.2 (hf i hi)
+    · simpa only [inv_mul_eq_div, one_div, Algebra.id.smul_eq_mul] using this
+    · simp only [one_div, inv_nonneg, Nat.cast_nonneg, imp_true_iff]
+    · simpa only [one_div, Finset.sum_const, nsmul_eq_mul] using mul_inv_cancel hs0.ne'
+#align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_pow
+
 theorem zpow_arith_mean_le_arith_mean_zpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
     (∑ i in s, w i * z i) ^ m ≤ ∑ i in s, w i * z i ^ m :=
@@ -106,6 +127,12 @@ theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in
       (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) n
 #align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_pow
 
+theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
+    (∑ x in s, f x) ^ (n + 1) / s.card ^ n ≤ ∑ x in s, f x ^ (n + 1) := by
+  simpa only [← NNReal.coe_le_coe, NNReal.coe_sum, Nonneg.coe_div, NNReal.coe_pow] using
+    @Real.pow_sum_div_card_le_sum_pow ι s (coe ∘ f) n fun _ _ => NNReal.coe_nonneg _
+#align nnreal.pow_sum_div_card_le_sum_pow NNReal.pow_sum_div_card_le_sum_pow
+
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ}

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 
 ! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit afdb4fa3b32d41106a4a09b371ce549ad7958abd
+! leanprover-community/mathlib commit 13bf7613c96a9fd66a81b9020a82cad9a6ea1fcf
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -124,6 +124,20 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0) (hw'
   · simp [hw', Fin.sum_univ_succ]
 #align nnreal.rpow_arith_mean_le_arith_mean2_rpow NNReal.rpow_arith_mean_le_arith_mean2_rpow
 
+/-- Unweighted mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
+theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
+    (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
+  by
+  rcases eq_or_lt_of_le hp with (rfl | h'p)
+  · simp only [rpow_one, sub_self, rpow_zero, one_mul]
+  convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂) (add_halves 1) hp
+  · simp only [one_div, inv_mul_cancel_left₀, Ne.def, bit0_eq_zero, one_ne_zero, not_false_iff]
+  · simp only [one_div, inv_mul_cancel_left₀, Ne.def, bit0_eq_zero, one_ne_zero, not_false_iff]
+  · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
+    simp only [mul_rpow, rpow_sub' _ A, div_eq_inv_mul, rpow_one, mul_one]
+    ring
+#align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpow
+
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ} (hp : 1 ≤ p) :
@@ -133,10 +147,6 @@ theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i)
       (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.arith_mean_le_rpow_mean NNReal.arith_mean_le_rpow_mean
 
-end NNReal
-
-namespace NNReal
-
 private theorem add_rpow_le_one_of_add_le_one {p : ℝ} (a b : ℝ≥0) (hab : a + b ≤ 1) (hp1 : 1 ≤ p) :
     a ^ p + b ^ p ≤ 1 :=
   by
@@ -269,9 +279,21 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
   · simp [hw', Fin.sum_univ_succ]
 #align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpow
 
-end ENNReal
-
-namespace ENNReal
+/-- Unweighted mean inequality, version for two elements of `ℝ≥0∞` and real exponents. -/
+theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1 ≤ p) :
+    (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p) :=
+  by
+  rcases eq_or_lt_of_le hp with (rfl | h'p)
+  · simp only [rpow_one, sub_self, rpow_zero, one_mul, le_refl]
+  convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂)
+      (ENNReal.add_halves 1) hp
+  · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
+  · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
+  · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
+    simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero two_ne_top,
+      div_eq_inv_mul, rpow_one, mul_one]
+    ring
+#align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow
 
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -48,7 +48,7 @@ universe u v
 
 open Finset
 
-open Classical BigOperators NNReal Ennreal
+open Classical BigOperators NNReal ENNReal
 
 noncomputable section
 
@@ -202,7 +202,7 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0) (hp : 0 ≤ p) (hp1 : p 
 
 end NNReal
 
-namespace Ennreal
+namespace ENNReal
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0∞`-valued
 functions and real exponents. -/
@@ -216,7 +216,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
   have hp_not_nonpos : ¬p ≤ 0 := by simp [hp_pos]
   have hp_not_neg : ¬p < 0 := by simp [hp_nonneg]
   have h_top_iff_rpow_top : ∀ (i : ι) (hi : i ∈ s), w i * z i = ⊤ ↔ w i * z i ^ p = ⊤ := by
-    simp [Ennreal.mul_eq_top, hp_pos, hp_nonneg, hp_not_nonpos, hp_not_neg]
+    simp [ENNReal.mul_eq_top, hp_pos, hp_nonneg, hp_not_nonpos, hp_not_neg]
   refine' le_of_top_imp_top_of_to_nnreal_le _ _
   · -- first, prove `(∑ i in s, w i * z i) ^ p = ⊤ → ∑ i in s, (w i * z i ^ p) = ⊤`
     rw [rpow_eq_top_iff, sum_eq_top_iff, sum_eq_top_iff]
@@ -255,9 +255,9 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
       rw [coe_finset_sum]
       refine' sum_congr rfl fun i hi => (coe_to_nnreal _).symm
       refine' (lt_top_of_sum_ne_top _ hi).Ne
-      exact hw'.symm ▸ Ennreal.one_ne_top
+      exact hw'.symm ▸ ENNReal.one_ne_top
     rwa [← coe_eq_coe, ← h_sum_nnreal]
-#align ennreal.rpow_arith_mean_le_arith_mean_rpow Ennreal.rpow_arith_mean_le_arith_mean_rpow
+#align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpow
 
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0∞` and real
 exponents. -/
@@ -267,48 +267,48 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
   have h := rpow_arith_mean_le_arith_mean_rpow univ ![w₁, w₂] ![z₁, z₂] _ hp
   · simpa [Fin.sum_univ_succ] using h
   · simp [hw', Fin.sum_univ_succ]
-#align ennreal.rpow_arith_mean_le_arith_mean2_rpow Ennreal.rpow_arith_mean_le_arith_mean2_rpow
+#align ennreal.rpow_arith_mean_le_arith_mean2_rpow ENNReal.rpow_arith_mean_le_arith_mean2_rpow
 
-end Ennreal
+end ENNReal
 
-namespace Ennreal
+namespace ENNReal
 
 theorem add_rpow_le_rpow_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) : a ^ p + b ^ p ≤ (a + b) ^ p :=
   by
   have hp_pos : 0 < p := by positivity
   by_cases h_top : a + b = ⊤
-  · rw [← @Ennreal.rpow_eq_top_iff_of_pos (a + b) p hp_pos] at h_top
+  · rw [← @ENNReal.rpow_eq_top_iff_of_pos (a + b) p hp_pos] at h_top
     rw [h_top]
     exact le_top
   obtain ⟨ha_top, hb_top⟩ := add_ne_top.mp h_top
   lift a to ℝ≥0 using ha_top
   lift b to ℝ≥0 using hb_top
-  simpa [← Ennreal.coe_rpow_of_nonneg _ hp_pos.le] using
-    Ennreal.coe_le_coe.2 (NNReal.add_rpow_le_rpow_add a b hp1)
-#align ennreal.add_rpow_le_rpow_add Ennreal.add_rpow_le_rpow_add
+  simpa [← ENNReal.coe_rpow_of_nonneg _ hp_pos.le] using
+    ENNReal.coe_le_coe.2 (NNReal.add_rpow_le_rpow_add a b hp1)
+#align ennreal.add_rpow_le_rpow_add ENNReal.add_rpow_le_rpow_add
 
 theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
     (a ^ p + b ^ p) ^ (1 / p) ≤ a + b :=
   by
-  rw [← @Ennreal.le_rpow_one_div_iff _ _ (1 / p) (by simp [lt_of_lt_of_le zero_lt_one hp1])]
+  rw [← @ENNReal.le_rpow_one_div_iff _ _ (1 / p) (by simp [lt_of_lt_of_le zero_lt_one hp1])]
   rw [one_div_one_div]
   exact add_rpow_le_rpow_add _ _ hp1
-#align ennreal.rpow_add_rpow_le_add Ennreal.rpow_add_rpow_le_add
+#align ennreal.rpow_add_rpow_le_add ENNReal.rpow_add_rpow_le_add
 
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) :=
   by
   have h_rpow : ∀ a : ℝ≥0∞, a ^ q = (a ^ p) ^ (q / p) := fun a => by
-    rw [← Ennreal.rpow_mul, _root_.mul_div_cancel' _ hp_pos.ne']
+    rw [← ENNReal.rpow_mul, _root_.mul_div_cancel' _ hp_pos.ne']
   have h_rpow_add_rpow_le_add :
     ((a ^ p) ^ (q / p) + (b ^ p) ^ (q / p)) ^ (1 / (q / p)) ≤ a ^ p + b ^ p :=
     by
     refine' rpow_add_rpow_le_add (a ^ p) (b ^ p) _
     rwa [one_le_div hp_pos]
-  rw [h_rpow a, h_rpow b, Ennreal.le_rpow_one_div_iff hp_pos, ← Ennreal.rpow_mul, mul_comm,
+  rw [h_rpow a, h_rpow b, ENNReal.le_rpow_one_div_iff hp_pos, ← ENNReal.rpow_mul, mul_comm,
     mul_one_div]
   rwa [one_div_div] at h_rpow_add_rpow_le_add
-#align ennreal.rpow_add_rpow_le Ennreal.rpow_add_rpow_le
+#align ennreal.rpow_add_rpow_le ENNReal.rpow_add_rpow_le
 
 theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 : p ≤ 1) :
     (a + b) ^ p ≤ a ^ p + b ^ p :=
@@ -319,9 +319,9 @@ theorem rpow_add_le_add_rpow {p : ℝ} (a b : ℝ≥0∞) (hp : 0 ≤ p) (hp1 :
     norm_num
   have h := rpow_add_rpow_le a b hp_pos hp1
   rw [one_div_one] at h
-  repeat' rw [Ennreal.rpow_one] at h
-  exact (Ennreal.le_rpow_one_div_iff hp_pos).mp h
-#align ennreal.rpow_add_le_add_rpow Ennreal.rpow_add_le_add_rpow
+  repeat' rw [ENNReal.rpow_one] at h
+  exact (ENNReal.le_rpow_one_div_iff hp_pos).mp h
+#align ennreal.rpow_add_le_add_rpow ENNReal.rpow_add_le_add_rpow
 
-end Ennreal
+end ENNReal
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 
 ! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit 7eaf3412966a5f94513e866fbf6de6d340e2ef32
+! leanprover-community/mathlib commit afdb4fa3b32d41106a4a09b371ce549ad7958abd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -216,7 +216,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
   have hp_not_nonpos : ¬p ≤ 0 := by simp [hp_pos]
   have hp_not_neg : ¬p < 0 := by simp [hp_nonneg]
   have h_top_iff_rpow_top : ∀ (i : ι) (hi : i ∈ s), w i * z i = ⊤ ↔ w i * z i ^ p = ⊤ := by
-    simp [hp_pos, hp_nonneg, hp_not_nonpos, hp_not_neg]
+    simp [Ennreal.mul_eq_top, hp_pos, hp_nonneg, hp_not_nonpos, hp_not_neg]
   refine' le_of_top_imp_top_of_to_nnreal_le _ _
   · -- first, prove `(∑ i in s, w i * z i) ^ p = ⊤ → ∑ i in s, (w i * z i ^ p) = ⊤`
     rw [rpow_eq_top_iff, sum_eq_top_iff, sum_eq_top_iff]

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

@@ -153,7 +153,7 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
   · simp only [rpow_one, sub_self, rpow_zero, one_mul]; rfl
   convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂) (add_halves 1) hp
     using 1
-  · simp only [one_div, inv_mul_cancel_left₀, Ne.def, mul_eq_zero, two_ne_zero, one_ne_zero,
+  · simp only [one_div, inv_mul_cancel_left₀, Ne, mul_eq_zero, two_ne_zero, one_ne_zero,
       not_false_iff]
   · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
     simp only [mul_rpow, rpow_sub' _ A, div_eq_inv_mul, rpow_one, mul_one]
@@ -259,7 +259,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑
     have h_top_rpow : ∀ a : ι, a ∈ s → w a * z a ^ p ≠ ⊤ := by
       intro i hi
       specialize h_top i hi
-      rwa [Ne.def, ← h_top_iff_rpow_top i hi]
+      rwa [Ne, ← h_top_iff_rpow_top i hi]
     -- put the `.toNNReal` inside the sums.
     simp_rw [toNNReal_sum h_top_rpow, ← toNNReal_rpow, toNNReal_sum h_top, toNNReal_mul, ←
       toNNReal_rpow]

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -75,7 +75,7 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
   · simp_rw [Finset.sum_empty, zero_pow n.succ_ne_zero, zero_div]; rfl
   · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
     suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
-      rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,
+      rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ (s.card : ℝ), ← div_div,
         div_le_iff hs0, div_mul, div_self hs0.ne', div_one] at this
     have :=
       @ConvexOn.map_sum_le ℝ ℝ ℝ ι _ _ _ _ _ _ (Set.Ici 0) (fun x => x ^ (n + 1)) s

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -319,7 +319,7 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0∞) (hp1 : 1 ≤ p) :
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0∞) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) := by
   have h_rpow : ∀ a : ℝ≥0∞, a ^ q = (a ^ p) ^ (q / p) := fun a => by
-    rw [← ENNReal.rpow_mul, _root_.mul_div_cancel' _ hp_pos.ne']
+    rw [← ENNReal.rpow_mul, mul_div_cancel₀ _ hp_pos.ne']
   have h_rpow_add_rpow_le_add :
     ((a ^ p) ^ (q / p) + (b ^ p) ^ (q / p)) ^ (1 / (q / p)) ≤ a ^ p + b ^ p := by
     refine' rpow_add_rpow_le_add (a ^ p) (b ^ p) _

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -47,7 +47,8 @@ universe u v
 
 open Finset
 
-open Classical BigOperators NNReal ENNReal
+open scoped Classical
+open BigOperators NNReal ENNReal
 
 noncomputable section
 

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -231,10 +231,8 @@ namespace ENNReal
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑ i in s, w i = 1) {p : ℝ}
     (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p := by
-  have hp_pos : 0 < p
-  positivity
-  have hp_nonneg : 0 ≤ p
-  positivity
+  have hp_pos : 0 < p := by positivity
+  have hp_nonneg : 0 ≤ p := by positivity
   have hp_not_neg : ¬p < 0 := by simp [hp_nonneg]
   have h_top_iff_rpow_top : ∀ (i : ι), i ∈ s → (w i * z i = ⊤ ↔ w i * z i ^ p = ⊤) := by
     simp [ENNReal.mul_eq_top, hp_pos, hp_nonneg, hp_not_neg]

by tweaking the definition of the AddMonoid and MonoidWithZero instances for WithTop. Also unprotect ENNReal.coe_injective and rename ENNReal.coe_eq_coe → ENNReal.coe_inj.

From LeanAPAP

@@ -274,7 +274,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑
       refine' sum_congr rfl fun i hi => (coe_toNNReal _).symm
       refine' (lt_top_of_sum_ne_top _ hi).ne
       exact hw'.symm ▸ ENNReal.one_ne_top
-    rwa [← coe_eq_coe, ← h_sum_nnreal]
+    rwa [← coe_inj, ← h_sum_nnreal]
 #align ennreal.rpow_arith_mean_le_arith_mean_rpow ENNReal.rpow_arith_mean_le_arith_mean_rpow
 
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0∞` and real

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -71,7 +71,7 @@ theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i
 theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s, 0 ≤ f a) :
     (∑ x in s, f x) ^ (n + 1) / (s.card : ℝ) ^ n ≤ ∑ x in s, f x ^ (n + 1) := by
   rcases s.eq_empty_or_nonempty with (rfl | hs)
-  · simp_rw [Finset.sum_empty, zero_pow' _ (Nat.succ_ne_zero n), zero_div]; rfl
+  · simp_rw [Finset.sum_empty, zero_pow n.succ_ne_zero, zero_div]; rfl
   · have hs0 : 0 < (s.card : ℝ) := Nat.cast_pos.2 hs.card_pos
     suffices (∑ x in s, f x / s.card) ^ (n + 1) ≤ ∑ x in s, f x ^ (n + 1) / s.card by
       rwa [← Finset.sum_div, ← Finset.sum_div, div_pow, pow_succ' (s.card : ℝ), ← div_div,

Some of these are already transitively imported, others aren't used at all (but not handled by noshake in #9772).

Mostly I wanted to avoid needing all of algebra imported (but unused!) in FilteredColimitCommutesFiniteLimit; there are now some assert_not_exists to preserve this.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -7,7 +7,6 @@ import Mathlib.Analysis.Convex.Jensen
 import Mathlib.Analysis.Convex.Mul
 import Mathlib.Analysis.Convex.SpecificFunctions.Basic
 import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
-import Mathlib.Tactic.Positivity
 
 #align_import analysis.mean_inequalities_pow from "leanprover-community/mathlib"@"ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f"
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 -/
 import Mathlib.Analysis.Convex.Jensen
+import Mathlib.Analysis.Convex.Mul
 import Mathlib.Analysis.Convex.SpecificFunctions.Basic
 import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
 import Mathlib.Tactic.Positivity

This better matches other lemma names.

From LeanAPAP

@@ -104,9 +104,9 @@ theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
   rw [← rpow_le_rpow_iff _ _ this, ← rpow_mul, one_div_mul_cancel (ne_of_gt this), rpow_one]
   exact rpow_arith_mean_le_arith_mean_rpow s w z hw hw' hz hp
   all_goals
-    apply_rules [sum_nonneg, rpow_nonneg_of_nonneg]
+    apply_rules [sum_nonneg, rpow_nonneg]
     intro i hi
-    apply_rules [mul_nonneg, rpow_nonneg_of_nonneg, hw i hi, hz i hi]
+    apply_rules [mul_nonneg, rpow_nonneg, hw i hi, hz i hi]
 #align real.arith_mean_le_rpow_mean Real.arith_mean_le_rpow_mean
 
 end Real

@@ -289,13 +289,10 @@ theorem rpow_arith_mean_le_arith_mean2_rpow (w₁ w₂ z₁ z₂ : ℝ≥0∞) (
 /-- Unweighted mean inequality, version for two elements of `ℝ≥0∞` and real exponents. -/
 theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1 ≤ p) :
     (z₁ + z₂) ^ p ≤ (2 : ℝ≥0∞) ^ (p - 1) * (z₁ ^ p + z₂ ^ p) := by
-  rcases eq_or_lt_of_le hp with (rfl | h'p)
-  · simp only [rpow_one, sub_self, rpow_zero, one_mul, le_refl]
   convert rpow_arith_mean_le_arith_mean2_rpow (1 / 2) (1 / 2) (2 * z₁) (2 * z₂)
       (ENNReal.add_halves 1) hp using 1
   · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
-  · have _ : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
-    simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero two_ne_top,
+  · simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero two_ne_top,
       ENNReal.div_eq_inv_mul, rpow_one, mul_one]
     ring
 #align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow

We prove that the product of nonnegative monovarying convex functions is convex. We take the opportunity to golf the various proofs of the convexity of x ↦ x ^ n.

@@ -64,7 +64,7 @@ theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
 theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) {n : ℕ} (hn : Even n) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
-  hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
+  hn.convexOn_pow.map_sum_le hw hw' fun _ _ => Set.mem_univ _
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
 
 /-- Specific case of Jensen's inequality for sums of powers -/

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -116,10 +116,10 @@ namespace NNReal
 /-- Weighted generalized mean inequality, version sums over finite sets, with `ℝ≥0`-valued
 functions and natural exponent. -/
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) (n : ℕ) :
-    (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n := by
-  exact_mod_cast
+    (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
+  mod_cast
     Real.pow_arith_mean_le_arith_mean_pow s _ _ (fun i _ => (w i).coe_nonneg)
-      (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) n
+      (mod_cast hw') (fun i _ => (z i).coe_nonneg) n
 #align nnreal.pow_arith_mean_le_arith_mean_pow NNReal.pow_arith_mean_le_arith_mean_pow
 
 theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
@@ -131,10 +131,10 @@ theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ}
-    (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p := by
-  exact_mod_cast
+    (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
+  mod_cast
     Real.rpow_arith_mean_le_arith_mean_rpow s _ _ (fun i _ => (w i).coe_nonneg)
-      (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) hp
+      (mod_cast hw') (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.rpow_arith_mean_le_arith_mean_rpow NNReal.rpow_arith_mean_le_arith_mean_rpow
 
 /-- Weighted generalized mean inequality, version for two elements of `ℝ≥0` and real exponents. -/
@@ -162,9 +162,9 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
 theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ} (hp : 1 ≤ p) :
-    ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
-  exact_mod_cast
-    Real.arith_mean_le_rpow_mean s _ _ (fun i _ => (w i).coe_nonneg) (by exact_mod_cast hw')
+    ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) :=
+  mod_cast
+    Real.arith_mean_le_rpow_mean s _ _ (fun i _ => (w i).coe_nonneg) (mod_cast hw')
       (fun i _ => (z i).coe_nonneg) hp
 #align nnreal.arith_mean_le_rpow_mean NNReal.arith_mean_le_rpow_mean
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -51,8 +51,6 @@ open Classical BigOperators NNReal ENNReal
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 variable {ι : Type u} (s : Finset ι)
 
 namespace Real

@@ -51,7 +51,7 @@ open Classical BigOperators NNReal ENNReal
 
 noncomputable section
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 variable {ι : Type u} (s : Finset ι)
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,17 +2,14 @@
 Copyright (c) 2019 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-
-! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Jensen
 import Mathlib.Analysis.Convex.SpecificFunctions.Basic
 import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
 import Mathlib.Tactic.Positivity
 
+#align_import analysis.mean_inequalities_pow from "leanprover-community/mathlib"@"ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f"
+
 /-!
 # Mean value inequalities
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -61,13 +61,13 @@ variable {ι : Type u} (s : Finset ι)
 namespace Real
 
 theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   (convexOn_pow n).map_sum_le hw hw' hz
 #align real.pow_arith_mean_le_arith_mean_pow Real.pow_arith_mean_le_arith_mean_pow
 
 theorem pow_arith_mean_le_arith_mean_pow_of_even (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) {n : ℕ} (hn : Even n) :
+    (hw' : ∑ i in s, w i = 1) {n : ℕ} (hn : Even n) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n :=
   hn.convexOn_pow.map_sum_le hw hw' fun _ _ => trivial
 #align real.pow_arith_mean_le_arith_mean_pow_of_even Real.pow_arith_mean_le_arith_mean_pow_of_even
@@ -91,20 +91,20 @@ theorem pow_sum_div_card_le_sum_pow {f : ι → ℝ} (n : ℕ) (hf : ∀ a ∈ s
 #align real.pow_sum_div_card_le_sum_pow Real.pow_sum_div_card_le_sum_pow
 
 theorem zpow_arith_mean_le_arith_mean_zpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 < z i) (m : ℤ) :
     (∑ i in s, w i * z i) ^ m ≤ ∑ i in s, w i * z i ^ m :=
   (convexOn_zpow m).map_sum_le hw hw' hz
 #align real.zpow_arith_mean_le_arith_mean_zpow Real.zpow_arith_mean_le_arith_mean_zpow
 
 theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p :=
   (convexOn_rpow hp).map_sum_le hw hw' hz
 #align real.rpow_arith_mean_le_arith_mean_rpow Real.rpow_arith_mean_le_arith_mean_rpow
 
-theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : (∑ i in s, w i) = 1)
+theorem arith_mean_le_rpow_mean (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : ∑ i in s, w i = 1)
     (hz : ∀ i ∈ s, 0 ≤ z i) {p : ℝ} (hp : 1 ≤ p) :
-    (∑ i in s, w i * z i) ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
+    ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
   have : 0 < p := by positivity
   rw [← rpow_le_rpow_iff _ _ this, ← rpow_mul, one_div_mul_cancel (ne_of_gt this), rpow_one]
   exact rpow_arith_mean_le_arith_mean_rpow s w z hw hw' hz hp
@@ -120,7 +120,7 @@ namespace NNReal
 
 /-- Weighted generalized mean inequality, version sums over finite sets, with `ℝ≥0`-valued
 functions and natural exponent. -/
-theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) (n : ℕ) :
+theorem pow_arith_mean_le_arith_mean_pow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) (n : ℕ) :
     (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n := by
   exact_mod_cast
     Real.pow_arith_mean_le_arith_mean_pow s _ _ (fun i _ => (w i).coe_nonneg)
@@ -135,7 +135,7 @@ theorem pow_sum_div_card_le_sum_pow (f : ι → ℝ≥0) (n : ℕ) :
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
-theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
+theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ}
     (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p := by
   exact_mod_cast
     Real.rpow_arith_mean_le_arith_mean_rpow s _ _ (fun i _ => (w i).coe_nonneg)
@@ -166,8 +166,8 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0`-valued
 functions and real exponents. -/
-theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) {p : ℝ} (hp : 1 ≤ p) :
-    (∑ i in s, w i * z i) ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
+theorem arith_mean_le_rpow_mean (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) {p : ℝ} (hp : 1 ≤ p) :
+    ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p) := by
   exact_mod_cast
     Real.arith_mean_le_rpow_mean s _ _ (fun i _ => (w i).coe_nonneg) (by exact_mod_cast hw')
       (fun i _ => (z i).coe_nonneg) hp
@@ -234,7 +234,7 @@ namespace ENNReal
 
 /-- Weighted generalized mean inequality, version for sums over finite sets, with `ℝ≥0∞`-valued
 functions and real exponents. -/
-theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑ i in s, w i) = 1) {p : ℝ}
+theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : ∑ i in s, w i = 1) {p : ℝ}
     (hp : 1 ≤ p) : (∑ i in s, w i * z i) ^ p ≤ ∑ i in s, w i * z i ^ p := by
   have hp_pos : 0 < p
   positivity
@@ -257,7 +257,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
     intro h_top_rpow_sum _
     -- show hypotheses needed to put the `.toNNReal` inside the sums.
     have h_top : ∀ a : ι, a ∈ s → w a * z a ≠ ⊤ :=
-      haveI h_top_sum : (∑ i : ι in s, w i * z i) ≠ ⊤ := by
+      haveI h_top_sum : ∑ i : ι in s, w i * z i ≠ ⊤ := by
         intro h
         rw [h, top_rpow_of_pos hp_pos] at h_top_rpow_sum
         exact h_top_rpow_sum rfl
@@ -274,7 +274,7 @@ theorem rpow_arith_mean_le_arith_mean_rpow (w z : ι → ℝ≥0∞) (hw' : (∑
       NNReal.rpow_arith_mean_le_arith_mean_rpow s (fun i => (w i).toNNReal)
         (fun i => (z i).toNNReal) _ hp
     -- verify the hypothesis `∑ i in s, (w i).toNNReal = 1`, using `∑ i in s, w i = 1` .
-    have h_sum_nnreal : (∑ i in s, w i) = ↑(∑ i in s, (w i).toNNReal) := by
+    have h_sum_nnreal : ∑ i in s, w i = ↑(∑ i in s, (w i).toNNReal) := by
       rw [coe_finset_sum]
       refine' sum_congr rfl fun i hi => (coe_toNNReal _).symm
       refine' (lt_top_of_sum_ne_top _ hi).ne

Also correct some simps. Partially forward-port leanprover-community/mathlib#18731

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 
 ! This file was ported from Lean 3 source module analysis.mean_inequalities_pow
-! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
+! leanprover-community/mathlib commit ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -160,7 +160,7 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0) {p : ℝ} (hp : 1 
   · simp only [one_div, inv_mul_cancel_left₀, Ne.def, mul_eq_zero, two_ne_zero, one_ne_zero,
       not_false_iff]
   · have A : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
-    simp only [mul_rpow, rpow_sub' _ A, _root_.div_eq_inv_mul, rpow_one, mul_one]
+    simp only [mul_rpow, rpow_sub' _ A, div_eq_inv_mul, rpow_one, mul_one]
     ring
 #align nnreal.rpow_add_le_mul_rpow_add_rpow NNReal.rpow_add_le_mul_rpow_add_rpow
 
@@ -207,7 +207,7 @@ theorem rpow_add_rpow_le_add {p : ℝ} (a b : ℝ≥0) (hp1 : 1 ≤ p) :
 theorem rpow_add_rpow_le {p q : ℝ} (a b : ℝ≥0) (hp_pos : 0 < p) (hpq : p ≤ q) :
     (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p) := by
   have h_rpow : ∀ a : ℝ≥0, a ^ q = (a ^ p) ^ (q / p) := fun a => by
-    rw [← NNReal.rpow_mul, _root_.div_eq_inv_mul, ← mul_assoc, _root_.mul_inv_cancel hp_pos.ne.symm,
+    rw [← NNReal.rpow_mul, div_eq_inv_mul, ← mul_assoc, _root_.mul_inv_cancel hp_pos.ne.symm,
       one_mul]
   have h_rpow_add_rpow_le_add :
     ((a ^ p) ^ (q / p) + (b ^ p) ^ (q / p)) ^ (1 / (q / p)) ≤ a ^ p + b ^ p := by
@@ -301,7 +301,7 @@ theorem rpow_add_le_mul_rpow_add_rpow (z₁ z₂ : ℝ≥0∞) {p : ℝ} (hp : 1
   · simp [← mul_assoc, ENNReal.inv_mul_cancel two_ne_zero two_ne_top]
   · have _ : p - 1 ≠ 0 := ne_of_gt (sub_pos.2 h'p)
     simp only [mul_rpow_of_nonneg _ _ (zero_le_one.trans hp), rpow_sub _ _ two_ne_zero two_ne_top,
-      div_eq_inv_mul, rpow_one, mul_one]
+      ENNReal.div_eq_inv_mul, rpow_one, mul_one]
     ring
 #align ennreal.rpow_add_le_mul_rpow_add_rpow ENNReal.rpow_add_le_mul_rpow_add_rpow
 

Co-authored-by: Komyyy <pol_tta@outlook.jp>