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

@@ -5,8 +5,8 @@ Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 -/
 import Analysis.Convex.Jensen
 import Analysis.Convex.SpecificFunctions.Basic
-import Analysis.SpecialFunctions.Pow.Nnreal
-import Data.Real.ConjugateExponents
+import Analysis.SpecialFunctions.Pow.NNReal
+import Data.Real.ConjExponents
 
 #align_import analysis.mean_inequalities from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 
@@ -366,8 +366,8 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
     _ ≤ 1 / Real.toNNReal p + 1 / Real.toNNReal q :=
       by
       refine' add_le_add _ _
-      · rwa [div_le_iff hp_ne_zero, div_mul_cancel _ hp_ne_zero]
-      · rwa [div_le_iff hq_ne_zero, div_mul_cancel _ hq_ne_zero]
+      · rwa [div_le_iff hp_ne_zero, div_mul_cancel₀ _ hp_ne_zero]
+      · rwa [div_le_iff hq_ne_zero, div_mul_cancel₀ _ hq_ne_zero]
     _ = 1 := hpq.inv_add_inv_conj_nnreal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
@@ -518,7 +518,7 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q
         refine' fun y => mul_div_cancel_left_of_imp fun h => _
         simpa [h, hpq.ne_zero]
       simp only [Set.mem_setOf_eq, div_rpow, ← sum_div, ← rpow_mul,
-        div_mul_cancel _ hpq.symm.ne_zero, rpow_one, div_le_iff hf, one_mul, hpq.mul_eq_add, ←
+        div_mul_cancel₀ _ hpq.symm.ne_zero, rpow_one, div_le_iff hf, one_mul, hpq.mul_eq_add, ←
         rpow_sub' _ A, _root_.add_sub_cancel, le_refl, true_and_iff, ← mul_div_assoc, B]
       rw [div_eq_iff, ← rpow_add hf, hpq.inv_add_inv_conj, rpow_one]
       simpa [hpq.symm.ne_zero] using hf

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

@@ -124,9 +124,9 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
     · rw [hzi]; exact zero_rpow hwi
   -- If all numbers `z i` with non-zero weight are positive, then we apply Jensen's inequality
   -- for `exp` and numbers `log (z i)` with weights `w i`.
-  · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A 
+  · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A
     have := convex_on_exp.map_sum_le hw hw' fun i _ => Set.mem_univ <| log (z i)
-    simp only [NormedSpace.exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this 
+    simp only [NormedSpace.exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this
     convert this using 1 <;> [apply prod_congr rfl; apply sum_congr rfl] <;> intro i hi
     · cases' eq_or_lt_of_le (hz i hi) with hz hz
       · simp [A i hi hz.symm]
@@ -331,7 +331,7 @@ theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjExponent
   · refine' le_trans le_top (le_of_eq _)
     repeat' rw [div_eq_mul_inv]
     cases h <;> rw [h] <;> simp [h, hpq.pos, hpq.symm.pos]
-  push_neg at h 
+  push_neg at h
   -- if a ≠ ⊤ and b ≠ ⊤, use the nnreal version: nnreal.young_inequality_real
   rw [← coe_to_nnreal h.left, ← coe_to_nnreal h.right, ← coe_mul, coe_rpow_of_nonneg _ hpq.nonneg,
     coe_rpow_of_nonneg _ hpq.symm.nonneg, ENNReal.ofReal, ENNReal.ofReal, ←
@@ -378,7 +378,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
     inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
   intro i his
   left
-  rw [sum_eq_zero_iff] at hf 
+  rw [sum_eq_zero_iff] at hf
   exact (rpow_eq_zero_iff.mp (hf i his)).left
 
 #print NNReal.inner_le_Lp_mul_Lq /-
@@ -401,8 +401,8 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExp
   let g' i := g i / (∑ i in s, g i ^ q) ^ (1 / q)
   suffices ∑ i in s, f' i * g' i ≤ 1
     by
-    simp_rw [f', g', div_mul_div_comm, ← sum_div] at this 
-    rwa [div_le_iff, one_mul] at this 
+    simp_rw [f', g', div_mul_div_comm, ← sum_div] at this
+    rwa [div_le_iff, one_mul] at this
     refine' mul_ne_zero _ _
     · rw [Ne.def, rpow_eq_zero_iff, not_and_or]; exact Or.inl hF_zero
     · rw [Ne.def, rpow_eq_zero_iff, not_and_or]; exact Or.inl hG_zero
@@ -541,7 +541,7 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
   · simp [Finset.sum_add_distrib]
   have hpq := Real.IsConjExponent.conjExponent hp
   have := is_greatest_Lp s (f + g) hpq
-  simp only [Pi.add_apply, add_mul, sum_add_distrib] at this 
+  simp only [Pi.add_apply, add_mul, sum_add_distrib] at this
   rcases this.1 with ⟨φ, hφ, H⟩
   rw [← H]
   exact
@@ -633,7 +633,7 @@ theorem inner_le_Lp_mul_Lq (hpq : IsConjExponent p q) :
     NNReal.coe_le_coe.2
       (NNReal.inner_le_Lp_mul_Lq s (fun i => ⟨_, abs_nonneg (f i)⟩) (fun i => ⟨_, abs_nonneg (g i)⟩)
         hpq)
-  push_cast at this 
+  push_cast at this
   refine' le_trans (sum_le_sum fun i hi => _) this
   simp only [← abs_mul, le_abs_self]
 #align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lq
@@ -648,7 +648,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   have :=
     NNReal.coe_le_coe.2
       (NNReal.rpow_sum_le_const_mul_sum_rpow s (fun i => ⟨_, abs_nonneg (f i)⟩) hp)
-  push_cast at this 
+  push_cast at this
   exact this
 #align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpow
 -/
@@ -664,7 +664,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
   have :=
     NNReal.coe_le_coe.2
       (NNReal.Lp_add_le s (fun i => ⟨_, abs_nonneg (f i)⟩) (fun i => ⟨_, abs_nonneg (g i)⟩) hp)
-  push_cast at this 
+  push_cast at this
   refine' le_trans (rpow_le_rpow _ (sum_le_sum fun i hi => _) _) this <;>
     simp [sum_nonneg, rpow_nonneg_of_nonneg, abs_nonneg, le_trans zero_le_one hp, abs_add,
       rpow_le_rpow]
@@ -732,7 +732,7 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjExponent q) {A B : 
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast at hf_sum hg_sum 
+  norm_cast at hf_sum hg_sum
   obtain ⟨C, hC, H⟩ := NNReal.inner_le_Lp_mul_Lq_hasSum hpq hf_sum hg_sum
   refine' ⟨C, C.prop, hC, _⟩
   norm_cast
@@ -812,7 +812,7 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast at hfA hgB 
+  norm_cast at hfA hgB
   obtain ⟨C, hC₁, hC₂⟩ := NNReal.Lp_add_le_hasSum hp hfA hgB
   use C
   norm_cast
@@ -841,7 +841,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases H <;> simp [H i hi]
     have : ∑ i in s, f i * g i = ∑ i in s, 0 := sum_congr rfl this
     simp [this]
-  push_neg at H 
+  push_neg at H
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤
   · cases H' <;> simp [H', -one_div, H]
   replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤
@@ -853,7 +853,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
       (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => ENNReal.toNNReal (f i))
         (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
   simp [← ENNReal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
-    le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this 
+    le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
   convert this using 1 <;> [skip; congr 2] <;> [skip; skip; simp; skip; simp] <;>
     · apply Finset.sum_congr rfl fun i hi => _;
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
@@ -898,7 +898,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
     ENNReal.coe_le_coe.2
       (@NNReal.Lp_add_le _ s (fun i => ENNReal.toNNReal (f i)) (fun i => ENNReal.toNNReal (g i)) _
         hp)
-  push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this 
+  push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this
   convert this using 2 <;> [skip; congr 1; congr 1] <;>
     · apply Finset.sum_congr rfl fun i hi => _; simp [H'.1 i hi, H'.2 i hi]
 #align ennreal.Lp_add_le ENNReal.Lp_add_le

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

@@ -275,7 +275,7 @@ namespace Real
 #print Real.young_inequality_of_nonneg /-
 /-- Young's inequality, a version for nonnegative real numbers. -/
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
-    (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
+    (hpq : p.IsConjExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
   simpa [← rpow_mul, ha, hb, hpq.ne_zero, hpq.symm.ne_zero, div_eq_inv_mul] using
     geom_mean_le_arith_mean2_weighted hpq.one_div_nonneg hpq.symm.one_div_nonneg
       (rpow_nonneg_of_nonneg ha p) (rpow_nonneg_of_nonneg hb q) hpq.inv_add_inv_conj
@@ -284,7 +284,7 @@ theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
 
 #print Real.young_inequality /-
 /-- Young's inequality, a version for arbitrary real numbers. -/
-theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
   calc
     a * b ≤ |a * b| := le_abs_self (a * b)
@@ -309,7 +309,7 @@ theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 /
 
 #print NNReal.young_inequality_real /-
 /-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/
-theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ p / Real.toNNReal p + b ^ q / Real.toNNReal q :=
   by
   nth_rw 1 [← Real.coe_toNNReal p hpq.nonneg]
@@ -324,7 +324,7 @@ namespace ENNReal
 
 #print ENNReal.young_inequality /-
 /-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
-theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q :=
   by
   by_cases h : a = ⊤ ∨ b = ⊤
@@ -353,7 +353,7 @@ section HolderMinkowski
 namespace NNReal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p ≤ 1) (hg : ∑ i in s, g i ^ q ≤ 1) :
+    (hpq : p.IsConjExponent q) (hf : ∑ i in s, f i ^ p ≤ 1) (hg : ∑ i in s, g i ^ q ≤ 1) :
     ∑ i in s, f i * g i ≤ 1 :=
   by
   have hp_ne_zero : Real.toNNReal p ≠ 0 := (zero_lt_one.trans hpq.one_lt_nnreal).Ne.symm
@@ -371,7 +371,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
     _ = 1 := hpq.inv_add_inv_conj_nnreal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p = 0) :
+    (hpq : p.IsConjExponent q) (hf : ∑ i in s, f i ^ p = 0) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
   simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, MulZeroClass.zero_mul,
@@ -385,7 +385,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
-theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
   by_cases hF_zero : ∑ i in s, f i ^ p = 0
@@ -421,7 +421,7 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_has_sum`. -/
-theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
+theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
       ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
@@ -446,7 +446,7 @@ theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsCo
 -/
 
 #print NNReal.summable_mul_of_Lp_Lq /-
-theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
+theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).1
@@ -454,7 +454,7 @@ theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConj
 -/
 
 #print NNReal.inner_le_Lp_mul_Lq_tsum' /-
-theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
+theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
@@ -466,9 +466,9 @@ theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsC
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum`.  -/
-theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : HasSum (fun i => f i ^ p) (A ^ p))
-    (hg : HasSum (fun i => g i ^ q) (B ^ q)) : ∃ C, C ≤ A * B ∧ HasSum (fun i => f i * g i) C :=
+theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
+    (hf : HasSum (fun i => f i ^ p) (A ^ p)) (hg : HasSum (fun i => g i ^ q) (B ^ q)) :
+    ∃ C, C ≤ A * B ∧ HasSum (fun i => f i * g i) C :=
   by
   obtain ⟨H₁, H₂⟩ := inner_le_Lp_mul_Lq_tsum hpq hf.summable hg.summable
   have hA : A = (∑' i : ι, f i ^ p) ^ (1 / p) := by rw [hf.tsum_eq, rpow_inv_rpow_self hpq.ne_zero]
@@ -490,7 +490,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
   cases' eq_or_lt_of_le hp with hp hp
   · simp [← hp]
   let q : ℝ := p / (p - 1)
-  have hpq : p.is_conjugate_exponent q := by rw [Real.isConjugateExponent_iff hp]
+  have hpq : p.is_conjugate_exponent q := by rw [Real.isConjExponent_iff hp]
   have hp₁ : 1 / p * p = 1 := one_div_mul_cancel hpq.ne_zero
   have hq : 1 / q * p = p - 1 := by
     rw [← hpq.div_conj_eq_sub_one]
@@ -504,7 +504,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
 #print NNReal.isGreatest_Lp /-
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
 `∑ i in s, f i * g i` over functions `g` of `L_q` seminorm less than or equal to one. -/
-theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' {g | ∑ i in s, g i ^ q ≤ 1})
       ((∑ i in s, f i ^ p) ^ (1 / p)) :=
   by
@@ -539,7 +539,7 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
   -- The result is trivial when `p = 1`, so we can assume `1 < p`.
   rcases eq_or_lt_of_le hp with (rfl | hp);
   · simp [Finset.sum_add_distrib]
-  have hpq := Real.isConjugateExponent_conjugateExponent hp
+  have hpq := Real.IsConjExponent.conjExponent hp
   have := is_greatest_Lp s (f + g) hpq
   simp only [Pi.add_apply, add_mul, sum_add_distrib] at this 
   rcases this.1 with ⟨φ, hφ, H⟩
@@ -626,7 +626,7 @@ variable (f g : ι → ℝ) {p q : ℝ}
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
-theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
+theorem inner_le_Lp_mul_Lq (hpq : IsConjExponent p q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, |f i| ^ p) ^ (1 / p) * (∑ i in s, |g i| ^ q) ^ (1 / q) :=
   by
   have :=
@@ -677,7 +677,7 @@ variable {f g}
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued nonnegative functions. -/
-theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
+theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
     (hg : ∀ i ∈ s, 0 ≤ g i) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   convert inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
@@ -690,7 +690,7 @@ theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `ℝ`-valued functions.
 For an alternative version, convenient if the infinite sums are already expressed as `p`-th powers,
 see `inner_le_Lp_mul_Lq_has_sum_of_nonneg`. -/
-theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
+theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
       ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
@@ -703,7 +703,7 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
 -/
 
 #print Real.summable_mul_of_Lp_Lq_of_nonneg /-
-theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
+theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).1
@@ -711,7 +711,7 @@ theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : 
 -/
 
 #print Real.inner_le_Lp_mul_Lq_tsum_of_nonneg' /-
-theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
+theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
@@ -723,7 +723,7 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf :
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum_of_nonneg`.  -/
-theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B : ℝ} (hA : 0 ≤ A)
+theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjExponent q) {A B : ℝ} (hA : 0 ≤ A)
     (hB : 0 ≤ B) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : HasSum (fun i => f i ^ p) (A ^ p)) (hg_sum : HasSum (fun i => g i ^ q) (B ^ q)) :
     ∃ C : ℝ, 0 ≤ C ∧ C ≤ A * B ∧ HasSum (fun i => f i * g i) C :=
@@ -830,7 +830,7 @@ variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
-theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
+theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
   by_cases H : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0
@@ -870,7 +870,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   cases' eq_or_lt_of_le hp with hp hp
   · simp [← hp]
   let q : ℝ := p / (p - 1)
-  have hpq : p.is_conjugate_exponent q := by rw [Real.isConjugateExponent_iff hp]
+  have hpq : p.is_conjugate_exponent q := by rw [Real.isConjExponent_iff hp]
   have hp₁ : 1 / p * p = 1 := one_div_mul_cancel hpq.ne_zero
   have hq : 1 / q * p = p - 1 := by
     rw [← hpq.div_conj_eq_sub_one]

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

@@ -200,7 +200,7 @@ for two `nnreal` numbers. -/
 theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
     w₁ + w₂ = 1 → p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ := by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
-    Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one] using
+    Fintype.univ_ofIsEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one] using
     geom_mean_le_arith_mean_weighted univ ![w₁, w₂] ![p₁, p₂]
 #align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weighted
 -/
@@ -211,7 +211,7 @@ theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
   by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
-    Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
+    Fintype.univ_ofIsEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃] ![p₁, p₂, p₃]
 #align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weighted
 -/
@@ -223,7 +223,7 @@ theorem geom_mean_le_arith_mean4_weighted (w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
         w₁ * p₁ + w₂ * p₂ + w₃ * p₃ + w₄ * p₄ :=
   by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
-    Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
+    Fintype.univ_ofIsEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃, w₄] ![p₁, p₂, p₃, p₄]
 #align nnreal.geom_mean_le_arith_mean4_weighted NNReal.geom_mean_le_arith_mean4_weighted
 -/

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

@@ -236,7 +236,7 @@ namespace Real
 theorem geom_mean_le_arith_mean2_weighted {w₁ w₂ p₁ p₂ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hw : w₁ + w₂ = 1) : p₁ ^ w₁ * p₂ ^ w₂ ≤ w₁ * p₁ + w₂ * p₂ :=
   NNReal.geom_mean_le_arith_mean2_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩ <|
-    NNReal.coe_eq.1 <| by assumption
+    NNReal.coe_inj.1 <| by assumption
 #align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weighted
 -/
 
@@ -246,7 +246,7 @@ theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ}
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
   NNReal.geom_mean_le_arith_mean3_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨w₃, hw₃⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩
       ⟨p₃, hp₃⟩ <|
-    NNReal.coe_eq.1 hw
+    NNReal.coe_inj.1 hw
 #align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weighted
 -/
 
@@ -257,7 +257,7 @@ theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ * p₄ ^ w₄ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ + w₄ * p₄ :=
   NNReal.geom_mean_le_arith_mean4_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨w₃, hw₃⟩ ⟨w₄, hw₄⟩ ⟨p₁, hp₁⟩
       ⟨p₂, hp₂⟩ ⟨p₃, hp₃⟩ ⟨p₄, hp₄⟩ <|
-    NNReal.coe_eq.1 <| by assumption
+    NNReal.coe_inj.1 <| by assumption
 #align real.geom_mean_le_arith_mean4_weighted Real.geom_mean_le_arith_mean4_weighted
 -/
 
@@ -303,7 +303,7 @@ namespace NNReal
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
 theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 / p + 1 / q = 1) :
     a * b ≤ a ^ (p : ℝ) / p + b ^ (q : ℝ) / q :=
-  Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_eq.2 hpq⟩
+  Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_inj.2 hpq⟩
 #align nnreal.young_inequality NNReal.young_inequality
 -/
 

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

@@ -126,7 +126,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
   -- for `exp` and numbers `log (z i)` with weights `w i`.
   · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A 
     have := convex_on_exp.map_sum_le hw hw' fun i _ => Set.mem_univ <| log (z i)
-    simp only [exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this 
+    simp only [NormedSpace.exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this 
     convert this using 1 <;> [apply prod_congr rfl; apply sum_congr rfl] <;> intro i hi
     · cases' eq_or_lt_of_le (hz i hi) with hz hz
       · simp [A i hi hz.symm]

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.Data.Real.ConjugateExponents
+import Analysis.Convex.Jensen
+import Analysis.Convex.SpecificFunctions.Basic
+import Analysis.SpecialFunctions.Pow.Nnreal
+import Data.Real.ConjugateExponents
 
 #align_import analysis.mean_inequalities from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! 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.Data.Real.ConjugateExponents
 
+#align_import analysis.mean_inequalities from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Mean value inequalities
 

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

@@ -113,6 +113,7 @@ section GeomMeanLeArithMean
 
 namespace Real
 
+#print Real.geom_mean_le_arith_mean_weighted /-
 /-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**, weighted
 version for real-valued nonnegative functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
@@ -137,7 +138,9 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
       · simp [A i hi hz.symm]
       · rw [exp_log hz]
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
+-/
 
+#print Real.geom_mean_weighted_of_constant /-
 theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     ∏ i in s, z i ^ w i = x :=
@@ -155,7 +158,9 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
       rw [← hx i his hi]
       exact hz i his
 #align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constant
+-/
 
+#print Real.arith_mean_weighted_of_constant /-
 theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : ∑ i in s, w i = 1)
     (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : ∑ i in s, w i * z i = x :=
   calc
@@ -167,12 +172,15 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : ∑
       · rw [hx i hi hwi]
     _ = x := by rw [← sum_mul, hw', one_mul]
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
+-/
 
+#print Real.geom_mean_eq_arith_mean_weighted_of_constant /-
 theorem geom_mean_eq_arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     ∏ i in s, z i ^ w i = ∑ i in s, w i * z i := by
   rw [geom_mean_weighted_of_constant, arith_mean_weighted_of_constant] <;> assumption
 #align real.geom_mean_eq_arith_mean_weighted_of_constant Real.geom_mean_eq_arith_mean_weighted_of_constant
+-/
 
 end Real
 
@@ -189,6 +197,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : ∑ i in
 #align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weighted
 -/
 
+#print NNReal.geom_mean_le_arith_mean2_weighted /-
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for two `nnreal` numbers. -/
 theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
@@ -197,7 +206,9 @@ theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
     Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one] using
     geom_mean_le_arith_mean_weighted univ ![w₁, w₂] ![p₁, p₂]
 #align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weighted
+-/
 
+#print NNReal.geom_mean_le_arith_mean3_weighted /-
 theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ≥0) :
     w₁ + w₂ + w₃ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
@@ -206,7 +217,9 @@ theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ
     Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃] ![p₁, p₂, p₃]
 #align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weighted
+-/
 
+#print NNReal.geom_mean_le_arith_mean4_weighted /-
 theorem geom_mean_le_arith_mean4_weighted (w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ≥0) :
     w₁ + w₂ + w₃ + w₄ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) * p₄ ^ (w₄ : ℝ) ≤
@@ -216,17 +229,21 @@ theorem geom_mean_le_arith_mean4_weighted (w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
     Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃, w₄] ![p₁, p₂, p₃, p₄]
 #align nnreal.geom_mean_le_arith_mean4_weighted NNReal.geom_mean_le_arith_mean4_weighted
+-/
 
 end NNReal
 
 namespace Real
 
+#print Real.geom_mean_le_arith_mean2_weighted /-
 theorem geom_mean_le_arith_mean2_weighted {w₁ w₂ p₁ p₂ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hw : w₁ + w₂ = 1) : p₁ ^ w₁ * p₂ ^ w₂ ≤ w₁ * p₁ + w₂ * p₂ :=
   NNReal.geom_mean_le_arith_mean2_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩ <|
     NNReal.coe_eq.1 <| by assumption
 #align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weighted
+-/
 
+#print Real.geom_mean_le_arith_mean3_weighted /-
 theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hw₃ : 0 ≤ w₃) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃) (hw : w₁ + w₂ + w₃ = 1) :
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
@@ -234,7 +251,9 @@ theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ}
       ⟨p₃, hp₃⟩ <|
     NNReal.coe_eq.1 hw
 #align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weighted
+-/
 
+#print Real.geom_mean_le_arith_mean4_weighted /-
 theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ} (hw₁ : 0 ≤ w₁)
     (hw₂ : 0 ≤ w₂) (hw₃ : 0 ≤ w₃) (hw₄ : 0 ≤ w₄) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃)
     (hp₄ : 0 ≤ p₄) (hw : w₁ + w₂ + w₃ + w₄ = 1) :
@@ -243,6 +262,7 @@ theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
       ⟨p₂, hp₂⟩ ⟨p₃, hp₃⟩ ⟨p₄, hp₄⟩ <|
     NNReal.coe_eq.1 <| by assumption
 #align real.geom_mean_le_arith_mean4_weighted Real.geom_mean_le_arith_mean4_weighted
+-/
 
 end Real
 
@@ -255,6 +275,7 @@ section Young
 
 namespace Real
 
+#print Real.young_inequality_of_nonneg /-
 /-- Young's inequality, a version for nonnegative real numbers. -/
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
@@ -262,7 +283,9 @@ theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     geom_mean_le_arith_mean2_weighted hpq.one_div_nonneg hpq.symm.one_div_nonneg
       (rpow_nonneg_of_nonneg ha p) (rpow_nonneg_of_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
+-/
 
+#print Real.young_inequality /-
 /-- Young's inequality, a version for arbitrary real numbers. -/
 theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
@@ -272,18 +295,22 @@ theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q)
     _ ≤ |a| ^ p / p + |b| ^ q / q :=
       Real.young_inequality_of_nonneg (abs_nonneg a) (abs_nonneg b) hpq
 #align real.young_inequality Real.young_inequality
+-/
 
 end Real
 
 namespace NNReal
 
+#print NNReal.young_inequality /-
 /-- Young's inequality, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
 theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 / p + 1 / q = 1) :
     a * b ≤ a ^ (p : ℝ) / p + b ^ (q : ℝ) / q :=
   Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_eq.2 hpq⟩
 #align nnreal.young_inequality NNReal.young_inequality
+-/
 
+#print NNReal.young_inequality_real /-
 /-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/
 theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ a ^ p / Real.toNNReal p + b ^ q / Real.toNNReal q :=
@@ -292,11 +319,13 @@ theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateEx
   nth_rw 1 [← Real.coe_toNNReal q hpq.symm.nonneg]
   exact young_inequality a b hpq.one_lt_nnreal hpq.inv_add_inv_conj_nnreal
 #align nnreal.young_inequality_real NNReal.young_inequality_real
+-/
 
 end NNReal
 
 namespace ENNReal
 
+#print ENNReal.young_inequality /-
 /-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
 theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q :=
@@ -313,6 +342,7 @@ theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExpo
     @coe_div (Real.toNNReal q) _ (by simp [hpq.symm.pos]), ← coe_add, coe_le_coe]
   exact NNReal.young_inequality_real a.to_nnreal b.to_nnreal hpq
 #align ennreal.young_inequality ENNReal.young_inequality
+-/
 
 end ENNReal
 
@@ -354,6 +384,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
   rw [sum_eq_zero_iff] at hf 
   exact (rpow_eq_zero_iff.mp (hf i his)).left
 
+#print NNReal.inner_le_Lp_mul_Lq /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
@@ -386,7 +417,9 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
     simp_rw [g', div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.symm.ne_zero,
       rpow_one, div_self hG_zero]
 #align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lq
+-/
 
+#print NNReal.inner_le_Lp_mul_Lq_tsum /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
@@ -413,19 +446,25 @@ theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsCo
   have H₂ : Summable _ := (hasSum_of_isLUB _ (isLUB_ciSup bdd)).Summable
   exact ⟨H₂, tsum_le_of_sum_le H₂ H₁⟩
 #align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsum
+-/
 
+#print NNReal.summable_mul_of_Lp_Lq /-
 theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).1
 #align nnreal.summable_mul_of_Lp_Lq NNReal.summable_mul_of_Lp_Lq
+-/
 
+#print NNReal.inner_le_Lp_mul_Lq_tsum' /-
 theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
+-/
 
+#print NNReal.inner_le_Lp_mul_Lq_hasSum /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
@@ -442,7 +481,9 @@ theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q :
   · simpa [hA, hB] using H₂
   · simpa only [rpow_self_rpow_inv hpq.ne_zero] using H₁.has_sum
 #align nnreal.inner_le_Lp_mul_Lq_has_sum NNReal.inner_le_Lp_mul_Lq_hasSum
+-/
 
+#print NNReal.rpow_sum_le_const_mul_sum_rpow /-
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0`-valued functions.
 -/
@@ -461,6 +502,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
     Pi.one_apply, sum_const, Nat.smul_one_eq_coe] using
     NNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
 #align nnreal.rpow_sum_le_const_mul_sum_rpow NNReal.rpow_sum_le_const_mul_sum_rpow
+-/
 
 #print NNReal.isGreatest_Lp /-
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
@@ -490,6 +532,7 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExpon
 #align nnreal.is_greatest_Lp NNReal.isGreatest_Lp
 -/
 
+#print NNReal.Lp_add_le /-
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `nnreal`-valued functions. -/
 theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
@@ -507,7 +550,9 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
   exact
     add_le_add ((is_greatest_Lp s f hpq).2 ⟨φ, hφ, rfl⟩) ((is_greatest_Lp s g hpq).2 ⟨φ, hφ, rfl⟩)
 #align nnreal.Lp_add_le NNReal.Lp_add_le
+-/
 
+#print NNReal.Lp_add_le_tsum /-
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `nnreal`-valued functions. For an alternative version, convenient if the
@@ -538,18 +583,24 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
   rw [NNReal.rpow_one_div_le_iff Pos]
   refine' tsum_le_of_sum_le H₂ H₁
 #align nnreal.Lp_add_le_tsum NNReal.Lp_add_le_tsum
+-/
 
+#print NNReal.summable_Lp_add /-
 theorem summable_Lp_add {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)
     (hg : Summable fun i => g i ^ p) : Summable fun i => (f i + g i) ^ p :=
   (Lp_add_le_tsum hp hf hg).1
 #align nnreal.summable_Lp_add NNReal.summable_Lp_add
+-/
 
+#print NNReal.Lp_add_le_tsum' /-
 theorem Lp_add_le_tsum' {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)
     (hg : Summable fun i => g i ^ p) :
     (∑' i, (f i + g i) ^ p) ^ (1 / p) ≤ (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) :=
   (Lp_add_le_tsum hp hf hg).2
 #align nnreal.Lp_add_le_tsum' NNReal.Lp_add_le_tsum'
+-/
 
+#print NNReal.Lp_add_le_hasSum /-
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `nnreal`-valued functions. For an alternative version, convenient if the
@@ -566,6 +617,7 @@ theorem Lp_add_le_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p : ℝ} (hp :
   · simpa [hA, hB] using H₂
   · simpa only [rpow_self_rpow_inv hp'] using H₁.has_sum
 #align nnreal.Lp_add_le_has_sum NNReal.Lp_add_le_hasSum
+-/
 
 end NNReal
 
@@ -573,6 +625,7 @@ namespace Real
 
 variable (f g : ι → ℝ) {p q : ℝ}
 
+#print Real.inner_le_Lp_mul_Lq /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
@@ -587,7 +640,9 @@ theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
   refine' le_trans (sum_le_sum fun i hi => _) this
   simp only [← abs_mul, le_abs_self]
 #align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lq
+-/
 
+#print Real.rpow_sum_le_const_mul_sum_rpow /-
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ`-valued functions. -/
 theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
@@ -599,7 +654,9 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   push_cast at this 
   exact this
 #align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpow
+-/
 
+#print Real.Lp_add_le /-
 -- for some reason `exact_mod_cast` can't replace this argument
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `real`-valued functions. -/
@@ -615,9 +672,11 @@ theorem Lp_add_le (hp : 1 ≤ p) :
     simp [sum_nonneg, rpow_nonneg_of_nonneg, abs_nonneg, le_trans zero_le_one hp, abs_add,
       rpow_le_rpow]
 #align real.Lp_add_le Real.Lp_add_le
+-/
 
 variable {f g}
 
+#print Real.inner_le_Lp_mul_Lq_of_nonneg /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued nonnegative functions. -/
@@ -627,7 +686,9 @@ theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i
   convert inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 #align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonneg
+-/
 
+#print Real.inner_le_Lp_mul_Lq_tsum_of_nonneg /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `ℝ`-valued functions.
 For an alternative version, convenient if the infinite sums are already expressed as `p`-th powers,
@@ -642,19 +703,25 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
   norm_cast at *
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
+-/
 
+#print Real.summable_mul_of_Lp_Lq_of_nonneg /-
 theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).1
 #align real.summable_mul_of_Lp_Lq_of_nonneg Real.summable_mul_of_Lp_Lq_of_nonneg
+-/
 
+#print Real.inner_le_Lp_mul_Lq_tsum_of_nonneg' /-
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'
+-/
 
+#print Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
@@ -674,7 +741,9 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   norm_cast
   exact H
 #align real.inner_le_Lp_mul_Lq_has_sum_of_nonneg Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg
+-/
 
+#print Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg /-
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with nonnegative `ℝ`-valued
 functions. -/
@@ -683,7 +752,9 @@ theorem rpow_sum_le_const_mul_sum_rpow_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈
   convert rpow_sum_le_const_mul_sum_rpow s f hp using 2 <;> apply sum_congr rfl <;> intro i hi <;>
     simp only [abs_of_nonneg, hf i hi]
 #align real.rpow_sum_le_const_mul_sum_rpow_of_nonneg Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg
+-/
 
+#print Real.Lp_add_le_of_nonneg /-
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ`-valued nonnegative
 functions. -/
@@ -695,7 +766,9 @@ theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : 
       intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 #align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonneg
+-/
 
+#print Real.Lp_add_le_tsum_of_nonneg /-
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
@@ -710,19 +783,25 @@ theorem Lp_add_le_tsum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : 
   norm_cast at *
   exact NNReal.Lp_add_le_tsum hp hf_sum hg_sum
 #align real.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonneg
+-/
 
+#print Real.summable_Lp_add_of_nonneg /-
 theorem summable_Lp_add_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ p) :
     Summable fun i => (f i + g i) ^ p :=
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).1
 #align real.summable_Lp_add_of_nonneg Real.summable_Lp_add_of_nonneg
+-/
 
+#print Real.Lp_add_le_tsum_of_nonneg' /-
 theorem Lp_add_le_tsum_of_nonneg' (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ p) :
     (∑' i, (f i + g i) ^ p) ^ (1 / p) ≤ (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) :=
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).2
 #align real.Lp_add_le_tsum_of_nonneg' Real.Lp_add_le_tsum_of_nonneg'
+-/
 
+#print Real.Lp_add_le_hasSum_of_nonneg /-
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
@@ -742,6 +821,7 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
   norm_cast
   exact ⟨zero_le _, hC₁, hC₂⟩
 #align real.Lp_add_le_has_sum_of_nonneg Real.Lp_add_le_hasSum_of_nonneg
+-/
 
 end Real
 
@@ -749,6 +829,7 @@ namespace ENNReal
 
 variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 
+#print ENNReal.inner_le_Lp_mul_Lq /-
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
@@ -780,7 +861,9 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
     · apply Finset.sum_congr rfl fun i hi => _;
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
+-/
 
+#print ENNReal.rpow_sum_le_const_mul_sum_rpow /-
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0∞`-valued functions.
 -/
@@ -799,7 +882,9 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
     one_mul, one_rpow, rpow_one, Pi.one_apply, sum_const, Nat.smul_one_eq_coe] using
     ENNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
 #align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpow
+-/
 
+#print ENNReal.Lp_add_le /-
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ≥0∞` valued nonnegative
 functions. -/
@@ -820,6 +905,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
   convert this using 2 <;> [skip; congr 1; congr 1] <;>
     · apply Finset.sum_congr rfl fun i hi => _; simp [H'.1 i hi, H'.2 i hi]
 #align ennreal.Lp_add_le ENNReal.Lp_add_le
+-/
 
 end ENNReal
 

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

@@ -116,8 +116,7 @@ namespace Real
 /-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**, weighted
 version for real-valued nonnegative functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) :
-    (∏ i in s, z i ^ w i) ≤ ∑ i in s, w i * z i :=
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) : ∏ i in s, z i ^ w i ≤ ∑ i in s, w i * z i :=
   by
   -- If some number `z i` equals zero and has non-zero weight, then LHS is 0 and RHS is nonnegative.
   by_cases A : ∃ i ∈ s, z i = 0 ∧ w i ≠ 0
@@ -140,10 +139,10 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
 
 theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
-    (∏ i in s, z i ^ w i) = x :=
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
+    ∏ i in s, z i ^ w i = x :=
   calc
-    (∏ i in s, z i ^ w i) = ∏ i in s, x ^ w i :=
+    ∏ i in s, z i ^ w i = ∏ i in s, x ^ w i :=
       by
       refine' prod_congr rfl fun i hi => _
       cases' eq_or_ne (w i) 0 with h₀ h₀
@@ -151,16 +150,16 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
       · rw [hx i hi h₀]
     _ = x := by
       rw [← rpow_sum_of_nonneg _ hw, hw', rpow_one]
-      have : (∑ i in s, w i) ≠ 0 := by rw [hw']; exact one_ne_zero
+      have : ∑ i in s, w i ≠ 0 := by rw [hw']; exact one_ne_zero
       obtain ⟨i, his, hi⟩ := exists_ne_zero_of_sum_ne_zero this
       rw [← hx i his hi]
       exact hz i his
 #align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constant
 
-theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑ i in s, w i) = 1)
-    (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : (∑ i in s, w i * z i) = x :=
+theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : ∑ i in s, w i = 1)
+    (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : ∑ i in s, w i * z i = x :=
   calc
-    (∑ i in s, w i * z i) = ∑ i in s, w i * x :=
+    ∑ i in s, w i * z i = ∑ i in s, w i * x :=
       by
       refine' sum_congr rfl fun i hi => _
       cases' eq_or_ne (w i) 0 with hwi hwi
@@ -170,8 +169,8 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
 
 theorem geom_mean_eq_arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
-    (∏ i in s, z i ^ w i) = ∑ i in s, w i * z i := by
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
+    ∏ i in s, z i ^ w i = ∑ i in s, w i * z i := by
   rw [geom_mean_weighted_of_constant, arith_mean_weighted_of_constant] <;> assumption
 #align real.geom_mean_eq_arith_mean_weighted_of_constant Real.geom_mean_eq_arith_mean_weighted_of_constant
 
@@ -182,8 +181,8 @@ namespace NNReal
 #print NNReal.geom_mean_le_arith_mean_weighted /-
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for `nnreal`-valued functions. -/
-theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) :
-    (∏ i in s, z i ^ (w i : ℝ)) ≤ ∑ i in s, w i * z i := by
+theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) :
+    ∏ i in s, z i ^ (w i : ℝ) ≤ ∑ i in s, w i * z i := by
   exact_mod_cast
     Real.geom_mean_le_arith_mean_weighted _ _ _ (fun i _ => (w i).coe_nonneg)
       (by assumption_mod_cast) fun i _ => (z i).coe_nonneg
@@ -327,13 +326,13 @@ section HolderMinkowski
 namespace NNReal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) ≤ 1) (hg : (∑ i in s, g i ^ q) ≤ 1) :
-    (∑ i in s, f i * g i) ≤ 1 :=
+    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p ≤ 1) (hg : ∑ i in s, g i ^ q ≤ 1) :
+    ∑ i in s, f i * g i ≤ 1 :=
   by
   have hp_ne_zero : Real.toNNReal p ≠ 0 := (zero_lt_one.trans hpq.one_lt_nnreal).Ne.symm
   have hq_ne_zero : Real.toNNReal q ≠ 0 := (zero_lt_one.trans hpq.symm.one_lt_nnreal).Ne.symm
   calc
-    (∑ i in s, f i * g i) ≤ ∑ i in s, f i ^ p / Real.toNNReal p + g i ^ q / Real.toNNReal q :=
+    ∑ i in s, f i * g i ≤ ∑ i in s, (f i ^ p / Real.toNNReal p + g i ^ q / Real.toNNReal q) :=
       Finset.sum_le_sum fun i his => young_inequality_real (f i) (g i) hpq
     _ = (∑ i in s, f i ^ p) / Real.toNNReal p + (∑ i in s, g i ^ q) / Real.toNNReal q := by
       rw [sum_add_distrib, sum_div, sum_div]
@@ -345,8 +344,8 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
     _ = 1 := hpq.inv_add_inv_conj_nnreal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) = 0) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
+    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p = 0) :
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
   simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, MulZeroClass.zero_mul,
     inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
@@ -359,20 +358,20 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
-  by_cases hF_zero : (∑ i in s, f i ^ p) = 0
+  by_cases hF_zero : ∑ i in s, f i ^ p = 0
   · exact inner_le_Lp_mul_Lp_of_norm_eq_zero s f g hpq hF_zero
-  by_cases hG_zero : (∑ i in s, g i ^ q) = 0
+  by_cases hG_zero : ∑ i in s, g i ^ q = 0
   ·
     calc
-      (∑ i in s, f i * g i) = ∑ i in s, g i * f i := by congr with i; rw [mul_comm]
+      ∑ i in s, f i * g i = ∑ i in s, g i * f i := by congr with i; rw [mul_comm]
       _ ≤ (∑ i in s, g i ^ q) ^ (1 / q) * (∑ i in s, f i ^ p) ^ (1 / p) :=
         (inner_le_Lp_mul_Lp_of_norm_eq_zero s g f hpq.symm hG_zero)
       _ = (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := mul_comm _ _
   let f' i := f i / (∑ i in s, f i ^ p) ^ (1 / p)
   let g' i := g i / (∑ i in s, g i ^ q) ^ (1 / q)
-  suffices (∑ i in s, f' i * g' i) ≤ 1
+  suffices ∑ i in s, f' i * g' i ≤ 1
     by
     simp_rw [f', g', div_mul_div_comm, ← sum_div] at this 
     rwa [div_le_iff, one_mul] at this 
@@ -395,10 +394,10 @@ functions. For an alternative version, convenient if the infinite sums are alrea
 theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
-      (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+      ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   by
   have H₁ :
-    ∀ s : Finset ι, (∑ i in s, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+    ∀ s : Finset ι, ∑ i in s, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
     by
     intro s
     refine' le_trans (inner_le_Lp_mul_Lq s f g hpq) (mul_le_mul _ _ bot_le bot_le)
@@ -423,7 +422,7 @@ theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConj
 
 theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
-    (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+    ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
 
@@ -467,12 +466,12 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
 `∑ i in s, f i * g i` over functions `g` of `L_q` seminorm less than or equal to one. -/
 theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
-    IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' {g | (∑ i in s, g i ^ q) ≤ 1})
+    IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' {g | ∑ i in s, g i ^ q ≤ 1})
       ((∑ i in s, f i ^ p) ^ (1 / p)) :=
   by
   constructor
   · use fun i => f i ^ p / f i / (∑ i in s, f i ^ p) ^ (1 / q)
-    by_cases hf : (∑ i in s, f i ^ p) = 0
+    by_cases hf : ∑ i in s, f i ^ p = 0
     · simp [hf, hpq.ne_zero, hpq.symm.ne_zero]
     · have A : p + q - q ≠ 0 := by simp [hpq.ne_zero]
       have B : ∀ y : ℝ≥0, y * y ^ p / y = y ^ p :=
@@ -521,7 +520,7 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
   have pos : 0 < p := lt_of_lt_of_le zero_lt_one hp
   have H₁ :
     ∀ s : Finset ι,
-      (∑ i in s, (f i + g i) ^ p) ≤ ((∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p)) ^ p :=
+      ∑ i in s, (f i + g i) ^ p ≤ ((∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p)) ^ p :=
     by
     intro s
     rw [← NNReal.rpow_one_div_le_iff Pos]
@@ -578,7 +577,7 @@ variable (f g : ι → ℝ) {p q : ℝ}
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, |f i| ^ p) ^ (1 / p) * (∑ i in s, |g i| ^ q) ^ (1 / q) :=
+    ∑ i in s, f i * g i ≤ (∑ i in s, |f i| ^ p) ^ (1 / p) * (∑ i in s, |g i| ^ q) ^ (1 / q) :=
   by
   have :=
     NNReal.coe_le_coe.2
@@ -624,7 +623,7 @@ variable {f g}
 with real-valued nonnegative functions. -/
 theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
     (hg : ∀ i ∈ s, 0 ≤ g i) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   convert inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 #align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonneg
@@ -636,7 +635,7 @@ see `inner_le_Lp_mul_Lq_has_sum_of_nonneg`. -/
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
-      (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+      ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
@@ -652,7 +651,7 @@ theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : 
 
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
-    (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+    ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'
 
@@ -754,7 +753,7 @@ variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
   by_cases H : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0
   · replace H : (∀ i ∈ s, f i = 0) ∨ ∀ i ∈ s, g i = 0
@@ -762,7 +761,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
       simpa [ENNReal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
         sum_eq_zero_iff_of_nonneg] using H
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases H <;> simp [H i hi]
-    have : (∑ i in s, f i * g i) = ∑ i in s, 0 := sum_congr rfl this
+    have : ∑ i in s, f i * g i = ∑ i in s, 0 := sum_congr rfl this
     simp [this]
   push_neg at H 
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -155,7 +155,6 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
       obtain ⟨i, his, hi⟩ := exists_ne_zero_of_sum_ne_zero this
       rw [← hx i his hi]
       exact hz i his
-    
 #align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constant
 
 theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑ i in s, w i) = 1)
@@ -168,7 +167,6 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑
       · rw [hwi, MulZeroClass.zero_mul, MulZeroClass.zero_mul]
       · rw [hx i hi hwi]
     _ = x := by rw [← sum_mul, hw', one_mul]
-    
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
 
 theorem geom_mean_eq_arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
@@ -274,7 +272,6 @@ theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q)
     _ = |a| * |b| := (abs_mul a b)
     _ ≤ |a| ^ p / p + |b| ^ q / q :=
       Real.young_inequality_of_nonneg (abs_nonneg a) (abs_nonneg b) hpq
-    
 #align real.young_inequality Real.young_inequality
 
 end Real
@@ -346,7 +343,6 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
       · rwa [div_le_iff hp_ne_zero, div_mul_cancel _ hp_ne_zero]
       · rwa [div_le_iff hq_ne_zero, div_mul_cancel _ hq_ne_zero]
     _ = 1 := hpq.inv_add_inv_conj_nnreal
-    
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
     (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) = 0) :
@@ -374,7 +370,6 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
       _ ≤ (∑ i in s, g i ^ q) ^ (1 / q) * (∑ i in s, f i ^ p) ^ (1 / p) :=
         (inner_le_Lp_mul_Lp_of_norm_eq_zero s g f hpq.symm hG_zero)
       _ = (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := mul_comm _ _
-      
   let f' i := f i / (∑ i in s, f i ^ p) ^ (1 / p)
   let g' i := g i / (∑ i in s, g i ^ q) ^ (1 / q)
   suffices (∑ i in s, f' i * g' i) ≤ 1

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

@@ -309,7 +309,7 @@ theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExpo
   · refine' le_trans le_top (le_of_eq _)
     repeat' rw [div_eq_mul_inv]
     cases h <;> rw [h] <;> simp [h, hpq.pos, hpq.symm.pos]
-  push_neg  at h 
+  push_neg at h 
   -- if a ≠ ⊤ and b ≠ ⊤, use the nnreal version: nnreal.young_inequality_real
   rw [← coe_to_nnreal h.left, ← coe_to_nnreal h.right, ← coe_mul, coe_rpow_of_nonneg _ hpq.nonneg,
     coe_rpow_of_nonneg _ hpq.symm.nonneg, ENNReal.ofReal, ENNReal.ofReal, ←
@@ -472,7 +472,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
 `∑ i in s, f i * g i` over functions `g` of `L_q` seminorm less than or equal to one. -/
 theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
-    IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' { g | (∑ i in s, g i ^ q) ≤ 1 })
+    IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' {g | (∑ i in s, g i ^ q) ≤ 1})
       ((∑ i in s, f i ^ p) ^ (1 / p)) :=
   by
   constructor
@@ -645,7 +645,7 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
   by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
-  norm_cast  at *
+  norm_cast at *
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
 
@@ -674,7 +674,7 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast  at hf_sum hg_sum 
+  norm_cast at hf_sum hg_sum 
   obtain ⟨C, hC, H⟩ := NNReal.inner_le_Lp_mul_Lq_hasSum hpq hf_sum hg_sum
   refine' ⟨C, C.prop, hC, _⟩
   norm_cast
@@ -713,7 +713,7 @@ theorem Lp_add_le_tsum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : 
   by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
-  norm_cast  at *
+  norm_cast at *
   exact NNReal.Lp_add_le_tsum hp hf_sum hg_sum
 #align real.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonneg
 
@@ -742,7 +742,7 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast  at hfA hgB 
+  norm_cast at hfA hgB 
   obtain ⟨C, hC₁, hC₂⟩ := NNReal.Lp_add_le_hasSum hp hfA hgB
   use C
   norm_cast
@@ -769,7 +769,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases H <;> simp [H i hi]
     have : (∑ i in s, f i * g i) = ∑ i in s, 0 := sum_congr rfl this
     simp [this]
-  push_neg  at H 
+  push_neg at H 
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤
   · cases H' <;> simp [H', -one_div, H]
   replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤

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

@@ -127,10 +127,10 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
     · rw [hzi]; exact zero_rpow hwi
   -- If all numbers `z i` with non-zero weight are positive, then we apply Jensen's inequality
   -- for `exp` and numbers `log (z i)` with weights `w i`.
-  · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A
+  · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A 
     have := convex_on_exp.map_sum_le hw hw' fun i _ => Set.mem_univ <| log (z i)
-    simp only [exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this
-    convert this using 1 <;> [apply prod_congr rfl;apply sum_congr rfl] <;> intro i hi
+    simp only [exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this 
+    convert this using 1 <;> [apply prod_congr rfl; apply sum_congr rfl] <;> intro i hi
     · cases' eq_or_lt_of_le (hz i hi) with hz hz
       · simp [A i hi hz.symm]
       · exact rpow_def_of_pos hz _
@@ -309,7 +309,7 @@ theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExpo
   · refine' le_trans le_top (le_of_eq _)
     repeat' rw [div_eq_mul_inv]
     cases h <;> rw [h] <;> simp [h, hpq.pos, hpq.symm.pos]
-  push_neg  at h
+  push_neg  at h 
   -- if a ≠ ⊤ and b ≠ ⊤, use the nnreal version: nnreal.young_inequality_real
   rw [← coe_to_nnreal h.left, ← coe_to_nnreal h.right, ← coe_mul, coe_rpow_of_nonneg _ hpq.nonneg,
     coe_rpow_of_nonneg _ hpq.symm.nonneg, ENNReal.ofReal, ENNReal.ofReal, ←
@@ -356,7 +356,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
     inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
   intro i his
   left
-  rw [sum_eq_zero_iff] at hf
+  rw [sum_eq_zero_iff] at hf 
   exact (rpow_eq_zero_iff.mp (hf i his)).left
 
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
@@ -379,8 +379,8 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
   let g' i := g i / (∑ i in s, g i ^ q) ^ (1 / q)
   suffices (∑ i in s, f' i * g' i) ≤ 1
     by
-    simp_rw [f', g', div_mul_div_comm, ← sum_div] at this
-    rwa [div_le_iff, one_mul] at this
+    simp_rw [f', g', div_mul_div_comm, ← sum_div] at this 
+    rwa [div_le_iff, one_mul] at this 
     refine' mul_ne_zero _ _
     · rw [Ne.def, rpow_eq_zero_iff, not_and_or]; exact Or.inl hF_zero
     · rw [Ne.def, rpow_eq_zero_iff, not_and_or]; exact Or.inl hG_zero
@@ -507,7 +507,7 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
   · simp [Finset.sum_add_distrib]
   have hpq := Real.isConjugateExponent_conjugateExponent hp
   have := is_greatest_Lp s (f + g) hpq
-  simp only [Pi.add_apply, add_mul, sum_add_distrib] at this
+  simp only [Pi.add_apply, add_mul, sum_add_distrib] at this 
   rcases this.1 with ⟨φ, hφ, H⟩
   rw [← H]
   exact
@@ -533,7 +533,7 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
     refine' le_trans (Lp_add_le s f g hp) (add_le_add _ _) <;>
         rw [NNReal.rpow_le_rpow_iff (one_div_pos.mpr Pos)] <;>
       refine' sum_le_tsum _ (fun _ _ => zero_le _) _
-    exacts[hf, hg]
+    exacts [hf, hg]
   have bdd : BddAbove (Set.range fun s => ∑ i in s, (f i + g i) ^ p) :=
     by
     refine' ⟨((∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p)) ^ p, _⟩
@@ -589,7 +589,7 @@ theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
     NNReal.coe_le_coe.2
       (NNReal.inner_le_Lp_mul_Lq s (fun i => ⟨_, abs_nonneg (f i)⟩) (fun i => ⟨_, abs_nonneg (g i)⟩)
         hpq)
-  push_cast at this
+  push_cast at this 
   refine' le_trans (sum_le_sum fun i hi => _) this
   simp only [← abs_mul, le_abs_self]
 #align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lq
@@ -602,7 +602,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   have :=
     NNReal.coe_le_coe.2
       (NNReal.rpow_sum_le_const_mul_sum_rpow s (fun i => ⟨_, abs_nonneg (f i)⟩) hp)
-  push_cast at this
+  push_cast at this 
   exact this
 #align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpow
 
@@ -616,7 +616,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
   have :=
     NNReal.coe_le_coe.2
       (NNReal.Lp_add_le s (fun i => ⟨_, abs_nonneg (f i)⟩) (fun i => ⟨_, abs_nonneg (g i)⟩) hp)
-  push_cast at this
+  push_cast at this 
   refine' le_trans (rpow_le_rpow _ (sum_le_sum fun i hi => _) _) this <;>
     simp [sum_nonneg, rpow_nonneg_of_nonneg, abs_nonneg, le_trans zero_le_one hp, abs_add,
       rpow_le_rpow]
@@ -674,7 +674,7 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast  at hf_sum hg_sum
+  norm_cast  at hf_sum hg_sum 
   obtain ⟨C, hC, H⟩ := NNReal.inner_le_Lp_mul_Lq_hasSum hpq hf_sum hg_sum
   refine' ⟨C, C.prop, hC, _⟩
   norm_cast
@@ -697,7 +697,7 @@ theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : 
     (∑ i in s, (f i + g i) ^ p) ^ (1 / p) ≤
       (∑ i in s, f i ^ p) ^ (1 / p) + (∑ i in s, g i ^ p) ^ (1 / p) :=
   by
-  convert Lp_add_le s f g hp using 2 <;> [skip;congr 1;congr 1] <;> apply sum_congr rfl <;>
+  convert Lp_add_le s f g hp using 2 <;> [skip; congr 1; congr 1] <;> apply sum_congr rfl <;>
       intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 #align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonneg
@@ -742,7 +742,7 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast  at hfA hgB
+  norm_cast  at hfA hgB 
   obtain ⟨C, hC₁, hC₂⟩ := NNReal.Lp_add_le_hasSum hp hfA hgB
   use C
   norm_cast
@@ -769,7 +769,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases H <;> simp [H i hi]
     have : (∑ i in s, f i * g i) = ∑ i in s, 0 := sum_congr rfl this
     simp [this]
-  push_neg  at H
+  push_neg  at H 
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤
   · cases H' <;> simp [H', -one_div, H]
   replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤
@@ -781,8 +781,8 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
       (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => ENNReal.toNNReal (f i))
         (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
   simp [← ENNReal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
-    le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
-  convert this using 1 <;> [skip;congr 2] <;> [skip;skip;simp;skip;simp] <;>
+    le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this 
+  convert this using 1 <;> [skip; congr 2] <;> [skip; skip; simp; skip; simp] <;>
     · apply Finset.sum_congr rfl fun i hi => _;
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
@@ -822,8 +822,8 @@ theorem Lp_add_le (hp : 1 ≤ p) :
     ENNReal.coe_le_coe.2
       (@NNReal.Lp_add_le _ s (fun i => ENNReal.toNNReal (f i)) (fun i => ENNReal.toNNReal (g i)) _
         hp)
-  push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this
-  convert this using 2 <;> [skip;congr 1;congr 1] <;>
+  push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this 
+  convert this using 2 <;> [skip; congr 1; congr 1] <;>
     · apply Finset.sum_congr rfl fun i hi => _; simp [H'.1 i hi, H'.2 i hi]
 #align ennreal.Lp_add_le ENNReal.Lp_add_le
 

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

@@ -100,7 +100,7 @@ universe u v
 
 open Finset
 
-open Classical BigOperators NNReal ENNReal
+open scoped Classical BigOperators NNReal ENNReal
 
 noncomputable section
 
@@ -181,6 +181,7 @@ end Real
 
 namespace NNReal
 
+#print NNReal.geom_mean_le_arith_mean_weighted /-
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for `nnreal`-valued functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) :
@@ -189,6 +190,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in
     Real.geom_mean_le_arith_mean_weighted _ _ _ (fun i _ => (w i).coe_nonneg)
       (by assumption_mod_cast) fun i _ => (z i).coe_nonneg
 #align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weighted
+-/
 
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for two `nnreal` numbers. -/

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

@@ -113,12 +113,6 @@ section GeomMeanLeArithMean
 
 namespace Real
 
-/- warning: real.geom_mean_le_arith_mean_weighted -> Real.geom_mean_le_arith_mean_weighted 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))) -> (LE.le.{0} Real Real.hasLe (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) (w i))) (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))))
-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))) -> (LE.le.{0} Real Real.instLEReal (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) (w i))) (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))))
-Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weightedₓ'. -/
 /-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**, weighted
 version for real-valued nonnegative functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
@@ -145,12 +139,6 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
       · rw [exp_log hz]
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
 
-/- warning: real.geom_mean_weighted_of_constant -> Real.geom_mean_weighted_of_constant is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) (w i))) x)
-but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) (w i))) x)
-Case conversion may be inaccurate. Consider using '#align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constantₓ'. -/
 theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     (∏ i in s, z i ^ w i) = x :=
@@ -170,12 +158,6 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
     
 #align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constant
 
-/- warning: real.arith_mean_weighted_of_constant -> Real.arith_mean_weighted_of_constant is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : Real), (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) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (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))) x)
-but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : Real), (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) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (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))) x)
-Case conversion may be inaccurate. Consider using '#align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constantₓ'. -/
 theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑ i in s, w i) = 1)
     (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : (∑ i in s, w i * z i) = x :=
   calc
@@ -189,12 +171,6 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑
     
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
 
-/- warning: real.geom_mean_eq_arith_mean_weighted_of_constant -> Real.geom_mean_eq_arith_mean_weighted_of_constant is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) (w i))) (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))))
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) (w i))) (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))))
-Case conversion may be inaccurate. Consider using '#align real.geom_mean_eq_arith_mean_weighted_of_constant Real.geom_mean_eq_arith_mean_weighted_of_constantₓ'. -/
 theorem geom_mean_eq_arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     (∏ i in s, z i ^ w i) = ∑ i in s, w i * z i := by
@@ -205,12 +181,6 @@ end Real
 
 namespace NNReal
 
-/- warning: nnreal.geom_mean_le_arith_mean_weighted -> NNReal.geom_mean_le_arith_mean_weighted 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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Finset.prod.{0, u1} NNReal ι (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (z i) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) (w i)))) (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))))
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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))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Finset.prod.{0, u1} NNReal ι (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (z i) (NNReal.toReal (w i)))) (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))))
-Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weightedₓ'. -/
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for `nnreal`-valued functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) :
@@ -220,12 +190,6 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in
       (by assumption_mod_cast) fun i _ => (z i).coe_nonneg
 #align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weighted
 
-/- warning: nnreal.geom_mean_le_arith_mean2_weighted -> NNReal.geom_mean_le_arith_mean2_weighted is a dubious translation:
-lean 3 declaration is
-  forall (w₁ : NNReal) (w₂ : NNReal) (p₁ : NNReal) (p₂ : 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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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) p₁ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₂ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₂))) (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 p₁) (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 p₂)))
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-  forall (w₁ : NNReal) (w₂ : NNReal) (p₁ : NNReal) (p₂ : 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))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (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) p₁ (NNReal.toReal w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₂ (NNReal.toReal w₂))) (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 p₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ p₂)))
-Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weightedₓ'. -/
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for two `nnreal` numbers. -/
 theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
@@ -235,12 +199,6 @@ theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
     geom_mean_le_arith_mean_weighted univ ![w₁, w₂] ![p₁, p₂]
 #align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weighted
 
-/- warning: nnreal.geom_mean_le_arith_mean3_weighted -> NNReal.geom_mean_le_arith_mean3_weighted is a dubious translation:
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-  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : 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))))) (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) w₃) (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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) (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) p₁ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₂ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₃ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₃))) (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))))) (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 p₁) (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 p₂)) (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))))) w₃ p₃)))
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-  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : 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))))) (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) w₃) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (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) p₁ (NNReal.toReal w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₂ (NNReal.toReal w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₃ (NNReal.toReal w₃))) (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))))) (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 p₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ p₂)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₃ p₃)))
-Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weightedₓ'. -/
 theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ≥0) :
     w₁ + w₂ + w₃ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
@@ -250,12 +208,6 @@ theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃] ![p₁, p₂, p₃]
 #align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weighted
 
-/- warning: nnreal.geom_mean_le_arith_mean4_weighted -> NNReal.geom_mean_le_arith_mean4_weighted is a dubious translation:
-lean 3 declaration is
-  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (w₄ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : NNReal) (p₄ : 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))))) (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))))) (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) w₃) w₄) (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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) (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))))) (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) p₁ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₂ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₃ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₃))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₄))) (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))))) (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))))) (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 p₁) (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 p₂)) (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))))) w₃ p₃)) (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))))) w₄ p₄)))
-but is expected to have type
-  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (w₄ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : NNReal) (p₄ : 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))))) (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))))) (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) w₃) w₄) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (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) p₁ (NNReal.toReal w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₂ (NNReal.toReal w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₃ (NNReal.toReal w₃))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₄ (NNReal.toReal w₄))) (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))))) (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))))) (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 p₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ p₂)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₃ p₃)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₄ p₄)))
-Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean4_weighted NNReal.geom_mean_le_arith_mean4_weightedₓ'. -/
 theorem geom_mean_le_arith_mean4_weighted (w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ≥0) :
     w₁ + w₂ + w₃ + w₄ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) * p₄ ^ (w₄ : ℝ) ≤
@@ -270,24 +222,12 @@ end NNReal
 
 namespace Real
 
-/- warning: real.geom_mean_le_arith_mean2_weighted -> Real.geom_mean_le_arith_mean2_weighted is a dubious translation:
-lean 3 declaration is
-  forall {w₁ : Real} {w₂ : Real} {p₁ : Real} {p₂ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₂) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) w₁ w₂) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₂ w₂)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₂ p₂)))
-but is expected to have type
-  forall {w₁ : Real} {w₂ : Real} {p₁ : Real} {p₂ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₂) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) w₁ w₂) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₂ w₂)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₂ p₂)))
-Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weightedₓ'. -/
 theorem geom_mean_le_arith_mean2_weighted {w₁ w₂ p₁ p₂ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hw : w₁ + w₂ = 1) : p₁ ^ w₁ * p₂ ^ w₂ ≤ w₁ * p₁ + w₂ * p₂ :=
   NNReal.geom_mean_le_arith_mean2_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩ <|
     NNReal.coe_eq.1 <| by assumption
 #align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weighted
 
-/- warning: real.geom_mean_le_arith_mean3_weighted -> Real.geom_mean_le_arith_mean3_weighted is a dubious translation:
-lean 3 declaration is
-  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₃) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₃) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) w₁ w₂) w₃) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₃ w₃)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₃ p₃)))
-but is expected to have type
-  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₃) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₃) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) w₁ w₂) w₃) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₃ w₃)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₃ p₃)))
-Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weightedₓ'. -/
 theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hw₃ : 0 ≤ w₃) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃) (hw : w₁ + w₂ + w₃ = 1) :
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
@@ -296,9 +236,6 @@ theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ}
     NNReal.coe_eq.1 hw
 #align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weighted
 
-/- warning: real.geom_mean_le_arith_mean4_weighted -> Real.geom_mean_le_arith_mean4_weighted is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean4_weighted Real.geom_mean_le_arith_mean4_weightedₓ'. -/
 theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ} (hw₁ : 0 ≤ w₁)
     (hw₂ : 0 ≤ w₂) (hw₃ : 0 ≤ w₃) (hw₄ : 0 ≤ w₄) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃)
     (hp₄ : 0 ≤ p₄) (hw : w₁ + w₂ + w₃ + w₄ = 1) :
@@ -319,12 +256,6 @@ section Young
 
 namespace Real
 
-/- warning: real.young_inequality_of_nonneg -> Real.young_inequality_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {a : Real} {b : Real} {p : Real} {q : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) b) -> (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) a p) p) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) b q) q)))
-but is expected to have type
-  forall {a : Real} {b : Real} {p : Real} {q : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) b) -> (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) a p) p) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) b q) q)))
-Case conversion may be inaccurate. Consider using '#align real.young_inequality_of_nonneg Real.young_inequality_of_nonnegₓ'. -/
 /-- Young's inequality, a version for nonnegative real numbers. -/
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
@@ -333,12 +264,6 @@ theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
       (rpow_nonneg_of_nonneg ha p) (rpow_nonneg_of_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
 
-/- warning: real.young_inequality -> Real.young_inequality is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (b : Real) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) a) p) p) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) b) q) q)))
-but is expected to have type
-  forall (a : Real) (b : Real) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) a) p) p) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) b) q) q)))
-Case conversion may be inaccurate. Consider using '#align real.young_inequality Real.young_inequalityₓ'. -/
 /-- Young's inequality, a version for arbitrary real numbers. -/
 theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
@@ -354,12 +279,6 @@ end Real
 
 namespace NNReal
 
-/- warning: nnreal.young_inequality -> NNReal.young_inequality is a dubious translation:
-lean 3 declaration is
-  forall (a : NNReal) (b : NNReal) {p : NNReal} {q : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))))) p) -> (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))))) p) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))))) q)) (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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) p)) p) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) q)) q)))
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-Case conversion may be inaccurate. Consider using '#align nnreal.young_inequality NNReal.young_inequalityₓ'. -/
 /-- Young's inequality, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
 theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 / p + 1 / q = 1) :
@@ -367,12 +286,6 @@ theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 /
   Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_eq.2 hpq⟩
 #align nnreal.young_inequality NNReal.young_inequality
 
-/- warning: nnreal.young_inequality_real -> NNReal.young_inequality_real is a dubious translation:
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-  forall (a : NNReal) (b : NNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (Real.toNNReal p)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b q) (Real.toNNReal q))))
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-  forall (a : NNReal) (b : NNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (Real.toNNReal p)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b q) (Real.toNNReal q))))
-Case conversion may be inaccurate. Consider using '#align nnreal.young_inequality_real NNReal.young_inequality_realₓ'. -/
 /-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/
 theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ a ^ p / Real.toNNReal p + b ^ q / Real.toNNReal q :=
@@ -386,12 +299,6 @@ end NNReal
 
 namespace ENNReal
 
-/- warning: ennreal.young_inequality -> ENNReal.young_inequality is a dubious translation:
-lean 3 declaration is
-  forall (a : ENNReal) (b : ENNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent 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))))) (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)))))))) a b) (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)))))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a p) (ENNReal.ofReal p)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b q) (ENNReal.ofReal q))))
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-  forall (a : ENNReal) (b : ENNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent 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))))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) a b) (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)))))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a p) (ENNReal.ofReal p)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b q) (ENNReal.ofReal q))))
-Case conversion may be inaccurate. Consider using '#align ennreal.young_inequality ENNReal.young_inequalityₓ'. -/
 /-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
 theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q :=
@@ -450,12 +357,6 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
   rw [sum_eq_zero_iff] at hf
   exact (rpow_eq_zero_iff.mp (hf i his)).left
 
-/- warning: nnreal.inner_le_Lp_mul_Lq -> NNReal.inner_le_Lp_mul_Lq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lqₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
@@ -490,12 +391,6 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
       rpow_one, div_self hG_zero]
 #align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lq
 
-/- warning: nnreal.inner_le_Lp_mul_Lq_tsum -> NNReal.inner_le_Lp_mul_Lq_tsum is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (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))))) (f i) (g i))) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (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))))) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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)))))
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-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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)))))
-Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsumₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
@@ -523,36 +418,18 @@ theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsCo
   exact ⟨H₂, tsum_le_of_sum_le H₂ H₁⟩
 #align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsum
 
-/- warning: nnreal.summable_mul_of_Lp_Lq -> NNReal.summable_mul_of_Lp_Lq is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (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))))) (f i) (g i)))
-but is expected to have type
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.summable_mul_of_Lp_Lq NNReal.summable_mul_of_Lp_Lqₓ'. -/
 theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).1
 #align nnreal.summable_mul_of_Lp_Lq NNReal.summable_mul_of_Lp_Lq
 
-/- warning: nnreal.inner_le_Lp_mul_Lq_tsum' -> NNReal.inner_le_Lp_mul_Lq_tsum' is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (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))))) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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))))
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-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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))))
-Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'ₓ'. -/
 theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
 
-/- warning: nnreal.inner_le_Lp_mul_Lq_has_sum -> NNReal.inner_le_Lp_mul_Lq_hasSum is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {A : NNReal} {B : NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) A p)) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) B q)) -> (Exists.{1} NNReal (fun (C : NNReal) => And (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) C (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))))) A B)) (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (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))))) (f i) (g i)) C)))
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-Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq_has_sum NNReal.inner_le_Lp_mul_Lq_hasSumₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
@@ -570,12 +447,6 @@ theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q :
   · simpa only [rpow_self_rpow_inv hpq.ne_zero] using H₁.has_sum
 #align nnreal.inner_le_Lp_mul_Lq_has_sum NNReal.inner_le_Lp_mul_Lq_hasSum
 
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-Case conversion may be inaccurate. Consider using '#align nnreal.rpow_sum_le_const_mul_sum_rpow NNReal.rpow_sum_le_const_mul_sum_rpowₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0`-valued functions.
 -/
@@ -623,12 +494,6 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExpon
 #align nnreal.is_greatest_Lp NNReal.isGreatest_Lp
 -/
 
-/- warning: nnreal.Lp_add_le -> NNReal.Lp_add_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.Lp_add_le NNReal.Lp_add_leₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `nnreal`-valued functions. -/
 theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
@@ -647,12 +512,6 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     add_le_add ((is_greatest_Lp s f hpq).2 ⟨φ, hφ, rfl⟩) ((is_greatest_Lp s g hpq).2 ⟨φ, hφ, rfl⟩)
 #align nnreal.Lp_add_le NNReal.Lp_add_le
 
-/- warning: nnreal.Lp_add_le_tsum -> NNReal.Lp_add_le_tsum is a dubious translation:
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-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> 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) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) p)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => 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))))) (f i) (g i)) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g 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)))))
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-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) p)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => 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))))) (f i) (g i)) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g 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.Lp_add_le_tsum NNReal.Lp_add_le_tsumₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `nnreal`-valued functions. For an alternative version, convenient if the
@@ -684,35 +543,17 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
   refine' tsum_le_of_sum_le H₂ H₁
 #align nnreal.Lp_add_le_tsum NNReal.Lp_add_le_tsum
 
-/- warning: nnreal.summable_Lp_add -> NNReal.summable_Lp_add is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> 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) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => 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))))) (f i) (g i)) p))
-but is expected to have type
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => 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))))) (f i) (g i)) p))
-Case conversion may be inaccurate. Consider using '#align nnreal.summable_Lp_add NNReal.summable_Lp_addₓ'. -/
 theorem summable_Lp_add {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)
     (hg : Summable fun i => g i ^ p) : Summable fun i => (f i + g i) ^ p :=
   (Lp_add_le_tsum hp hf hg).1
 #align nnreal.summable_Lp_add NNReal.summable_Lp_add
 
-/- warning: nnreal.Lp_add_le_tsum' -> NNReal.Lp_add_le_tsum' is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> 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) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g 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}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g 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.Lp_add_le_tsum' NNReal.Lp_add_le_tsum'ₓ'. -/
 theorem Lp_add_le_tsum' {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)
     (hg : Summable fun i => g i ^ p) :
     (∑' i, (f i + g i) ^ p) ^ (1 / p) ≤ (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) :=
   (Lp_add_le_tsum hp hf hg).2
 #align nnreal.Lp_add_le_tsum' NNReal.Lp_add_le_tsum'
 
-/- warning: nnreal.Lp_add_le_has_sum -> NNReal.Lp_add_le_hasSum is a dubious translation:
-lean 3 declaration is
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-  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {A : NNReal} {B : NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) A p)) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) B p)) -> (Exists.{1} NNReal (fun (C : NNReal) => And (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) C (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)) (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => 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))))) (f i) (g i)) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) C p))))
-Case conversion may be inaccurate. Consider using '#align nnreal.Lp_add_le_has_sum NNReal.Lp_add_le_hasSumₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `nnreal`-valued functions. For an alternative version, convenient if the
@@ -736,12 +577,6 @@ namespace Real
 
 variable (f g : ι → ℝ) {p q : ℝ}
 
-/- warning: real.inner_le_Lp_mul_Lq -> Real.inner_le_Lp_mul_Lq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lqₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
@@ -757,12 +592,6 @@ theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
   simp only [← abs_mul, le_abs_self]
 #align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lq
 
-/- warning: real.rpow_sum_le_const_mul_sum_rpow -> Real.rpow_sum_le_const_mul_sum_rpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpowₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ`-valued functions. -/
 theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
@@ -775,12 +604,6 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   exact this
 #align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpow
 
-/- warning: real.Lp_add_le -> Real.Lp_add_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.Lp_add_le Real.Lp_add_leₓ'. -/
 -- for some reason `exact_mod_cast` can't replace this argument
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `real`-valued functions. -/
@@ -799,12 +622,6 @@ theorem Lp_add_le (hp : 1 ≤ p) :
 
 variable {f g}
 
-/- warning: real.inner_le_Lp_mul_Lq_of_nonneg -> Real.inner_le_Lp_mul_Lq_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonnegₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued nonnegative functions. -/
@@ -815,12 +632,6 @@ theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 #align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonnegₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `ℝ`-valued functions.
 For an alternative version, convenient if the infinite sums are already expressed as `p`-th powers,
@@ -836,36 +647,18 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align real.summable_mul_of_Lp_Lq_of_nonneg Real.summable_mul_of_Lp_Lq_of_nonnegₓ'. -/
 theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).1
 #align real.summable_mul_of_Lp_Lq_of_nonneg Real.summable_mul_of_Lp_Lq_of_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'ₓ'. -/
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'
 
-/- warning: real.inner_le_Lp_mul_Lq_has_sum_of_nonneg -> Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg is a dubious translation:
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-  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall {A : Real} {B : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) A) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) B) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) A p)) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) q) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) B q)) -> (Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (And (LE.le.{0} Real Real.instLEReal C (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) A B)) (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) (g i)) C)))))
-Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_has_sum_of_nonneg Real.inner_le_Lp_mul_Lq_hasSum_of_nonnegₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
@@ -886,12 +679,6 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   exact H
 #align real.inner_le_Lp_mul_Lq_has_sum_of_nonneg Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg
 
-/- warning: real.rpow_sum_le_const_mul_sum_rpow_of_nonneg -> Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.rpow_sum_le_const_mul_sum_rpow_of_nonneg Real.rpow_sum_le_const_mul_sum_rpow_of_nonnegₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with nonnegative `ℝ`-valued
 functions. -/
@@ -901,12 +688,6 @@ theorem rpow_sum_le_const_mul_sum_rpow_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈
     simp only [abs_of_nonneg, hf i hi]
 #align real.rpow_sum_le_const_mul_sum_rpow_of_nonneg Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg
 
-/- warning: real.Lp_add_le_of_nonneg -> Real.Lp_add_le_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonnegₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ`-valued nonnegative
 functions. -/
@@ -919,12 +700,6 @@ theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : 
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 #align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align real.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonnegₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
@@ -940,36 +715,18 @@ theorem Lp_add_le_tsum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : 
   exact NNReal.Lp_add_le_tsum hp hf_sum hg_sum
 #align real.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonneg
 
-/- warning: real.summable_Lp_add_of_nonneg -> Real.summable_Lp_add_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.summable_Lp_add_of_nonneg Real.summable_Lp_add_of_nonnegₓ'. -/
 theorem summable_Lp_add_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ p) :
     Summable fun i => (f i + g i) ^ p :=
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).1
 #align real.summable_Lp_add_of_nonneg Real.summable_Lp_add_of_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align real.Lp_add_le_tsum_of_nonneg' Real.Lp_add_le_tsum_of_nonneg'ₓ'. -/
 theorem Lp_add_le_tsum_of_nonneg' (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ p) :
     (∑' i, (f i + g i) ^ p) ^ (1 / p) ≤ (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) :=
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).2
 #align real.Lp_add_le_tsum_of_nonneg' Real.Lp_add_le_tsum_of_nonneg'
 
-/- warning: real.Lp_add_le_has_sum_of_nonneg -> Real.Lp_add_le_hasSum_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.Lp_add_le_has_sum_of_nonneg Real.Lp_add_le_hasSum_of_nonnegₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
@@ -996,12 +753,6 @@ namespace ENNReal
 
 variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 
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-Case conversion may be inaccurate. Consider using '#align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lqₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
@@ -1034,12 +785,6 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
 
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-Case conversion may be inaccurate. Consider using '#align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpowₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0∞`-valued functions.
 -/
@@ -1059,12 +804,6 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
     ENNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
 #align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpow
 
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> ENNReal) (g : ι -> 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) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => 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)))))))) (f i) (g 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)) (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) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (g 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 ennreal.Lp_add_le ENNReal.Lp_add_leₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ≥0∞` valued nonnegative
 functions. -/

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

@@ -130,8 +130,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
   · rcases A with ⟨i, his, hzi, hwi⟩
     rw [prod_eq_zero his]
     · exact sum_nonneg fun j hj => mul_nonneg (hw j hj) (hz j hj)
-    · rw [hzi]
-      exact zero_rpow hwi
+    · rw [hzi]; exact zero_rpow hwi
   -- If all numbers `z i` with non-zero weight are positive, then we apply Jensen's inequality
   -- for `exp` and numbers `log (z i)` with weights `w i`.
   · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A
@@ -164,9 +163,7 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
       · rw [hx i hi h₀]
     _ = x := by
       rw [← rpow_sum_of_nonneg _ hw, hw', rpow_one]
-      have : (∑ i in s, w i) ≠ 0 := by
-        rw [hw']
-        exact one_ne_zero
+      have : (∑ i in s, w i) ≠ 0 := by rw [hw']; exact one_ne_zero
       obtain ⟨i, his, hi⟩ := exists_ne_zero_of_sum_ne_zero this
       rw [← hx i his hi]
       exact hz i his
@@ -470,10 +467,7 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
   by_cases hG_zero : (∑ i in s, g i ^ q) = 0
   ·
     calc
-      (∑ i in s, f i * g i) = ∑ i in s, g i * f i :=
-        by
-        congr with i
-        rw [mul_comm]
+      (∑ i in s, f i * g i) = ∑ i in s, g i * f i := by congr with i; rw [mul_comm]
       _ ≤ (∑ i in s, g i ^ q) ^ (1 / q) * (∑ i in s, f i ^ p) ^ (1 / p) :=
         (inner_le_Lp_mul_Lp_of_norm_eq_zero s g f hpq.symm hG_zero)
       _ = (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := mul_comm _ _
@@ -485,10 +479,8 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
     simp_rw [f', g', div_mul_div_comm, ← sum_div] at this
     rwa [div_le_iff, one_mul] at this
     refine' mul_ne_zero _ _
-    · rw [Ne.def, rpow_eq_zero_iff, not_and_or]
-      exact Or.inl hF_zero
-    · rw [Ne.def, rpow_eq_zero_iff, not_and_or]
-      exact Or.inl hG_zero
+    · rw [Ne.def, rpow_eq_zero_iff, not_and_or]; exact Or.inl hF_zero
+    · rw [Ne.def, rpow_eq_zero_iff, not_and_or]; exact Or.inl hG_zero
   refine' inner_le_Lp_mul_Lp_of_norm_le_one s f' g' hpq (le_of_eq _) (le_of_eq _)
   ·
     simp_rw [f', div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.ne_zero, rpow_one,
@@ -1038,7 +1030,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
   simp [← ENNReal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
     le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
   convert this using 1 <;> [skip;congr 2] <;> [skip;skip;simp;skip;simp] <;>
-    · apply Finset.sum_congr rfl fun i hi => _
+    · apply Finset.sum_congr rfl fun i hi => _;
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
 
@@ -1091,8 +1083,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
         hp)
   push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this
   convert this using 2 <;> [skip;congr 1;congr 1] <;>
-    · apply Finset.sum_congr rfl fun i hi => _
-      simp [H'.1 i hi, H'.2 i hi]
+    · apply Finset.sum_congr rfl fun i hi => _; simp [H'.1 i hi, H'.2 i hi]
 #align ennreal.Lp_add_le ENNReal.Lp_add_le
 
 end ENNReal

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
-! 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.Data.Real.ConjugateExponents
 /-!
 # 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 inequalities for finite sums, including AM-GM inequality,
 Young's inequality, Hölder inequality, and Minkowski inequality. Versions for integrals of some of
 these inequalities are available in `measure_theory.mean_inequalities`.
@@ -297,10 +300,7 @@ theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ}
 #align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weighted
 
 /- warning: real.geom_mean_le_arith_mean4_weighted -> Real.geom_mean_le_arith_mean4_weighted is a dubious translation:
-lean 3 declaration is
-  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {w₄ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real} {p₄ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₃) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₄) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₃) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₄) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) w₁ w₂) w₃) w₄) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₃ w₃)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₄ w₄)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₃ p₃)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₄ p₄)))
-but is expected to have type
-  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {w₄ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real} {p₄ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₃) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₄) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₃) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₄) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) w₁ w₂) w₃) w₄) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₃ w₃)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₄ w₄)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₃ p₃)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₄ p₄)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean4_weighted Real.geom_mean_le_arith_mean4_weightedₓ'. -/
 theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ} (hw₁ : 0 ≤ w₁)
     (hw₂ : 0 ≤ w₂) (hw₃ : 0 ≤ w₃) (hw₄ : 0 ≤ w₄) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃)
@@ -441,7 +441,6 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
       · rwa [div_le_iff hq_ne_zero, div_mul_cancel _ hq_ne_zero]
     _ = 1 := hpq.inv_add_inv_conj_nnreal
     
-#align nnreal.inner_le_Lp_mul_Lp_of_norm_le_one nnreal.inner_le_Lp_mul_Lp_of_norm_le_one
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
     (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) = 0) :
@@ -453,7 +452,6 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
   left
   rw [sum_eq_zero_iff] at hf
   exact (rpow_eq_zero_iff.mp (hf i his)).left
-#align nnreal.inner_le_Lp_mul_Lp_of_norm_eq_zero nnreal.inner_le_Lp_mul_Lp_of_norm_eq_zero
 
 /- warning: nnreal.inner_le_Lp_mul_Lq -> NNReal.inner_le_Lp_mul_Lq is a dubious translation:
 lean 3 declaration is

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

@@ -110,6 +110,12 @@ section GeomMeanLeArithMean
 
 namespace Real
 
+/- warning: real.geom_mean_le_arith_mean_weighted -> Real.geom_mean_le_arith_mean_weighted 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))) -> (LE.le.{0} Real Real.hasLe (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) (w i))) (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))))
+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))) -> (LE.le.{0} Real Real.instLEReal (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) (w i))) (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))))
+Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weightedₓ'. -/
 /-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**, weighted
 version for real-valued nonnegative functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
@@ -137,6 +143,12 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
       · rw [exp_log hz]
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
 
+/- warning: real.geom_mean_weighted_of_constant -> Real.geom_mean_weighted_of_constant is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) (w i))) x)
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) (w i))) x)
+Case conversion may be inaccurate. Consider using '#align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constantₓ'. -/
 theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     (∏ i in s, z i ^ w i) = x :=
@@ -158,6 +170,12 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
     
 #align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constant
 
+/- warning: real.arith_mean_weighted_of_constant -> Real.arith_mean_weighted_of_constant is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : Real), (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) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (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))) x)
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : Real), (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) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (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))) x)
+Case conversion may be inaccurate. Consider using '#align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constantₓ'. -/
 theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑ i in s, w i) = 1)
     (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : (∑ i in s, w i * z i) = x :=
   calc
@@ -171,6 +189,12 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑
     
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
 
+/- warning: real.geom_mean_eq_arith_mean_weighted_of_constant -> Real.geom_mean_eq_arith_mean_weighted_of_constant is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (z i) (w i))) (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))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (w : ι -> Real) (z : ι -> Real) (x : 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 (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Ne.{1} Real (w i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (z i) x)) -> (Eq.{1} Real (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (z i) (w i))) (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))))
+Case conversion may be inaccurate. Consider using '#align real.geom_mean_eq_arith_mean_weighted_of_constant Real.geom_mean_eq_arith_mean_weighted_of_constantₓ'. -/
 theorem geom_mean_eq_arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     (∏ i in s, z i ^ w i) = ∑ i in s, w i * z i := by
@@ -181,6 +205,12 @@ end Real
 
 namespace NNReal
 
+/- warning: nnreal.geom_mean_le_arith_mean_weighted -> NNReal.geom_mean_le_arith_mean_weighted 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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Finset.prod.{0, u1} NNReal ι (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (z i) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) (w i)))) (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))))
+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))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Finset.prod.{0, u1} NNReal ι (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (z i) (NNReal.toReal (w i)))) (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))))
+Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weightedₓ'. -/
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for `nnreal`-valued functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) :
@@ -190,6 +220,12 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in
       (by assumption_mod_cast) fun i _ => (z i).coe_nonneg
 #align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weighted
 
+/- warning: nnreal.geom_mean_le_arith_mean2_weighted -> NNReal.geom_mean_le_arith_mean2_weighted is a dubious translation:
+lean 3 declaration is
+  forall (w₁ : NNReal) (w₂ : NNReal) (p₁ : NNReal) (p₂ : 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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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) p₁ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₂ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₂))) (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 p₁) (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 p₂)))
+but is expected to have type
+  forall (w₁ : NNReal) (w₂ : NNReal) (p₁ : NNReal) (p₂ : 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))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (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) p₁ (NNReal.toReal w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₂ (NNReal.toReal w₂))) (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 p₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ p₂)))
+Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weightedₓ'. -/
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for two `nnreal` numbers. -/
 theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
@@ -199,6 +235,12 @@ theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
     geom_mean_le_arith_mean_weighted univ ![w₁, w₂] ![p₁, p₂]
 #align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weighted
 
+/- warning: nnreal.geom_mean_le_arith_mean3_weighted -> NNReal.geom_mean_le_arith_mean3_weighted is a dubious translation:
+lean 3 declaration is
+  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : 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))))) (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) w₃) (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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) (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) p₁ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₂ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₃ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₃))) (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))))) (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 p₁) (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 p₂)) (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))))) w₃ p₃)))
+but is expected to have type
+  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : 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))))) (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) w₃) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (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) p₁ (NNReal.toReal w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₂ (NNReal.toReal w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₃ (NNReal.toReal w₃))) (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))))) (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 p₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ p₂)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₃ p₃)))
+Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weightedₓ'. -/
 theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ≥0) :
     w₁ + w₂ + w₃ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
@@ -208,6 +250,12 @@ theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃] ![p₁, p₂, p₃]
 #align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weighted
 
+/- warning: nnreal.geom_mean_le_arith_mean4_weighted -> NNReal.geom_mean_le_arith_mean4_weighted is a dubious translation:
+lean 3 declaration is
+  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (w₄ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : NNReal) (p₄ : 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))))) (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))))) (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) w₃) w₄) (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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) (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))))) (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) p₁ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₂ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₃ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₃))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) p₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) w₄))) (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))))) (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))))) (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 p₁) (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 p₂)) (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))))) w₃ p₃)) (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))))) w₄ p₄)))
+but is expected to have type
+  forall (w₁ : NNReal) (w₂ : NNReal) (w₃ : NNReal) (w₄ : NNReal) (p₁ : NNReal) (p₂ : NNReal) (p₃ : NNReal) (p₄ : 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))))) (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))))) (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) w₃) w₄) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (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) p₁ (NNReal.toReal w₁)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₂ (NNReal.toReal w₂))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₃ (NNReal.toReal w₃))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) p₄ (NNReal.toReal w₄))) (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))))) (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))))) (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 p₁) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₂ p₂)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₃ p₃)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) w₄ p₄)))
+Case conversion may be inaccurate. Consider using '#align nnreal.geom_mean_le_arith_mean4_weighted NNReal.geom_mean_le_arith_mean4_weightedₓ'. -/
 theorem geom_mean_le_arith_mean4_weighted (w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ≥0) :
     w₁ + w₂ + w₃ + w₄ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) * p₄ ^ (w₄ : ℝ) ≤
@@ -222,12 +270,24 @@ end NNReal
 
 namespace Real
 
+/- warning: real.geom_mean_le_arith_mean2_weighted -> Real.geom_mean_le_arith_mean2_weighted is a dubious translation:
+lean 3 declaration is
+  forall {w₁ : Real} {w₂ : Real} {p₁ : Real} {p₂ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₂) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) w₁ w₂) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₂ w₂)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₂ p₂)))
+but is expected to have type
+  forall {w₁ : Real} {w₂ : Real} {p₁ : Real} {p₂ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₂) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) w₁ w₂) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₂ w₂)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₂ p₂)))
+Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weightedₓ'. -/
 theorem geom_mean_le_arith_mean2_weighted {w₁ w₂ p₁ p₂ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hw : w₁ + w₂ = 1) : p₁ ^ w₁ * p₂ ^ w₂ ≤ w₁ * p₁ + w₂ * p₂ :=
   NNReal.geom_mean_le_arith_mean2_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩ <|
     NNReal.coe_eq.1 <| by assumption
 #align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weighted
 
+/- warning: real.geom_mean_le_arith_mean3_weighted -> Real.geom_mean_le_arith_mean3_weighted is a dubious translation:
+lean 3 declaration is
+  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₃) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₃) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) w₁ w₂) w₃) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₃ w₃)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₃ p₃)))
+but is expected to have type
+  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₃) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₃) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) w₁ w₂) w₃) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₃ w₃)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₃ p₃)))
+Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weightedₓ'. -/
 theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hw₃ : 0 ≤ w₃) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃) (hw : w₁ + w₂ + w₃ = 1) :
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
@@ -236,6 +296,12 @@ theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ}
     NNReal.coe_eq.1 hw
 #align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weighted
 
+/- warning: real.geom_mean_le_arith_mean4_weighted -> Real.geom_mean_le_arith_mean4_weighted is a dubious translation:
+lean 3 declaration is
+  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {w₄ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real} {p₄ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₃) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) w₄) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₁) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₂) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₃) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p₄) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) w₁ w₂) w₃) w₄) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₃ w₃)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) p₄ w₄)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₃ p₃)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) w₄ p₄)))
+but is expected to have type
+  forall {w₁ : Real} {w₂ : Real} {w₃ : Real} {w₄ : Real} {p₁ : Real} {p₂ : Real} {p₃ : Real} {p₄ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₃) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) w₄) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₁) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₂) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₃) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p₄) -> (Eq.{1} Real (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) w₁ w₂) w₃) w₄) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₁ w₁) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₂ w₂)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₃ w₃)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) p₄ w₄)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₁ p₁) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₂ p₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₃ p₃)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) w₄ p₄)))
+Case conversion may be inaccurate. Consider using '#align real.geom_mean_le_arith_mean4_weighted Real.geom_mean_le_arith_mean4_weightedₓ'. -/
 theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ} (hw₁ : 0 ≤ w₁)
     (hw₂ : 0 ≤ w₂) (hw₃ : 0 ≤ w₃) (hw₄ : 0 ≤ w₄) (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hp₃ : 0 ≤ p₃)
     (hp₄ : 0 ≤ p₄) (hw : w₁ + w₂ + w₃ + w₄ = 1) :
@@ -256,6 +322,12 @@ section Young
 
 namespace Real
 
+/- warning: real.young_inequality_of_nonneg -> Real.young_inequality_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {a : Real} {b : Real} {p : Real} {q : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) b) -> (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) a p) p) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) b q) q)))
+but is expected to have type
+  forall {a : Real} {b : Real} {p : Real} {q : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) b) -> (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) a p) p) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) b q) q)))
+Case conversion may be inaccurate. Consider using '#align real.young_inequality_of_nonneg Real.young_inequality_of_nonnegₓ'. -/
 /-- Young's inequality, a version for nonnegative real numbers. -/
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
@@ -264,6 +336,12 @@ theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
       (rpow_nonneg_of_nonneg ha p) (rpow_nonneg_of_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
 
+/- warning: real.young_inequality -> Real.young_inequality is a dubious translation:
+lean 3 declaration is
+  forall (a : Real) (b : Real) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) a) p) p) (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 Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) b) q) q)))
+but is expected to have type
+  forall (a : Real) (b : Real) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a b) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) a) p) p) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) b) q) q)))
+Case conversion may be inaccurate. Consider using '#align real.young_inequality Real.young_inequalityₓ'. -/
 /-- Young's inequality, a version for arbitrary real numbers. -/
 theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
@@ -279,6 +357,12 @@ end Real
 
 namespace NNReal
 
+/- warning: nnreal.young_inequality -> NNReal.young_inequality is a dubious translation:
+lean 3 declaration is
+  forall (a : NNReal) (b : NNReal) {p : NNReal} {q : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))))) p) -> (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))))) p) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))))) q)) (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)))))))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) p)) p) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) q)) q)))
+but is expected to have type
+  forall (a : NNReal) (b : NNReal) {p : NNReal} {q : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) p) -> (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) p) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) q)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a (NNReal.toReal p)) p) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b (NNReal.toReal q)) q)))
+Case conversion may be inaccurate. Consider using '#align nnreal.young_inequality NNReal.young_inequalityₓ'. -/
 /-- Young's inequality, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
 theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 / p + 1 / q = 1) :
@@ -286,6 +370,12 @@ theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 /
   Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_eq.2 hpq⟩
 #align nnreal.young_inequality NNReal.young_inequality
 
+/- warning: nnreal.young_inequality_real -> NNReal.young_inequality_real is a dubious translation:
+lean 3 declaration is
+  forall (a : NNReal) (b : NNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (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))))) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) a p) (Real.toNNReal p)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) b q) (Real.toNNReal q))))
+but is expected to have type
+  forall (a : NNReal) (b : NNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (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))))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) a p) (Real.toNNReal p)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) b q) (Real.toNNReal q))))
+Case conversion may be inaccurate. Consider using '#align nnreal.young_inequality_real NNReal.young_inequality_realₓ'. -/
 /-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/
 theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ a ^ p / Real.toNNReal p + b ^ q / Real.toNNReal q :=
@@ -299,6 +389,12 @@ end NNReal
 
 namespace ENNReal
 
+/- warning: ennreal.young_inequality -> ENNReal.young_inequality is a dubious translation:
+lean 3 declaration is
+  forall (a : ENNReal) (b : ENNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent 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))))) (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)))))))) a b) (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)))))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a p) (ENNReal.ofReal p)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) b q) (ENNReal.ofReal q))))
+but is expected to have type
+  forall (a : ENNReal) (b : ENNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent 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))))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) a b) (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)))))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a p) (ENNReal.ofReal p)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) b q) (ENNReal.ofReal q))))
+Case conversion may be inaccurate. Consider using '#align ennreal.young_inequality ENNReal.young_inequalityₓ'. -/
 /-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
 theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
     a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q :=
@@ -359,6 +455,12 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
   exact (rpow_eq_zero_iff.mp (hf i his)).left
 #align nnreal.inner_le_Lp_mul_Lp_of_norm_eq_zero nnreal.inner_le_Lp_mul_Lp_of_norm_eq_zero
 
+/- warning: nnreal.inner_le_Lp_mul_Lq -> NNReal.inner_le_Lp_mul_Lq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (g : ι -> NNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (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))))) (f i) (g i))) (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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (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) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (g : ι -> NNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (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)) (f i) (g i))) (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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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))))
+Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lqₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
@@ -398,6 +500,12 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
       rpow_one, div_self hG_zero]
 #align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lq
 
+/- warning: nnreal.inner_le_Lp_mul_Lq_tsum -> NNReal.inner_le_Lp_mul_Lq_tsum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (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))))) (f i) (g i))) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (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))))) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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)))))
+Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsumₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
@@ -425,18 +533,36 @@ theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsCo
   exact ⟨H₂, tsum_le_of_sum_le H₂ H₁⟩
 #align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsum
 
+/- warning: nnreal.summable_mul_of_Lp_Lq -> NNReal.summable_mul_of_Lp_Lq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (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))))) (f i) (g i)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i)))
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_mul_of_Lp_Lq NNReal.summable_mul_of_Lp_Lqₓ'. -/
 theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).1
 #align nnreal.summable_mul_of_Lp_Lq NNReal.summable_mul_of_Lp_Lq
 
+/- warning: nnreal.inner_le_Lp_mul_Lq_tsum' -> NNReal.inner_le_Lp_mul_Lq_tsum' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (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))))) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i))) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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))))
+Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'ₓ'. -/
 theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
 
+/- warning: nnreal.inner_le_Lp_mul_Lq_has_sum -> NNReal.inner_le_Lp_mul_Lq_hasSum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {A : NNReal} {B : NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) A p)) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) B q)) -> (Exists.{1} NNReal (fun (C : NNReal) => And (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) C (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))))) A B)) (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (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))))) (f i) (g i)) C)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {A : NNReal} {B : NNReal} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) A p)) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) q) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) B q)) -> (Exists.{1} NNReal (fun (C : NNReal) => And (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) C (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) A B)) (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) (g i)) C)))
+Case conversion may be inaccurate. Consider using '#align nnreal.inner_le_Lp_mul_Lq_has_sum NNReal.inner_le_Lp_mul_Lq_hasSumₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
@@ -454,6 +580,12 @@ theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q :
   · simpa only [rpow_self_rpow_inv hpq.ne_zero] using H₁.has_sum
 #align nnreal.inner_le_Lp_mul_Lq_has_sum NNReal.inner_le_Lp_mul_Lq_hasSum
 
+/- warning: nnreal.rpow_sum_le_const_mul_sum_rpow -> NNReal.rpow_sum_le_const_mul_sum_rpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> 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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => f i)) 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) ((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)) (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))))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> 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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => f i)) 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) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Finset.card.{u1} ι s)) (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)))) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p))))
+Case conversion may be inaccurate. Consider using '#align nnreal.rpow_sum_le_const_mul_sum_rpow NNReal.rpow_sum_le_const_mul_sum_rpowₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0`-valued functions.
 -/
@@ -473,6 +605,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
     NNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
 #align nnreal.rpow_sum_le_const_mul_sum_rpow NNReal.rpow_sum_le_const_mul_sum_rpow
 
+#print NNReal.isGreatest_Lp /-
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
 `∑ i in s, f i * g i` over functions `g` of `L_q` seminorm less than or equal to one. -/
 theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
@@ -498,7 +631,14 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExpon
     simpa only [mul_one] using
       mul_le_mul_left' (NNReal.rpow_le_one hg (le_of_lt hpq.symm.one_div_pos)) _
 #align nnreal.is_greatest_Lp NNReal.isGreatest_Lp
+-/
 
+/- warning: nnreal.Lp_add_le -> NNReal.Lp_add_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (g : ι -> 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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => 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))))) (f i) (g 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)) (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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (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) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g 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) (f : ι -> NNReal) (g : ι -> 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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => 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))))) (f i) (g 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)) (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) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g 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.Lp_add_le NNReal.Lp_add_leₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `nnreal`-valued functions. -/
 theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
@@ -517,6 +657,12 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     add_le_add ((is_greatest_Lp s f hpq).2 ⟨φ, hφ, rfl⟩) ((is_greatest_Lp s g hpq).2 ⟨φ, hφ, rfl⟩)
 #align nnreal.Lp_add_le NNReal.Lp_add_le
 
+/- warning: nnreal.Lp_add_le_tsum -> NNReal.Lp_add_le_tsum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> 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) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) p)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => 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))))) (f i) (g i)) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g 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}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) p)) -> (And (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => 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))))) (f i) (g i)) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g 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.Lp_add_le_tsum NNReal.Lp_add_le_tsumₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `nnreal`-valued functions. For an alternative version, convenient if the
@@ -548,17 +694,35 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
   refine' tsum_le_of_sum_le H₂ H₁
 #align nnreal.Lp_add_le_tsum NNReal.Lp_add_le_tsum
 
+/- warning: nnreal.summable_Lp_add -> NNReal.summable_Lp_add is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> 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) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => 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))))) (f i) (g i)) p))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => 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))))) (f i) (g i)) p))
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_Lp_add NNReal.summable_Lp_addₓ'. -/
 theorem summable_Lp_add {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)
     (hg : Summable fun i => g i ^ p) : Summable fun i => (f i + g i) ^ p :=
   (Lp_add_le_tsum hp hf hg).1
 #align nnreal.summable_Lp_add NNReal.summable_Lp_add
 
+/- warning: nnreal.Lp_add_le_tsum' -> NNReal.Lp_add_le_tsum' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> 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) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g 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}} {f : ι -> NNReal} {g : ι -> NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p)) -> (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) 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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => 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))))) (f i) (g 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)) (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) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f 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)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g 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.Lp_add_le_tsum' NNReal.Lp_add_le_tsum'ₓ'. -/
 theorem Lp_add_le_tsum' {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)
     (hg : Summable fun i => g i ^ p) :
     (∑' i, (f i + g i) ^ p) ^ (1 / p) ≤ (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) :=
   (Lp_add_le_tsum hp hf hg).2
 #align nnreal.Lp_add_le_tsum' NNReal.Lp_add_le_tsum'
 
+/- warning: nnreal.Lp_add_le_has_sum -> NNReal.Lp_add_le_hasSum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {A : NNReal} {B : 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) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (f i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) A p)) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (g i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) B p)) -> (Exists.{1} NNReal (fun (C : NNReal) => And (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) C (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)) (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => 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))))) (f i) (g i)) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) C p))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> NNReal} {g : ι -> NNReal} {A : NNReal} {B : NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (f i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) A p)) -> (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (g i) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) B p)) -> (Exists.{1} NNReal (fun (C : NNReal) => And (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) C (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)) (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => 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))))) (f i) (g i)) p) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) C p))))
+Case conversion may be inaccurate. Consider using '#align nnreal.Lp_add_le_has_sum NNReal.Lp_add_le_hasSumₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `nnreal`-valued functions. For an alternative version, convenient if the
@@ -582,6 +746,12 @@ namespace Real
 
 variable (f g : ι → ℝ) {p q : ℝ}
 
+/- warning: real.inner_le_Lp_mul_Lq -> Real.inner_le_Lp_mul_Lq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Real) (g : ι -> Real) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (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) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (g i)) 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))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Real) (g : ι -> Real) {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (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) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (g i)) 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))))
+Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lqₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
@@ -597,6 +767,12 @@ theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
   simp only [← abs_mul, le_abs_self]
 #align real.inner_le_Lp_mul_Lq Real.inner_le_Lp_mul_Lq
 
+/- warning: real.rpow_sum_le_const_mul_sum_rpow -> Real.rpow_sum_le_const_mul_sum_rpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Real) {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) => Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f i))) p) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) ((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)) (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))))) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f i)) p))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Real) {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) => Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f i))) p) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast (Finset.card.{u1} ι s)) (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)))) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f i)) p))))
+Case conversion may be inaccurate. Consider using '#align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpowₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ`-valued functions. -/
 theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
@@ -609,6 +785,12 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   exact this
 #align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpow
 
+/- warning: real.Lp_add_le -> Real.Lp_add_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Real) (g : ι -> Real) {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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (g 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) (f : ι -> Real) (g : ι -> Real) {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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (g 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.Lp_add_le Real.Lp_add_leₓ'. -/
 -- for some reason `exact_mod_cast` can't replace this argument
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `real`-valued functions. -/
@@ -627,6 +809,12 @@ theorem Lp_add_le (hp : 1 ≤ p) :
 
 variable {f g}
 
+/- warning: real.inner_le_Lp_mul_Lq_of_nonneg -> Real.inner_le_Lp_mul_Lq_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (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))) (f i))) -> (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))) (g i))) -> (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) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) 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))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (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)) (f i))) -> (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)) (g i))) -> (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) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) 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))))
+Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonnegₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued nonnegative functions. -/
@@ -637,6 +825,12 @@ theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 #align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonneg
 
+/- warning: real.inner_le_Lp_mul_Lq_tsum_of_nonneg -> Real.inner_le_Lp_mul_Lq_tsum_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) q)) -> (And (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) (g i))) (LE.le.{0} Real Real.hasLe (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) 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)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) q)) -> (And (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) (g i))) (LE.le.{0} Real Real.instLEReal (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) 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)))))
+Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonnegₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `ℝ`-valued functions.
 For an alternative version, convenient if the infinite sums are already expressed as `p`-th powers,
@@ -652,18 +846,36 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
 
+/- warning: real.summable_mul_of_Lp_Lq_of_nonneg -> Real.summable_mul_of_Lp_Lq_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) q)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) (g i)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) q)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) (g i)))
+Case conversion may be inaccurate. Consider using '#align real.summable_mul_of_Lp_Lq_of_nonneg Real.summable_mul_of_Lp_Lq_of_nonnegₓ'. -/
 theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).1
 #align real.summable_mul_of_Lp_Lq_of_nonneg Real.summable_mul_of_Lp_Lq_of_nonneg
 
+/- warning: real.inner_le_Lp_mul_Lq_tsum_of_nonneg' -> Real.inner_le_Lp_mul_Lq_tsum_of_nonneg' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) q)) -> (LE.le.{0} Real Real.hasLe (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) 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))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) q)) -> (LE.le.{0} Real Real.instLEReal (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) (g i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) 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))))
+Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'ₓ'. -/
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'
 
+/- warning: real.inner_le_Lp_mul_Lq_has_sum_of_nonneg -> Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall {A : Real} {B : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) A) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) B) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) A p)) -> (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) q) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) B q)) -> (Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) (And (LE.le.{0} Real Real.hasLe C (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) A B)) (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (f i) (g i)) C)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real} {q : Real}, (Real.IsConjugateExponent p q) -> (forall {A : Real} {B : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) A) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) B) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) A p)) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) q) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) B q)) -> (Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (And (LE.le.{0} Real Real.instLEReal C (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) A B)) (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (f i) (g i)) C)))))
+Case conversion may be inaccurate. Consider using '#align real.inner_le_Lp_mul_Lq_has_sum_of_nonneg Real.inner_le_Lp_mul_Lq_hasSum_of_nonnegₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
@@ -684,6 +896,12 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   exact H
 #align real.inner_le_Lp_mul_Lq_has_sum_of_nonneg Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg
 
+/- warning: real.rpow_sum_le_const_mul_sum_rpow_of_nonneg -> Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} {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) -> (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))) (f i))) -> (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) => f i)) p) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) ((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)) (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))))) (Finset.sum.{0, u1} Real ι Real.addCommMonoid s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (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)) (f i))) -> (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) => f i)) p) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast (Finset.card.{u1} ι s)) (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)))) (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal s (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p))))
+Case conversion may be inaccurate. Consider using '#align real.rpow_sum_le_const_mul_sum_rpow_of_nonneg Real.rpow_sum_le_const_mul_sum_rpow_of_nonnegₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with nonnegative `ℝ`-valued
 functions. -/
@@ -693,6 +911,12 @@ theorem rpow_sum_le_const_mul_sum_rpow_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈
     simp only [abs_of_nonneg, hf i hi]
 #align real.rpow_sum_le_const_mul_sum_rpow_of_nonneg Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg
 
+/- warning: real.Lp_add_le_of_nonneg -> Real.Lp_add_le_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) {f : ι -> Real} {g : ι -> Real} {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) -> (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))) (f i))) -> (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))) (g i))) -> (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g 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) {f : ι -> Real} {g : ι -> Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (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)) (f i))) -> (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)) (g i))) -> (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g 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.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonnegₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ`-valued nonnegative
 functions. -/
@@ -705,6 +929,12 @@ theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : 
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 #align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonneg
 
+/- warning: real.Lp_add_le_tsum_of_nonneg -> Real.Lp_add_le_tsum_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {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) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) p)) -> (And (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g i)) p)) (LE.le.{0} Real Real.hasLe (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g 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}} {f : ι -> Real} {g : ι -> Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) p)) -> (And (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g i)) p)) (LE.le.{0} Real Real.instLEReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g 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.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonnegₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
@@ -720,18 +950,36 @@ theorem Lp_add_le_tsum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : 
   exact NNReal.Lp_add_le_tsum hp hf_sum hg_sum
 #align real.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonneg
 
+/- warning: real.summable_Lp_add_of_nonneg -> Real.summable_Lp_add_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {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) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g i)) p))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g i)) p))
+Case conversion may be inaccurate. Consider using '#align real.summable_Lp_add_of_nonneg Real.summable_Lp_add_of_nonnegₓ'. -/
 theorem summable_Lp_add_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ p) :
     Summable fun i => (f i + g i) ^ p :=
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).1
 #align real.summable_Lp_add_of_nonneg Real.summable_Lp_add_of_nonneg
 
+/- warning: real.Lp_add_le_tsum_of_nonneg' -> Real.Lp_add_le_tsum_of_nonneg' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {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) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p)) -> (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) p)) -> (LE.le.{0} Real Real.hasLe (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g 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}} {f : ι -> Real} {g : ι -> Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p)) -> (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) p)) -> (LE.le.{0} Real Real.instLEReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (tsum.{0, u1} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g 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.Lp_add_le_tsum_of_nonneg' Real.Lp_add_le_tsum_of_nonneg'ₓ'. -/
 theorem Lp_add_le_tsum_of_nonneg' (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ p) :
     (∑' i, (f i + g i) ^ p) ^ (1 / p) ≤ (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) :=
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).2
 #align real.Lp_add_le_tsum_of_nonneg' Real.Lp_add_le_tsum_of_nonneg'
 
+/- warning: real.Lp_add_le_has_sum_of_nonneg -> Real.Lp_add_le_hasSum_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {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) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g i)) -> (forall {A : Real} {B : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) A) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) B) -> (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) A p)) -> (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (g i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) B p)) -> (Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) (And (LE.le.{0} Real Real.hasLe C (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) A B)) (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (f i) (g i)) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) C p))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Real} {g : ι -> Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f i)) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g i)) -> (forall {A : Real} {B : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) A) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) B) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) A p)) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (g i) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) B p)) -> (Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (And (LE.le.{0} Real Real.instLEReal C (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) A B)) (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (f i) (g i)) p) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) C p))))))
+Case conversion may be inaccurate. Consider using '#align real.Lp_add_le_has_sum_of_nonneg Real.Lp_add_le_hasSum_of_nonnegₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
@@ -758,6 +1006,12 @@ namespace ENNReal
 
 variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 
+/- warning: ennreal.inner_le_Lp_mul_Lq -> ENNReal.inner_le_Lp_mul_Lq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> ENNReal) (g : ι -> ENNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent 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))))) (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)))))))) (f i) (g i))) (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) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (f 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)) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (g i) 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))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> ENNReal) (g : ι -> ENNReal) {p : Real} {q : Real}, (Real.IsConjugateExponent 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))))) (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)) (f i) (g i))) (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) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (g i) 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))))
+Case conversion may be inaccurate. Consider using '#align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lqₓ'. -/
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
@@ -790,6 +1044,12 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
 
+/- warning: ennreal.rpow_sum_le_const_mul_sum_rpow -> ENNReal.rpow_sum_le_const_mul_sum_rpow is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> 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) (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) => f i)) 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) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) (Finset.card.{u1} ι s)) (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))))) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (f i) p))))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> 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) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => f i)) 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) (Nat.cast.{0} ENNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (Finset.card.{u1} ι s)) (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)))) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (f i) p))))
+Case conversion may be inaccurate. Consider using '#align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpowₓ'. -/
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0∞`-valued functions.
 -/
@@ -809,6 +1069,12 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
     ENNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
 #align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpow
 
+/- warning: ennreal.Lp_add_le -> ENNReal.Lp_add_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> ENNReal) (g : ι -> 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) (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) => 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)))))))) (f i) (g 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)) (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) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (f 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)) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (g 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) (f : ι -> ENNReal) (g : ι -> 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) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => 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)))))))) (f i) (g 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)) (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) (Finset.sum.{0, u1} ENNReal ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (i : ι) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (f 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)) (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) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (g 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 ennreal.Lp_add_le ENNReal.Lp_add_leₓ'. -/
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ≥0∞` valued nonnegative
 functions. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -128,7 +128,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
   · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A
     have := convex_on_exp.map_sum_le hw hw' fun i _ => Set.mem_univ <| log (z i)
     simp only [exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this
-    convert this using 1 <;> [apply prod_congr rfl, apply sum_congr rfl] <;> intro i hi
+    convert this using 1 <;> [apply prod_congr rfl;apply sum_congr rfl] <;> intro i hi
     · cases' eq_or_lt_of_le (hz i hi) with hz hz
       · simp [A i hi hz.symm]
       · exact rpow_def_of_pos hz _
@@ -700,7 +700,7 @@ theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : 
     (∑ i in s, (f i + g i) ^ p) ^ (1 / p) ≤
       (∑ i in s, f i ^ p) ^ (1 / p) + (∑ i in s, g i ^ p) ^ (1 / p) :=
   by
-  convert Lp_add_le s f g hp using 2 <;> [skip, congr 1, congr 1] <;> apply sum_congr rfl <;>
+  convert Lp_add_le s f g hp using 2 <;> [skip;congr 1;congr 1] <;> apply sum_congr rfl <;>
       intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 #align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonneg
@@ -785,7 +785,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
         (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
   simp [← ENNReal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
     le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
-  convert this using 1 <;> [skip, congr 2] <;> [skip, skip, simp, skip, simp] <;>
+  convert this using 1 <;> [skip;congr 2] <;> [skip;skip;simp;skip;simp] <;>
     · apply Finset.sum_congr rfl fun i hi => _
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
@@ -826,7 +826,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
       (@NNReal.Lp_add_le _ s (fun i => ENNReal.toNNReal (f i)) (fun i => ENNReal.toNNReal (g i)) _
         hp)
   push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this
-  convert this using 2 <;> [skip, congr 1, congr 1] <;>
+  convert this using 2 <;> [skip;congr 1;congr 1] <;>
     · apply Finset.sum_congr rfl fun i hi => _
       simp [H'.1 i hi, H'.2 i hi]
 #align ennreal.Lp_add_le ENNReal.Lp_add_le

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
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
+! 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.Data.Real.ConjugateExponents
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -419,7 +419,7 @@ theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsCo
     refine' ⟨(∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q), _⟩
     rintro a ⟨s, rfl⟩
     exact H₁ s
-  have H₂ : Summable _ := (hasSum_of_isLUB _ (isLUB_csupᵢ bdd)).Summable
+  have H₂ : Summable _ := (hasSum_of_isLUB _ (isLUB_ciSup bdd)).Summable
   exact ⟨H₂, tsum_le_of_sum_le H₂ H₁⟩
 #align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsum
 
@@ -540,7 +540,7 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
     refine' ⟨((∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p)) ^ p, _⟩
     rintro a ⟨s, rfl⟩
     exact H₁ s
-  have H₂ : Summable _ := (hasSum_of_isLUB _ (isLUB_csupᵢ bdd)).Summable
+  have H₂ : Summable _ := (hasSum_of_isLUB _ (isLUB_ciSup bdd)).Summable
   refine' ⟨H₂, _⟩
   rw [NNReal.rpow_one_div_le_iff Pos]
   refine' tsum_le_of_sum_le H₂ H₁

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -163,7 +163,7 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑
       by
       refine' sum_congr rfl fun i hi => _
       cases' eq_or_ne (w i) 0 with hwi hwi
-      · rw [hwi, zero_mul, zero_mul]
+      · rw [hwi, MulZeroClass.zero_mul, MulZeroClass.zero_mul]
       · rw [hx i hi hwi]
     _ = x := by rw [← sum_mul, hw', one_mul]
     
@@ -349,8 +349,8 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
     (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) = 0) :
     (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) :=
   by
-  simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, zero_mul, inv_eq_zero, Ne.def,
-    not_false_iff, le_zero_iff, mul_eq_zero]
+  simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, MulZeroClass.zero_mul,
+    inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
   intro i his
   left
   rw [sum_eq_zero_iff] at hf

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -267,7 +267,7 @@ theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q)
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
   calc
     a * b ≤ |a * b| := le_abs_self (a * b)
-    _ = |a| * |b| := abs_mul a b
+    _ = |a| * |b| := (abs_mul a b)
     _ ≤ |a| ^ p / p + |b| ^ q / q :=
       Real.young_inequality_of_nonneg (abs_nonneg a) (abs_nonneg b) hpq
     
@@ -373,7 +373,7 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
         congr with i
         rw [mul_comm]
       _ ≤ (∑ i in s, g i ^ q) ^ (1 / q) * (∑ i in s, f i ^ p) ^ (1 / p) :=
-        inner_le_Lp_mul_Lp_of_norm_eq_zero s g f hpq.symm hG_zero
+        (inner_le_Lp_mul_Lp_of_norm_eq_zero s g f hpq.symm hG_zero)
       _ = (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := mul_comm _ _
       
   let f' i := f i / (∑ i in s, f i ^ p) ^ (1 / p)

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

@@ -95,7 +95,7 @@ universe u v
 
 open Finset
 
-open Classical BigOperators NNReal Ennreal
+open Classical BigOperators NNReal ENNReal
 
 noncomputable section
 
@@ -295,11 +295,11 @@ theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateEx
 
 end NNReal
 
-namespace Ennreal
+namespace ENNReal
 
 /-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
 theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
-    a * b ≤ a ^ p / Ennreal.ofReal p + b ^ q / Ennreal.ofReal q :=
+    a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q :=
   by
   by_cases h : a = ⊤ ∨ b = ⊤
   · refine' le_trans le_top (le_of_eq _)
@@ -308,13 +308,13 @@ theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExpo
   push_neg  at h
   -- if a ≠ ⊤ and b ≠ ⊤, use the nnreal version: nnreal.young_inequality_real
   rw [← coe_to_nnreal h.left, ← coe_to_nnreal h.right, ← coe_mul, coe_rpow_of_nonneg _ hpq.nonneg,
-    coe_rpow_of_nonneg _ hpq.symm.nonneg, Ennreal.ofReal, Ennreal.ofReal, ←
+    coe_rpow_of_nonneg _ hpq.symm.nonneg, ENNReal.ofReal, ENNReal.ofReal, ←
     @coe_div (Real.toNNReal p) _ (by simp [hpq.pos]), ←
     @coe_div (Real.toNNReal q) _ (by simp [hpq.symm.pos]), ← coe_add, coe_le_coe]
   exact NNReal.young_inequality_real a.to_nnreal b.to_nnreal hpq
-#align ennreal.young_inequality Ennreal.young_inequality
+#align ennreal.young_inequality ENNReal.young_inequality
 
-end Ennreal
+end ENNReal
 
 end Young
 
@@ -752,7 +752,7 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
 
 end Real
 
-namespace Ennreal
+namespace ENNReal
 
 variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 
@@ -765,7 +765,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
   by_cases H : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0
   · replace H : (∀ i ∈ s, f i = 0) ∨ ∀ i ∈ s, g i = 0
     ·
-      simpa [Ennreal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
+      simpa [ENNReal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
         sum_eq_zero_iff_of_nonneg] using H
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases H <;> simp [H i hi]
     have : (∑ i in s, f i * g i) = ∑ i in s, 0 := sum_congr rfl this
@@ -775,18 +775,18 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
   · cases H' <;> simp [H', -one_div, H]
   replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤
   ·
-    simpa [Ennreal.rpow_eq_top_iff, asymm hpq.pos, asymm hpq.symm.pos, hpq.pos, hpq.symm.pos,
-      Ennreal.sum_eq_top_iff, not_or] using H'
+    simpa [ENNReal.rpow_eq_top_iff, asymm hpq.pos, asymm hpq.symm.pos, hpq.pos, hpq.symm.pos,
+      ENNReal.sum_eq_top_iff, not_or] using H'
   have :=
-    Ennreal.coe_le_coe.2
-      (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => Ennreal.toNnreal (f i))
-        (fun i => Ennreal.toNnreal (g i)) _ _ hpq)
-  simp [← Ennreal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
+    ENNReal.coe_le_coe.2
+      (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => ENNReal.toNNReal (f i))
+        (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
+  simp [← ENNReal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
     le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
   convert this using 1 <;> [skip, congr 2] <;> [skip, skip, simp, skip, simp] <;>
     · apply Finset.sum_congr rfl fun i hi => _
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, with_top.coe_mul.symm]
-#align ennreal.inner_le_Lp_mul_Lq Ennreal.inner_le_Lp_mul_Lq
+#align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
 
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0∞`-valued functions.
@@ -802,10 +802,10 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   have hq : 1 / q * p = p - 1 := by
     rw [← hpq.div_conj_eq_sub_one]
     ring
-  simpa only [Ennreal.mul_rpow_of_nonneg _ _ hpq.nonneg, ← Ennreal.rpow_mul, hp₁, hq, coe_one,
+  simpa only [ENNReal.mul_rpow_of_nonneg _ _ hpq.nonneg, ← ENNReal.rpow_mul, hp₁, hq, coe_one,
     one_mul, one_rpow, rpow_one, Pi.one_apply, sum_const, Nat.smul_one_eq_coe] using
-    Ennreal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
-#align ennreal.rpow_sum_le_const_mul_sum_rpow Ennreal.rpow_sum_le_const_mul_sum_rpow
+    ENNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
+#align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpow
 
 /-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ≥0∞` valued nonnegative
@@ -818,18 +818,18 @@ theorem Lp_add_le (hp : 1 ≤ p) :
   · cases H' <;> simp [H', -one_div]
   have pos : 0 < p := lt_of_lt_of_le zero_lt_one hp
   replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤
-  · simpa [Ennreal.rpow_eq_top_iff, asymm Pos, Pos, Ennreal.sum_eq_top_iff, not_or] using H'
+  · simpa [ENNReal.rpow_eq_top_iff, asymm Pos, Pos, ENNReal.sum_eq_top_iff, not_or] using H'
   have :=
-    Ennreal.coe_le_coe.2
-      (@NNReal.Lp_add_le _ s (fun i => Ennreal.toNnreal (f i)) (fun i => Ennreal.toNnreal (g i)) _
+    ENNReal.coe_le_coe.2
+      (@NNReal.Lp_add_le _ s (fun i => ENNReal.toNNReal (f i)) (fun i => ENNReal.toNNReal (g i)) _
         hp)
-  push_cast [← Ennreal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this
+  push_cast [← ENNReal.coe_rpow_of_nonneg, le_of_lt Pos, le_of_lt (one_div_pos.2 Pos)] at this
   convert this using 2 <;> [skip, congr 1, congr 1] <;>
     · apply Finset.sum_congr rfl fun i hi => _
       simp [H'.1 i hi, H'.2 i hi]
-#align ennreal.Lp_add_le Ennreal.Lp_add_le
+#align ennreal.Lp_add_le ENNReal.Lp_add_le
 
-end Ennreal
+end ENNReal
 
 end HolderMinkowski
 

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

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -273,7 +273,7 @@ theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
   calc
     a * b ≤ |a * b| := le_abs_self (a * b)
-    _ = |a| * |b| := (abs_mul a b)
+    _ = |a| * |b| := abs_mul a b
     _ ≤ |a| ^ p / p + |b| ^ q / q :=
       Real.young_inequality_of_nonneg (abs_nonneg a) (abs_nonneg b) hpq
 #align real.young_inequality Real.young_inequality

@@ -122,7 +122,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
       exact zero_rpow hwi
   -- If all numbers `z i` with non-zero weight are positive, then we apply Jensen's inequality
   -- for `exp` and numbers `log (z i)` with weights `w i`.
-  · simp only [not_exists, not_and, Ne.def, Classical.not_not] at A
+  · simp only [not_exists, not_and, Ne, Classical.not_not] at A
     have := convexOn_exp.map_sum_le hw hw' fun i _ => Set.mem_univ <| log (z i)
     simp only [exp_sum, (· ∘ ·), smul_eq_mul, mul_comm (w _) (log _)] at this
     convert this using 1 <;> [apply prod_congr rfl;apply sum_congr rfl] <;> intro i hi
@@ -346,7 +346,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
     (hpq : p.IsConjExponent q) (hf : ∑ i in s, f i ^ p = 0) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, zero_mul,
-    inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
+    inv_eq_zero, Ne, not_false_iff, le_zero_iff, mul_eq_zero]
   intro i his
   left
   rw [sum_eq_zero_iff] at hf
@@ -373,9 +373,9 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExp
     simp_rw [f', g', div_mul_div_comm, ← sum_div] at this
     rwa [div_le_iff, one_mul] at this
     refine' mul_ne_zero _ _
-    · rw [Ne.def, rpow_eq_zero_iff, not_and_or]
+    · rw [Ne, rpow_eq_zero_iff, not_and_or]
       exact Or.inl hF_zero
-    · rw [Ne.def, rpow_eq_zero_iff, not_and_or]
+    · rw [Ne, rpow_eq_zero_iff, not_and_or]
       exact Or.inl hG_zero
   refine' inner_le_Lp_mul_Lp_of_norm_le_one s f' g' hpq (le_of_eq _) (le_of_eq _)
   · simp_rw [f', div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.ne_zero, rpow_one,

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 | |

@@ -338,8 +338,8 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
       rw [sum_add_distrib, sum_div, sum_div]
     _ ≤ 1 / Real.toNNReal p + 1 / Real.toNNReal q := by
       refine' add_le_add _ _
-      · rwa [div_le_iff hp_ne_zero, div_mul_cancel _ hp_ne_zero]
-      · rwa [div_le_iff hq_ne_zero, div_mul_cancel _ hq_ne_zero]
+      · rwa [div_le_iff hp_ne_zero, div_mul_cancel₀ _ hp_ne_zero]
+      · rwa [div_le_iff hq_ne_zero, div_mul_cancel₀ _ hq_ne_zero]
     _ = 1 := by simp_rw [one_div, hpq.toNNReal.inv_add_inv_conj]
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
@@ -486,8 +486,8 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q
         refine' fun y => mul_div_cancel_left_of_imp fun h => _
         simp [h, hpq.ne_zero]
       simp only [Set.mem_setOf_eq, div_rpow, ← sum_div, ← rpow_mul,
-        div_mul_cancel _ hpq.symm.ne_zero, rpow_one, div_le_iff hf, one_mul, hpq.mul_eq_add, ←
-        rpow_sub' _ A, _root_.add_sub_cancel, le_refl, true_and_iff, ← mul_div_assoc, B]
+        div_mul_cancel₀ _ hpq.symm.ne_zero, rpow_one, div_le_iff hf, one_mul, hpq.mul_eq_add, ←
+        rpow_sub' _ A, add_sub_cancel_right, le_refl, true_and_iff, ← mul_div_assoc, B]
       rw [div_eq_iff, ← rpow_add hf, one_div, one_div, hpq.inv_add_inv_conj, rpow_one]
       simpa [hpq.symm.ne_zero] using hf
   · rintro _ ⟨g, hg, rfl⟩

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.

@@ -92,7 +92,8 @@ less than or equal to the sum of the maximum values of the summands.
 
 universe u v
 
-open Finset Classical BigOperators NNReal ENNReal
+open scoped Classical
+open Finset BigOperators NNReal ENNReal
 
 set_option linter.uppercaseLean3 false
 

From LeanAPAP

@@ -107,7 +107,7 @@ section GeomMeanLEArithMean
 
 namespace Real
 
-/-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**, weighted
+/-- **AM-GM inequality**: The geometric mean is less than or equal to the arithmetic mean, weighted
 version for real-valued nonnegative functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) :
@@ -133,7 +133,7 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
       · rw [exp_log hz]
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
 
-/-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**. --/
+/-- **AM-GM inequality**: The **geometric mean is less than or equal to the arithmetic mean. --/
 theorem geom_mean_le_arith_mean {ι : Type*} (s : Finset ι) (w : ι → ℝ) (z : ι → ℝ)
     (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : 0 < ∑ i in s, w i) (hz : ∀ i ∈ s, 0 ≤ z i) :
     (∏ i in s, z i ^ w i) ^ (∑ i in s, w i)⁻¹  ≤  (∑ i in s, w i * z i) / (∑ i in s, w i) := by
@@ -186,8 +186,8 @@ end Real
 
 namespace NNReal
 
-/-- The geometric mean is less than or equal to the arithmetic mean, weighted version
-for `NNReal`-valued functions. -/
+/-- **AM-GM inequality**: The geometric mean is less than or equal to the arithmetic mean, weighted
+version for `NNReal`-valued functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) :
     (∏ i in s, z i ^ (w i : ℝ)) ≤ ∑ i in s, w i * z i :=
   mod_cast
@@ -195,8 +195,8 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : ∑ i in
       (by assumption_mod_cast) fun i _ => (z i).coe_nonneg
 #align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weighted
 
-/-- The geometric mean is less than or equal to the arithmetic mean, weighted version
-for two `NNReal` numbers. -/
+/-- **AM-GM inequality**: The geometric mean is less than or equal to the arithmetic mean, weighted
+version for two `NNReal` numbers. -/
 theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
     w₁ + w₂ = 1 → p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ := by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
@@ -259,7 +259,7 @@ section Young
 
 namespace Real
 
-/-- Young's inequality, a version for nonnegative real numbers. -/
+/-- **Young's inequality**, a version for nonnegative real numbers. -/
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     (hpq : p.IsConjExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
   simpa [← rpow_mul, ha, hb, hpq.ne_zero, hpq.symm.ne_zero, _root_.div_eq_inv_mul] using
@@ -267,7 +267,7 @@ theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
       (rpow_nonneg ha p) (rpow_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
 
-/-- Young's inequality, a version for arbitrary real numbers. -/
+/-- **Young's inequality**, a version for arbitrary real numbers. -/
 theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
   calc
@@ -281,14 +281,14 @@ end Real
 
 namespace NNReal
 
-/-- Young's inequality, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
+/-- **Young's inequality**, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
 theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ (p : ℝ) / p + b ^ (q : ℝ) / q :=
   Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg hpq.coe
 #align nnreal.young_inequality NNReal.young_inequality
 
-/-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/
+/-- **Young's inequality**, `ℝ≥0` version with real conjugate exponents. -/
 theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ p / Real.toNNReal p + b ^ q / Real.toNNReal q := by
   simpa [Real.coe_toNNReal, hpq.nonneg, hpq.symm.nonneg] using young_inequality a b hpq.toNNReal
@@ -298,7 +298,7 @@ end NNReal
 
 namespace ENNReal
 
-/-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
+/-- **Young's inequality**, `ℝ≥0∞` version with real conjugate exponents. -/
 theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q := by
   by_cases h : a = ⊤ ∨ b = ⊤
@@ -318,7 +318,7 @@ end ENNReal
 
 end Young
 
-section HolderMinkowski
+section HoelderMinkowski
 
 /-! ### Hölder's and Minkowski's inequalities -/
 
@@ -351,7 +351,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
   rw [sum_eq_zero_iff] at hf
   exact (rpow_eq_zero_iff.mp (hf i his)).left
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Hölder inequality**: The scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
@@ -383,7 +383,25 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExp
       rpow_one, div_self hG_zero]
 #align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lq
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Weighted Hölder inequality**. -/
+lemma inner_le_weight_mul_Lp (s : Finset ι) {p : ℝ} (hp : 1 ≤ p) (w f : ι → ℝ≥0) :
+    ∑ i in s, w i * f i ≤ (∑ i in s, w i) ^ (1 - p⁻¹) * (∑ i in s, w i * f i ^ p) ^ p⁻¹ := by
+  obtain rfl | hp := hp.eq_or_lt
+  · simp
+  calc
+    _ = ∑ i in s, w i ^ (1 - p⁻¹) * (w i ^ p⁻¹ * f i) := ?_
+    _ ≤ (∑ i in s, (w i ^ (1 - p⁻¹)) ^ (1 - p⁻¹)⁻¹) ^ (1 / (1 - p⁻¹)⁻¹) *
+          (∑ i in s, (w i ^ p⁻¹ * f i) ^ p) ^ (1 / p) :=
+        inner_le_Lp_mul_Lq _ _ _ (.symm ⟨hp, by simp⟩)
+    _ = _ := ?_
+  · congr with i
+    rw [← mul_assoc, ← rpow_of_add_eq _ one_ne_zero, rpow_one]
+    simp
+  · have hp₀ : p ≠ 0 := by positivity
+    have hp₁ : 1 - p⁻¹ ≠ 0 := by simp [sub_eq_zero, hp.ne']
+    simp [mul_rpow, div_inv_eq_mul, one_mul, one_div, hp₀, hp₁]
+
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_hasSum`. -/
@@ -419,7 +437,7 @@ theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsC
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum`.  -/
@@ -477,7 +495,7 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q
       mul_le_mul_left' (NNReal.rpow_le_one hg (le_of_lt hpq.symm.one_div_pos)) _
 #align nnreal.is_greatest_Lp NNReal.isGreatest_Lp
 
-/-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
+/-- **Minkowski inequality**: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `NNReal`-valued functions. -/
 theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     (∑ i in s, (f i + g i) ^ p) ^ (1 / p) ≤
@@ -494,7 +512,7 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
     add_le_add ((isGreatest_Lp s f hpq).2 ⟨φ, hφ, rfl⟩) ((isGreatest_Lp s g hpq).2 ⟨φ, hφ, rfl⟩)
 #align nnreal.Lp_add_le NNReal.Lp_add_le
 
-/-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
+/-- **Minkowski inequality**: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `NNReal`-valued functions. For an alternative version, convenient if the
 infinite sums are already expressed as `p`-th powers, see `Lp_add_le_hasSum_of_nonneg`. -/
@@ -534,7 +552,7 @@ theorem Lp_add_le_tsum' {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Su
   (Lp_add_le_tsum hp hf hg).2
 #align nnreal.Lp_add_le_tsum' NNReal.Lp_add_le_tsum'
 
-/-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
+/-- **Minkowski inequality**: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `NNReal`-valued functions. For an alternative version, convenient if the
 infinite sums are not already expressed as `p`-th powers, see `Lp_add_le_tsum_of_nonneg`.  -/
@@ -556,7 +574,7 @@ namespace Real
 
 variable (f g : ι → ℝ) {p q : ℝ}
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : IsConjExponent p q) :
@@ -582,7 +600,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
 #align real.rpow_sum_le_const_mul_sum_rpow Real.rpow_sum_le_const_mul_sum_rpow
 
 -- for some reason `exact_mod_cast` can't replace this argument
-/-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
+/-- **Minkowski inequality**: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `Real`-valued functions. -/
 theorem Lp_add_le (hp : 1 ≤ p) :
     (∑ i in s, |f i + g i| ^ p) ^ (1 / p) ≤
@@ -598,7 +616,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
 
 variable {f g}
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued nonnegative functions. -/
 theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
@@ -608,7 +626,17 @@ theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjExponent p q) (hf : ∀ i ∈
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 #align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonneg
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Weighted Hölder inequality**. -/
+lemma inner_le_weight_mul_Lp_of_nonneg (s : Finset ι) {p : ℝ} (hp : 1 ≤ p) (w f : ι → ℝ)
+    (hw : ∀ i, 0 ≤ w i) (hf : ∀ i, 0 ≤ f i) :
+    ∑ i in s, w i * f i ≤ (∑ i in s, w i) ^ (1 - p⁻¹) * (∑ i in s, w i * f i ^ p) ^ p⁻¹ := by
+  lift w to ι → ℝ≥0 using hw
+  lift f to ι → ℝ≥0 using hf
+  beta_reduce at *
+  norm_cast at *
+  exact NNReal.inner_le_weight_mul_Lp _ hp _ _
+
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `ℝ`-valued functions.
 For an alternative version, convenient if the infinite sums are already expressed as `p`-th powers,
 see `inner_le_Lp_mul_Lq_hasSum_of_nonneg`. -/
@@ -636,7 +664,7 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjExponent q) (hf : ∀
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum_of_nonneg`.  -/
@@ -665,7 +693,7 @@ theorem rpow_sum_le_const_mul_sum_rpow_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈
     simp only [abs_of_nonneg, hf i hi]
 #align real.rpow_sum_le_const_mul_sum_rpow_of_nonneg Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg
 
-/-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
+/-- **Minkowski inequality**: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ`-valued nonnegative
 functions. -/
 theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : ∀ i ∈ s, 0 ≤ g i) :
@@ -676,7 +704,7 @@ theorem Lp_add_le_of_nonneg (hp : 1 ≤ p) (hf : ∀ i ∈ s, 0 ≤ f i) (hg : 
     simp only [abs_of_nonneg, hf i hi, hg i hi, add_nonneg]
 #align real.Lp_add_le_of_nonneg Real.Lp_add_le_of_nonneg
 
-/-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
+/-- **Minkowski inequality**: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
 sums are already expressed as `p`-th powers, see `Lp_add_le_hasSum_of_nonneg`. -/
@@ -705,7 +733,7 @@ theorem Lp_add_le_tsum_of_nonneg' (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : 
   (Lp_add_le_tsum_of_nonneg hp hf hg hf_sum hg_sum).2
 #align real.Lp_add_le_tsum_of_nonneg' Real.Lp_add_le_tsum_of_nonneg'
 
-/-- Minkowski inequality: the `L_p` seminorm of the infinite sum of two vectors is less than or
+/-- **Minkowski inequality**: the `L_p` seminorm of the infinite sum of two vectors is less than or
 equal to the infinite sum of the `L_p`-seminorms of the summands, if these infinite sums both
 exist. A version for `ℝ`-valued functions. For an alternative version, convenient if the infinite
 sums are not already expressed as `p`-th powers, see `Lp_add_le_tsum_of_nonneg`. -/
@@ -734,7 +762,7 @@ namespace ENNReal
 
 variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 
-/-- Hölder inequality: the scalar product of two functions is bounded by the product of their
+/-- **Hölder inequality**: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
@@ -744,8 +772,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
       simpa [ENNReal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
         sum_eq_zero_iff_of_nonneg] using H
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases' H with H H <;> simp [H i hi]
-    have : ∑ i in s, f i * g i = ∑ i in s, 0 := sum_congr rfl this
-    simp [this]
+    simp [sum_eq_zero this]
   push_neg at H
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤
   · cases' H' with H' H' <;> simp [H', -one_div, -sum_eq_zero_iff, -rpow_eq_zero_iff, H]
@@ -761,6 +788,37 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
       simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
 
+/-- **Weighted Hölder inequality**. -/
+lemma inner_le_weight_mul_Lp_of_nonneg (s : Finset ι) {p : ℝ} (hp : 1 ≤ p) (w f : ι → ℝ≥0∞) :
+    ∑ i in s, w i * f i ≤ (∑ i in s, w i) ^ (1 - p⁻¹) * (∑ i in s, w i * f i ^ p) ^ p⁻¹ := by
+  obtain rfl | hp := hp.eq_or_lt
+  · simp
+  have hp₀ : 0 < p := by positivity
+  have hp₁ : p⁻¹ < 1 := inv_lt_one hp
+  by_cases H : (∑ i in s, w i) ^ (1 - p⁻¹) = 0 ∨ (∑ i in s, w i * f i ^ p) ^ p⁻¹ = 0
+  · replace H : (∀ i ∈ s, w i = 0) ∨ ∀ i ∈ s, w i = 0 ∨ f i = 0 := by
+      simpa [hp₀, hp₁, hp₀.not_lt, hp₁.not_lt, sum_eq_zero_iff_of_nonneg] using H
+    have (i) (hi : i ∈ s) : w i * f i = 0 := by cases' H with H H <;> simp [H i hi]
+    simp [sum_eq_zero this]
+  push_neg at H
+  by_cases H' : (∑ i in s, w i) ^ (1 - p⁻¹) = ⊤ ∨ (∑ i in s, w i * f i ^ p) ^ p⁻¹ = ⊤
+  · cases' H' with H' H' <;> simp [H', -one_div, -sum_eq_zero_iff, -rpow_eq_zero_iff, H]
+  replace H' : (∀ i ∈ s, w i ≠ ⊤) ∧ ∀ i ∈ s, w i * f i ^ p ≠ ⊤ := by
+    simpa [rpow_eq_top_iff,hp₀, hp₁, hp₀.not_lt, hp₁.not_lt, sum_eq_top_iff, not_or] using H'
+  have := coe_le_coe.2 $ NNReal.inner_le_weight_mul_Lp s hp.le (fun i ↦ ENNReal.toNNReal (w i))
+    fun i ↦ ENNReal.toNNReal (f i)
+  rw [coe_mul] at this
+  simp_rw [← coe_rpow_of_nonneg _ $ inv_nonneg.2 hp₀.le, coe_finset_sum, ENNReal.toNNReal_rpow,
+    ← ENNReal.toNNReal_mul, sum_congr rfl fun i hi ↦ coe_toNNReal (H'.2 i hi)] at this
+  simp [← ENNReal.coe_rpow_of_nonneg, hp₀.le, hp₁.le] at this
+  convert this using 2 with i hi
+  · obtain hw | hw := eq_or_ne (w i) 0
+    · simp [hw]
+    rw [coe_toNNReal (H'.1 _ hi), coe_toNNReal]
+    simpa [mul_eq_top, hw, hp₀, hp₀.not_lt, H'.1 _ hi] using H'.2 _ hi
+  · convert rfl with i hi
+    exact coe_toNNReal (H'.1 _ hi)
+
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the
 sum of the `p`-th powers of `f i`. Version for sums over finite sets, with `ℝ≥0∞`-valued functions.
 -/
@@ -779,7 +837,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
     ENNReal.rpow_le_rpow (inner_le_Lp_mul_Lq s 1 f hpq.symm) hpq.nonneg
 #align ennreal.rpow_sum_le_const_mul_sum_rpow ENNReal.rpow_sum_le_const_mul_sum_rpow
 
-/-- Minkowski inequality: the `L_p` seminorm of the sum of two vectors is less than or equal
+/-- **Minkowski inequality**: the `L_p` seminorm of the sum of two vectors is less than or equal
 to the sum of the `L_p`-seminorms of the summands. A version for `ℝ≥0∞` valued nonnegative
 functions. -/
 theorem Lp_add_le (hp : 1 ≤ p) :
@@ -802,4 +860,4 @@ theorem Lp_add_le (hp : 1 ≤ p) :
 
 end ENNReal
 
-end HolderMinkowski
+end HoelderMinkowski

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -369,7 +369,7 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExp
   let f' i := f i / (∑ i in s, f i ^ p) ^ (1 / p)
   let g' i := g i / (∑ i in s, g i ^ q) ^ (1 / q)
   suffices (∑ i in s, f' i * g' i) ≤ 1 by
-    simp_rw [div_mul_div_comm, ← sum_div] at this
+    simp_rw [f', g', div_mul_div_comm, ← sum_div] at this
     rwa [div_le_iff, one_mul] at this
     refine' mul_ne_zero _ _
     · rw [Ne.def, rpow_eq_zero_iff, not_and_or]
@@ -377,9 +377,9 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExp
     · rw [Ne.def, rpow_eq_zero_iff, not_and_or]
       exact Or.inl hG_zero
   refine' inner_le_Lp_mul_Lp_of_norm_le_one s f' g' hpq (le_of_eq _) (le_of_eq _)
-  · simp_rw [div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.ne_zero, rpow_one,
+  · simp_rw [f', div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.ne_zero, rpow_one,
       div_self hF_zero]
-  · simp_rw [div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.symm.ne_zero,
+  · simp_rw [g', div_rpow, ← sum_div, ← rpow_mul, one_div, inv_mul_cancel hpq.symm.ne_zero,
       rpow_one, div_self hG_zero]
 #align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lq
 

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -511,7 +511,7 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
     rw [← NNReal.rpow_one_div_le_iff pos]
     refine' le_trans (Lp_add_le s f g hp) (add_le_add _ _) <;>
         rw [NNReal.rpow_le_rpow_iff (one_div_pos.mpr pos)] <;>
-      refine' sum_le_tsum _ (fun _ _ => zero_le _) _
+      refine sum_le_tsum _ (fun _ _ => zero_le _) ?_
     exacts [hf, hg]
   have bdd : BddAbove (Set.range fun s => ∑ i in s, (f i + g i) ^ p) := by
     refine' ⟨((∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p)) ^ p, _⟩
@@ -520,7 +520,7 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
   have H₂ : Summable _ := (hasSum_of_isLUB _ (isLUB_ciSup bdd)).summable
   refine' ⟨H₂, _⟩
   rw [NNReal.rpow_one_div_le_iff pos]
-  refine' tsum_le_of_sum_le H₂ H₁
+  exact tsum_le_of_sum_le H₂ H₁
 #align nnreal.Lp_add_le_tsum NNReal.Lp_add_le_tsum
 
 theorem summable_Lp_add {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Summable fun i => f i ^ p)

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>

@@ -740,8 +740,8 @@ with `ℝ≥0∞`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   by_cases H : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0
-  · replace H : (∀ i ∈ s, f i = 0) ∨ ∀ i ∈ s, g i = 0
-    · simpa [ENNReal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
+  · replace H : (∀ i ∈ s, f i = 0) ∨ ∀ i ∈ s, g i = 0 := by
+      simpa [ENNReal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
         sum_eq_zero_iff_of_nonneg] using H
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases' H with H H <;> simp [H i hi]
     have : ∑ i in s, f i * g i = ∑ i in s, 0 := sum_congr rfl this
@@ -749,13 +749,11 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
   push_neg at H
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤
   · cases' H' with H' H' <;> simp [H', -one_div, -sum_eq_zero_iff, -rpow_eq_zero_iff, H]
-  replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤
-  · simpa [ENNReal.rpow_eq_top_iff, asymm hpq.pos, asymm hpq.symm.pos, hpq.pos, hpq.symm.pos,
+  replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤ := by
+    simpa [ENNReal.rpow_eq_top_iff, asymm hpq.pos, asymm hpq.symm.pos, hpq.pos, hpq.symm.pos,
       ENNReal.sum_eq_top_iff, not_or] using H'
-  have :=
-    ENNReal.coe_le_coe.2
-      (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => ENNReal.toNNReal (f i))
-        (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
+  have := ENNReal.coe_le_coe.2 (@NNReal.inner_le_Lp_mul_Lq _ s (fun i => ENNReal.toNNReal (f i))
+    (fun i => ENNReal.toNNReal (g i)) _ _ hpq)
   simp [← ENNReal.coe_rpow_of_nonneg, le_of_lt hpq.pos, le_of_lt hpq.one_div_pos,
     le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
   convert this using 1 <;> [skip; congr 2] <;> [skip; skip; simp; skip; simp] <;>
@@ -790,8 +788,8 @@ theorem Lp_add_le (hp : 1 ≤ p) :
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ p) ^ (1 / p) = ⊤
   · cases' H' with H' H' <;> simp [H', -one_div]
   have pos : 0 < p := lt_of_lt_of_le zero_lt_one hp
-  replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤
-  · simpa [ENNReal.rpow_eq_top_iff, asymm pos, pos, ENNReal.sum_eq_top_iff, not_or] using H'
+  replace H' : (∀ i ∈ s, f i ≠ ⊤) ∧ ∀ i ∈ s, g i ≠ ⊤ := by
+    simpa [ENNReal.rpow_eq_top_iff, asymm pos, pos, ENNReal.sum_eq_top_iff, not_or] using H'
   have :=
     ENNReal.coe_le_coe.2
       (@NNReal.Lp_add_le _ s (fun i => ENNReal.toNNReal (f i)) (fun i => ENNReal.toNNReal (g i)) _

It happens often that we have p q : ℝ≥0 that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with ℝ≥0 conjugates clumsy.

This PR

• introduces NNReal.IsConjExponent, NNReal.conjExponent
• renames Real.IsConjugateExponent, Real.conjugateExponent to Real.IsConjExponent, Real.conjExponent
• renames a few more lemmas to match up the Real and NNReal versions

From LeanAPAP

@@ -6,7 +6,7 @@ Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
 import Mathlib.Analysis.Convex.Jensen
 import Mathlib.Analysis.Convex.SpecificFunctions.Basic
 import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
-import Mathlib.Data.Real.ConjugateExponents
+import Mathlib.Data.Real.ConjExponents
 
 #align_import analysis.mean_inequalities from "leanprover-community/mathlib"@"8f9fea08977f7e450770933ee6abb20733b47c92"
 
@@ -261,14 +261,14 @@ namespace Real
 
 /-- Young's inequality, a version for nonnegative real numbers. -/
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
-    (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
+    (hpq : p.IsConjExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
   simpa [← rpow_mul, ha, hb, hpq.ne_zero, hpq.symm.ne_zero, _root_.div_eq_inv_mul] using
     geom_mean_le_arith_mean2_weighted hpq.inv_nonneg hpq.symm.inv_nonneg
       (rpow_nonneg ha p) (rpow_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
 
 /-- Young's inequality, a version for arbitrary real numbers. -/
-theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem young_inequality (a b : ℝ) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ |a| ^ p / p + |b| ^ q / q :=
   calc
     a * b ≤ |a * b| := le_abs_self (a * b)
@@ -283,17 +283,15 @@ namespace NNReal
 
 /-- Young's inequality, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
-theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : p⁻¹ + q⁻¹ = 1) :
+theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ (p : ℝ) / p + b ^ (q : ℝ) / q :=
-  Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_inj.2 hpq⟩
+  Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg hpq.coe
 #align nnreal.young_inequality NNReal.young_inequality
 
 /-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/
-theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem young_inequality_real (a b : ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ p / Real.toNNReal p + b ^ q / Real.toNNReal q := by
-  nth_rw 1 [← Real.coe_toNNReal p hpq.nonneg]
-  nth_rw 1 [← Real.coe_toNNReal q hpq.symm.nonneg]
-  exact young_inequality a b hpq.one_lt_nnreal hpq.inv_add_inv_conj_nnreal
+  simpa [Real.coe_toNNReal, hpq.nonneg, hpq.symm.nonneg] using young_inequality a b hpq.toNNReal
 #align nnreal.young_inequality_real NNReal.young_inequality_real
 
 end NNReal
@@ -301,7 +299,7 @@ end NNReal
 namespace ENNReal
 
 /-- Young's inequality, `ℝ≥0∞` version with real conjugate exponents. -/
-theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjExponent q) :
     a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal q := by
   by_cases h : a = ⊤ ∨ b = ⊤
   · refine' le_trans le_top (le_of_eq _)
@@ -328,10 +326,10 @@ section HolderMinkowski
 namespace NNReal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p ≤ 1) (hg : ∑ i in s, g i ^ q ≤ 1) :
+    (hpq : p.IsConjExponent q) (hf : ∑ i in s, f i ^ p ≤ 1) (hg : ∑ i in s, g i ^ q ≤ 1) :
     ∑ i in s, f i * g i ≤ 1 := by
-  have hp_ne_zero : Real.toNNReal p ≠ 0 := (zero_lt_one.trans hpq.one_lt_nnreal).ne.symm
-  have hq_ne_zero : Real.toNNReal q ≠ 0 := (zero_lt_one.trans hpq.symm.one_lt_nnreal).ne.symm
+  have hp_ne_zero : Real.toNNReal p ≠ 0 := (zero_lt_one.trans hpq.toNNReal.one_lt).ne.symm
+  have hq_ne_zero : Real.toNNReal q ≠ 0 := (zero_lt_one.trans hpq.toNNReal.symm.one_lt).ne.symm
   calc
     ∑ i in s, f i * g i ≤ ∑ i in s, (f i ^ p / Real.toNNReal p + g i ^ q / Real.toNNReal q) :=
       Finset.sum_le_sum fun i _ => young_inequality_real (f i) (g i) hpq
@@ -341,10 +339,10 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
       refine' add_le_add _ _
       · rwa [div_le_iff hp_ne_zero, div_mul_cancel _ hp_ne_zero]
       · rwa [div_le_iff hq_ne_zero, div_mul_cancel _ hq_ne_zero]
-    _ = 1 := by simp_rw [one_div, hpq.inv_add_inv_conj_nnreal]
+    _ = 1 := by simp_rw [one_div, hpq.toNNReal.inv_add_inv_conj]
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p = 0) :
+    (hpq : p.IsConjExponent q) (hf : ∑ i in s, f i ^ p = 0) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, zero_mul,
     inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
@@ -356,7 +354,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
-theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   by_cases hF_zero : ∑ i in s, f i ^ p = 0
   · exact inner_le_Lp_mul_Lp_of_norm_eq_zero s f g hpq hF_zero
@@ -389,7 +387,7 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_hasSum`. -/
-theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
+theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
       ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
@@ -409,13 +407,13 @@ theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsCo
   exact ⟨H₂, tsum_le_of_sum_le H₂ H₁⟩
 #align nnreal.inner_le_Lp_mul_Lq_tsum NNReal.inner_le_Lp_mul_Lq_tsum
 
-theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
+theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).1
 #align nnreal.summable_mul_of_Lp_Lq NNReal.summable_mul_of_Lp_Lq
 
-theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
+theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
@@ -426,7 +424,7 @@ theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsC
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum`.  -/
 theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : HasSum (fun i => f i ^ p) (A ^ p))
+    (hpq : p.IsConjExponent q) (hf : HasSum (fun i => f i ^ p) (A ^ p))
     (hg : HasSum (fun i => g i ^ q) (B ^ q)) : ∃ C, C ≤ A * B ∧ HasSum (fun i => f i * g i) C := by
   obtain ⟨H₁, H₂⟩ := inner_le_Lp_mul_Lq_tsum hpq hf.summable hg.summable
   have hA : A = (∑' i : ι, f i ^ p) ^ (1 / p) := by rw [hf.tsum_eq, rpow_inv_rpow_self hpq.ne_zero]
@@ -445,7 +443,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
   cases' eq_or_lt_of_le hp with hp hp
   · simp [← hp]
   let q : ℝ := p / (p - 1)
-  have hpq : p.IsConjugateExponent q := by rw [Real.isConjugateExponent_iff hp]
+  have hpq : p.IsConjExponent q := .conjExponent hp
   have hp₁ : 1 / p * p = 1 := one_div_mul_cancel hpq.ne_zero
   have hq : 1 / q * p = p - 1 := by
     rw [← hpq.div_conj_eq_sub_one]
@@ -457,7 +455,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
 
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
 `∑ i in s, f i * g i` over functions `g` of `L_q` seminorm less than or equal to one. -/
-theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
+theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjExponent q) :
     IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' { g | ∑ i in s, g i ^ q ≤ 1 })
       ((∑ i in s, f i ^ p) ^ (1 / p)) := by
   constructor
@@ -487,7 +485,7 @@ theorem Lp_add_le (f g : ι → ℝ≥0) {p : ℝ} (hp : 1 ≤ p) :
   -- The result is trivial when `p = 1`, so we can assume `1 < p`.
   rcases eq_or_lt_of_le hp with (rfl | hp);
   · simp [Finset.sum_add_distrib]
-  have hpq := Real.isConjugateExponent_conjugateExponent hp
+  have hpq := Real.IsConjExponent.conjExponent hp
   have := isGreatest_Lp s (f + g) hpq
   simp only [Pi.add_apply, add_mul, sum_add_distrib] at this
   rcases this.1 with ⟨φ, hφ, H⟩
@@ -561,7 +559,7 @@ variable (f g : ι → ℝ) {p q : ℝ}
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
-theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
+theorem inner_le_Lp_mul_Lq (hpq : IsConjExponent p q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, |f i| ^ p) ^ (1 / p) * (∑ i in s, |g i| ^ q) ^ (1 / q) := by
   have :=
     NNReal.coe_le_coe.2
@@ -603,7 +601,7 @@ variable {f g}
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued nonnegative functions. -/
-theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
+theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
     (hg : ∀ i ∈ s, 0 ≤ g i) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   convert inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
@@ -614,7 +612,7 @@ theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `ℝ`-valued functions.
 For an alternative version, convenient if the infinite sums are already expressed as `p`-th powers,
 see `inner_le_Lp_mul_Lq_hasSum_of_nonneg`. -/
-theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
+theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
       ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
@@ -626,13 +624,13 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
 
-theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
+theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     Summable fun i => f i * g i :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).1
 #align real.summable_mul_of_Lp_Lq_of_nonneg Real.summable_mul_of_Lp_Lq_of_nonneg
 
-theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
+theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
@@ -642,7 +640,7 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf :
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum_of_nonneg`.  -/
-theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B : ℝ} (hA : 0 ≤ A)
+theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjExponent q) {A B : ℝ} (hA : 0 ≤ A)
     (hB : 0 ≤ B) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i)
     (hf_sum : HasSum (fun i => f i ^ p) (A ^ p)) (hg_sum : HasSum (fun i => g i ^ q) (B ^ q)) :
     ∃ C : ℝ, 0 ≤ C ∧ C ≤ A * B ∧ HasSum (fun i => f i * g i) C := by
@@ -739,7 +737,7 @@ variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
-theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
+theorem inner_le_Lp_mul_Lq (hpq : p.IsConjExponent q) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   by_cases H : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0
   · replace H : (∀ i ∈ s, f i = 0) ∨ ∀ i ∈ s, g i = 0
@@ -773,7 +771,7 @@ theorem rpow_sum_le_const_mul_sum_rpow (hp : 1 ≤ p) :
   cases' eq_or_lt_of_le hp with hp hp
   · simp [← hp]
   let q : ℝ := p / (p - 1)
-  have hpq : p.IsConjugateExponent q := by rw [Real.isConjugateExponent_iff hp]
+  have hpq : p.IsConjExponent q := .conjExponent hp
   have hp₁ : 1 / p * p = 1 := one_div_mul_cancel hpq.ne_zero
   have hq : 1 / q * p = p - 1 := by
     rw [← hpq.div_conj_eq_sub_one]

I am keeping some 1 / p lemmas behind to keep the diff small but the goal is to get rid of them entirely.

@@ -263,7 +263,7 @@ namespace Real
 theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
   simpa [← rpow_mul, ha, hb, hpq.ne_zero, hpq.symm.ne_zero, _root_.div_eq_inv_mul] using
-    geom_mean_le_arith_mean2_weighted hpq.one_div_nonneg hpq.symm.one_div_nonneg
+    geom_mean_le_arith_mean2_weighted hpq.inv_nonneg hpq.symm.inv_nonneg
       (rpow_nonneg ha p) (rpow_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
 
@@ -283,7 +283,7 @@ namespace NNReal
 
 /-- Young's inequality, `ℝ≥0` version. We use `{p q : ℝ≥0}` in order to avoid constructing
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
-theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 / p + 1 / q = 1) :
+theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : p⁻¹ + q⁻¹ = 1) :
     a * b ≤ a ^ (p : ℝ) / p + b ^ (q : ℝ) / q :=
   Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_inj.2 hpq⟩
 #align nnreal.young_inequality NNReal.young_inequality
@@ -341,7 +341,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
       refine' add_le_add _ _
       · rwa [div_le_iff hp_ne_zero, div_mul_cancel _ hp_ne_zero]
       · rwa [div_le_iff hq_ne_zero, div_mul_cancel _ hq_ne_zero]
-    _ = 1 := hpq.inv_add_inv_conj_nnreal
+    _ = 1 := by simp_rw [one_div, hpq.inv_add_inv_conj_nnreal]
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
     (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p = 0) :
@@ -471,7 +471,7 @@ theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExpon
       simp only [Set.mem_setOf_eq, div_rpow, ← sum_div, ← rpow_mul,
         div_mul_cancel _ hpq.symm.ne_zero, rpow_one, div_le_iff hf, one_mul, hpq.mul_eq_add, ←
         rpow_sub' _ A, _root_.add_sub_cancel, le_refl, true_and_iff, ← mul_div_assoc, B]
-      rw [div_eq_iff, ← rpow_add hf, hpq.inv_add_inv_conj, rpow_one]
+      rw [div_eq_iff, ← rpow_add hf, one_div, one_div, hpq.inv_add_inv_conj, rpow_one]
       simpa [hpq.symm.ne_zero] using hf
   · rintro _ ⟨g, hg, rfl⟩
     apply le_trans (inner_le_Lp_mul_Lq s f g hpq)

Add a few missing lemmas about the coercion NNReal → Real. Remove a bunch of protected on the existing coercion lemmas (so that it matches the convention for other coercions). Rename NNReal.coe_eq to NNReal.coe_inj

From LeanAPAP

@@ -228,7 +228,7 @@ namespace Real
 theorem geom_mean_le_arith_mean2_weighted {w₁ w₂ p₁ p₂ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
     (hp₁ : 0 ≤ p₁) (hp₂ : 0 ≤ p₂) (hw : w₁ + w₂ = 1) : p₁ ^ w₁ * p₂ ^ w₂ ≤ w₁ * p₁ + w₂ * p₂ :=
   NNReal.geom_mean_le_arith_mean2_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩ <|
-    NNReal.coe_eq.1 <| by assumption
+    NNReal.coe_inj.1 <| by assumption
 #align real.geom_mean_le_arith_mean2_weighted Real.geom_mean_le_arith_mean2_weighted
 
 theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ} (hw₁ : 0 ≤ w₁) (hw₂ : 0 ≤ w₂)
@@ -236,7 +236,7 @@ theorem geom_mean_le_arith_mean3_weighted {w₁ w₂ w₃ p₁ p₂ p₃ : ℝ}
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ :=
   NNReal.geom_mean_le_arith_mean3_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨w₃, hw₃⟩ ⟨p₁, hp₁⟩ ⟨p₂, hp₂⟩
       ⟨p₃, hp₃⟩ <|
-    NNReal.coe_eq.1 hw
+    NNReal.coe_inj.1 hw
 #align real.geom_mean_le_arith_mean3_weighted Real.geom_mean_le_arith_mean3_weighted
 
 theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ} (hw₁ : 0 ≤ w₁)
@@ -245,7 +245,7 @@ theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
     p₁ ^ w₁ * p₂ ^ w₂ * p₃ ^ w₃ * p₄ ^ w₄ ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ + w₄ * p₄ :=
   NNReal.geom_mean_le_arith_mean4_weighted ⟨w₁, hw₁⟩ ⟨w₂, hw₂⟩ ⟨w₃, hw₃⟩ ⟨w₄, hw₄⟩ ⟨p₁, hp₁⟩
       ⟨p₂, hp₂⟩ ⟨p₃, hp₃⟩ ⟨p₄, hp₄⟩ <|
-    NNReal.coe_eq.1 <| by assumption
+    NNReal.coe_inj.1 <| by assumption
 #align real.geom_mean_le_arith_mean4_weighted Real.geom_mean_le_arith_mean4_weighted
 
 end Real
@@ -285,7 +285,7 @@ namespace NNReal
 witnesses of `0 ≤ p` and `0 ≤ q` for the denominators.  -/
 theorem young_inequality (a b : ℝ≥0) {p q : ℝ≥0} (hp : 1 < p) (hpq : 1 / p + 1 / q = 1) :
     a * b ≤ a ^ (p : ℝ) / p + b ^ (q : ℝ) / q :=
-  Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_eq.2 hpq⟩
+  Real.young_inequality_of_nonneg a.coe_nonneg b.coe_nonneg ⟨hp, NNReal.coe_inj.2 hpq⟩
 #align nnreal.young_inequality NNReal.young_inequality
 
 /-- Young's inequality, `ℝ≥0` version with real conjugate exponents. -/

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

@@ -762,7 +762,7 @@ theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
     le_of_lt hpq.symm.pos, le_of_lt hpq.symm.one_div_pos] at this
   convert this using 1 <;> [skip; congr 2] <;> [skip; skip; simp; skip; simp] <;>
     · refine Finset.sum_congr rfl fun i hi => ?_
-      simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul, WithTop.coe_mul.symm]
+      simp [H'.1 i hi, H'.2 i hi, -WithZero.coe_mul]
 #align ennreal.inner_le_Lp_mul_Lq ENNReal.inner_le_Lp_mul_Lq
 
 /-- For `1 ≤ p`, the `p`-th power of the sum of `f i` is bounded above by a constant times the

This better matches other lemma names.

From LeanAPAP

@@ -138,7 +138,7 @@ theorem geom_mean_le_arith_mean {ι : Type*} (s : Finset ι) (w : ι → ℝ) (z
     (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : 0 < ∑ i in s, w i) (hz : ∀ i ∈ s, 0 ≤ z i) :
     (∏ i in s, z i ^ w i) ^ (∑ i in s, w i)⁻¹  ≤  (∑ i in s, w i * z i) / (∑ i in s, w i) := by
   convert geom_mean_le_arith_mean_weighted s (fun i => (w i) / ∑ i in s, w i) z ?_ ?_ hz using 2
-  · rw [← finset_prod_rpow _ _ (fun i hi => rpow_nonneg_of_nonneg (hz _ hi) _) _]
+  · rw [← finset_prod_rpow _ _ (fun i hi => rpow_nonneg (hz _ hi) _) _]
     refine Finset.prod_congr rfl (fun _ ih => ?_)
     rw [div_eq_mul_inv, rpow_mul (hz _ ih)]
   · simp_rw [div_eq_mul_inv, mul_assoc, mul_comm, ← mul_assoc, ← Finset.sum_mul, mul_comm]
@@ -264,7 +264,7 @@ theorem young_inequality_of_nonneg {a b p q : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b)
     (hpq : p.IsConjugateExponent q) : a * b ≤ a ^ p / p + b ^ q / q := by
   simpa [← rpow_mul, ha, hb, hpq.ne_zero, hpq.symm.ne_zero, _root_.div_eq_inv_mul] using
     geom_mean_le_arith_mean2_weighted hpq.one_div_nonneg hpq.symm.one_div_nonneg
-      (rpow_nonneg_of_nonneg ha p) (rpow_nonneg_of_nonneg hb q) hpq.inv_add_inv_conj
+      (rpow_nonneg ha p) (rpow_nonneg hb q) hpq.inv_add_inv_conj
 #align real.young_inequality_of_nonneg Real.young_inequality_of_nonneg
 
 /-- Young's inequality, a version for arbitrary real numbers. -/
@@ -594,7 +594,7 @@ theorem Lp_add_le (hp : 1 ≤ p) :
       (NNReal.Lp_add_le s (fun i => ⟨_, abs_nonneg (f i)⟩) (fun i => ⟨_, abs_nonneg (g i)⟩) hp)
   push_cast at this
   refine' le_trans (rpow_le_rpow _ (sum_le_sum fun i _ => _) _) this <;>
-    simp [sum_nonneg, rpow_nonneg_of_nonneg, abs_nonneg, le_trans zero_le_one hp, abs_add,
+    simp [sum_nonneg, rpow_nonneg, abs_nonneg, le_trans zero_le_one hp, abs_add,
       rpow_le_rpow]
 #align real.Lp_add_le Real.Lp_add_le
 

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -152,7 +152,7 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
   calc
     ∏ i in s, z i ^ w i = ∏ i in s, x ^ w i := by
       refine' prod_congr rfl fun i hi => _
-      cases' eq_or_ne (w i) 0 with h₀ h₀
+      rcases eq_or_ne (w i) 0 with h₀ | h₀
       · rw [h₀, rpow_zero, rpow_zero]
       · rw [hx i hi h₀]
     _ = x := by
@@ -170,7 +170,7 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : ∑
   calc
     ∑ i in s, w i * z i = ∑ i in s, w i * x := by
       refine' sum_congr rfl fun i hi => _
-      cases' eq_or_ne (w i) 0 with hwi hwi
+      rcases eq_or_ne (w i) 0 with hwi | hwi
       · rw [hwi, zero_mul, zero_mul]
       · rw [hx i hi hwi]
     _ = x := by rw [← sum_mul, hw', one_mul]

Rationale: this instance creates (empty) data out of nothing, which may conflict with other data. If you have in the context [Fintype i] and case on whether i is empty or not, then this gave two non-defeq instances of [Fintype i] around.

@@ -200,7 +200,7 @@ for two `NNReal` numbers. -/
 theorem geom_mean_le_arith_mean2_weighted (w₁ w₂ p₁ p₂ : ℝ≥0) :
     w₁ + w₂ = 1 → p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ := by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
-    Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one] using
+    Finset.univ_eq_empty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one] using
     geom_mean_le_arith_mean_weighted univ ![w₁, w₂] ![p₁, p₂]
 #align nnreal.geom_mean_le_arith_mean2_weighted NNReal.geom_mean_le_arith_mean2_weighted
 
@@ -208,7 +208,7 @@ theorem geom_mean_le_arith_mean3_weighted (w₁ w₂ w₃ p₁ p₂ p₃ : ℝ
     w₁ + w₂ + w₃ = 1 →
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) ≤ w₁ * p₁ + w₂ * p₂ + w₃ * p₃ := by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
-    Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
+    Finset.univ_eq_empty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃] ![p₁, p₂, p₃]
 #align nnreal.geom_mean_le_arith_mean3_weighted NNReal.geom_mean_le_arith_mean3_weighted
 
@@ -217,7 +217,7 @@ theorem geom_mean_le_arith_mean4_weighted (w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
       p₁ ^ (w₁ : ℝ) * p₂ ^ (w₂ : ℝ) * p₃ ^ (w₃ : ℝ) * p₄ ^ (w₄ : ℝ) ≤
         w₁ * p₁ + w₂ * p₂ + w₃ * p₃ + w₄ * p₄ := by
   simpa only [Fin.prod_univ_succ, Fin.sum_univ_succ, Finset.prod_empty, Finset.sum_empty,
-    Fintype.univ_of_isEmpty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
+    Finset.univ_eq_empty, Fin.cons_succ, Fin.cons_zero, add_zero, mul_one, ← add_assoc,
     mul_assoc] using geom_mean_le_arith_mean_weighted univ ![w₁, w₂, w₃, w₄] ![p₁, p₂, p₃, p₄]
 #align nnreal.geom_mean_le_arith_mean4_weighted NNReal.geom_mean_le_arith_mean4_weighted
 

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>

@@ -189,8 +189,8 @@ namespace NNReal
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for `NNReal`-valued functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) :
-    (∏ i in s, z i ^ (w i : ℝ)) ≤ ∑ i in s, w i * z i := by
-  exact_mod_cast
+    (∏ i in s, z i ^ (w i : ℝ)) ≤ ∑ i in s, w i * z i :=
+  mod_cast
     Real.geom_mean_le_arith_mean_weighted _ _ _ (fun i _ => (w i).coe_nonneg)
       (by assumption_mod_cast) fun i _ => (z i).coe_nonneg
 #align nnreal.geom_mean_le_arith_mean_weighted NNReal.geom_mean_le_arith_mean_weighted

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>

@@ -98,8 +98,6 @@ set_option linter.uppercaseLean3 false
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 variable {ι : Type u} (s : Finset ι)
 
 section GeomMeanLEArithMean

We define the convex body convexBodySum and prove the following

theorem exists_ne_zero_mem_ringOfIntegers_of_norm_le {B : ℝ}
     (h : (minkowskiBound K) < volume (convexBodySum K B)) :
     ∃ (a : 𝓞 K), a ≠ 0 ∧ |Algebra.norm ℚ (a:K)| ≤ ((finrank ℚ K : ℝ)⁻¹ * B) ^ (finrank ℚ K) 

Computation of the volume (convexBodySum K B)) and applications of the result are coming in a following PR.

@@ -135,6 +135,19 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
       · rw [exp_log hz]
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
 
+/-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**. --/
+theorem geom_mean_le_arith_mean {ι : Type*} (s : Finset ι) (w : ι → ℝ) (z : ι → ℝ)
+    (hw : ∀ i ∈ s, 0 ≤ w i) (hw' : 0 < ∑ i in s, w i) (hz : ∀ i ∈ s, 0 ≤ z i) :
+    (∏ i in s, z i ^ w i) ^ (∑ i in s, w i)⁻¹  ≤  (∑ i in s, w i * z i) / (∑ i in s, w i) := by
+  convert geom_mean_le_arith_mean_weighted s (fun i => (w i) / ∑ i in s, w i) z ?_ ?_ hz using 2
+  · rw [← finset_prod_rpow _ _ (fun i hi => rpow_nonneg_of_nonneg (hz _ hi) _) _]
+    refine Finset.prod_congr rfl (fun _ ih => ?_)
+    rw [div_eq_mul_inv, rpow_mul (hz _ ih)]
+  · simp_rw [div_eq_mul_inv, mul_assoc, mul_comm, ← mul_assoc, ← Finset.sum_mul, mul_comm]
+  · exact fun _ hi => div_nonneg (hw _ hi) (le_of_lt hw')
+  · simp_rw [div_eq_mul_inv, ← Finset.sum_mul]
+    exact mul_inv_cancel (by linarith)
+
 theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
     (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
     ∏ i in s, z i ^ w i = x :=

This incorporates changes from

• #7845
• #7847
• #7853
• #7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

@@ -609,6 +609,8 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
       ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
+  -- After leanprover/lean4#2734, `norm_cast` needs help with beta reduction.
+  beta_reduce at *
   norm_cast at *
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
@@ -637,6 +639,8 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
+  -- After leanprover/lean4#2734, `norm_cast` needs help with beta reduction.
+  beta_reduce at *
   norm_cast at hf_sum hg_sum
   obtain ⟨C, hC, H⟩ := NNReal.inner_le_Lp_mul_Lq_hasSum hpq hf_sum hg_sum
   refine' ⟨C, C.prop, hC, _⟩
@@ -674,6 +678,8 @@ theorem Lp_add_le_tsum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : 
         (∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p) := by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
+  -- After leanprover/lean4#2734, `norm_cast` needs help with beta reduction.
+  beta_reduce at *
   norm_cast0 at *
   exact NNReal.Lp_add_le_tsum hp hf_sum hg_sum
 #align real.Lp_add_le_tsum_of_nonneg Real.Lp_add_le_tsum_of_nonneg
@@ -702,9 +708,13 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
+  -- After leanprover/lean4#2734, `norm_cast` needs help with beta reduction.
+  beta_reduce at hfA hgB
   norm_cast at hfA hgB
   obtain ⟨C, hC₁, hC₂⟩ := NNReal.Lp_add_le_hasSum hp hfA hgB
   use C
+  -- After leanprover/lean4#2734, `norm_cast` needs help with beta reduction.
+  beta_reduce
   norm_cast
   exact ⟨zero_le _, hC₁, hC₂⟩
 #align real.Lp_add_le_has_sum_of_nonneg Real.Lp_add_le_hasSum_of_nonneg

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -160,7 +160,7 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : ∑
     ∑ i in s, w i * z i = ∑ i in s, w i * x := by
       refine' sum_congr rfl fun i hi => _
       cases' eq_or_ne (w i) 0 with hwi hwi
-      · rw [hwi, MulZeroClass.zero_mul, MulZeroClass.zero_mul]
+      · rw [hwi, zero_mul, zero_mul]
       · rw [hx i hi hwi]
     _ = x := by rw [← sum_mul, hw', one_mul]
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
@@ -335,7 +335,7 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
     (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p = 0) :
     ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
-  simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, MulZeroClass.zero_mul,
+  simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, zero_mul,
     inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
   intro i his
   left

@@ -98,7 +98,7 @@ set_option linter.uppercaseLean3 false
 
 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
-! leanprover-community/mathlib commit 8f9fea08977f7e450770933ee6abb20733b47c92
-! 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.Data.Real.ConjugateExponents
 
+#align_import analysis.mean_inequalities from "leanprover-community/mathlib"@"8f9fea08977f7e450770933ee6abb20733b47c92"
+
 /-!
 # 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

@@ -115,8 +115,8 @@ namespace Real
 /-- AM-GM inequality: the **geometric mean is less than or equal to the arithmetic mean**, weighted
 version for real-valued nonnegative functions. -/
 theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) :
-    (∏ i in s, z i ^ w i) ≤ ∑ i in s, w i * z i := by
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) :
+    ∏ i in s, z i ^ w i ≤ ∑ i in s, w i * z i := by
   -- If some number `z i` equals zero and has non-zero weight, then LHS is 0 and RHS is nonnegative.
   by_cases A : ∃ i ∈ s, z i = 0 ∧ w i ≠ 0
   · rcases A with ⟨i, his, hzi, hwi⟩
@@ -139,10 +139,10 @@ theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ) (hw : ∀ i ∈ s, 0
 #align real.geom_mean_le_arith_mean_weighted Real.geom_mean_le_arith_mean_weighted
 
 theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
-    (∏ i in s, z i ^ w i) = x :=
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
+    ∏ i in s, z i ^ w i = x :=
   calc
-    (∏ i in s, z i ^ w i) = ∏ i in s, x ^ w i := by
+    ∏ i in s, z i ^ w i = ∏ i in s, x ^ w i := by
       refine' prod_congr rfl fun i hi => _
       cases' eq_or_ne (w i) 0 with h₀ h₀
       · rw [h₀, rpow_zero, rpow_zero]
@@ -157,10 +157,10 @@ theorem geom_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i
       exact hz i his
 #align real.geom_mean_weighted_of_constant Real.geom_mean_weighted_of_constant
 
-theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑ i in s, w i) = 1)
-    (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : (∑ i in s, w i * z i) = x :=
+theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : ∑ i in s, w i = 1)
+    (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) : ∑ i in s, w i * z i = x :=
   calc
-    (∑ i in s, w i * z i) = ∑ i in s, w i * x := by
+    ∑ i in s, w i * z i = ∑ i in s, w i * x := by
       refine' sum_congr rfl fun i hi => _
       cases' eq_or_ne (w i) 0 with hwi hwi
       · rw [hwi, MulZeroClass.zero_mul, MulZeroClass.zero_mul]
@@ -169,8 +169,8 @@ theorem arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw' : (∑
 #align real.arith_mean_weighted_of_constant Real.arith_mean_weighted_of_constant
 
 theorem geom_mean_eq_arith_mean_weighted_of_constant (w z : ι → ℝ) (x : ℝ) (hw : ∀ i ∈ s, 0 ≤ w i)
-    (hw' : (∑ i in s, w i) = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
-    (∏ i in s, z i ^ w i) = ∑ i in s, w i * z i := by
+    (hw' : ∑ i in s, w i = 1) (hz : ∀ i ∈ s, 0 ≤ z i) (hx : ∀ i ∈ s, w i ≠ 0 → z i = x) :
+    ∏ i in s, z i ^ w i = ∑ i in s, w i * z i := by
   rw [geom_mean_weighted_of_constant, arith_mean_weighted_of_constant] <;> assumption
 #align real.geom_mean_eq_arith_mean_weighted_of_constant Real.geom_mean_eq_arith_mean_weighted_of_constant
 
@@ -180,7 +180,7 @@ namespace NNReal
 
 /-- The geometric mean is less than or equal to the arithmetic mean, weighted version
 for `NNReal`-valued functions. -/
-theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : (∑ i in s, w i) = 1) :
+theorem geom_mean_le_arith_mean_weighted (w z : ι → ℝ≥0) (hw' : ∑ i in s, w i = 1) :
     (∏ i in s, z i ^ (w i : ℝ)) ≤ ∑ i in s, w i * z i := by
   exact_mod_cast
     Real.geom_mean_le_arith_mean_weighted _ _ _ (fun i _ => (w i).coe_nonneg)
@@ -320,12 +320,12 @@ section HolderMinkowski
 namespace NNReal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) ≤ 1) (hg : (∑ i in s, g i ^ q) ≤ 1) :
-    (∑ i in s, f i * g i) ≤ 1 := by
+    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p ≤ 1) (hg : ∑ i in s, g i ^ q ≤ 1) :
+    ∑ i in s, f i * g i ≤ 1 := by
   have hp_ne_zero : Real.toNNReal p ≠ 0 := (zero_lt_one.trans hpq.one_lt_nnreal).ne.symm
   have hq_ne_zero : Real.toNNReal q ≠ 0 := (zero_lt_one.trans hpq.symm.one_lt_nnreal).ne.symm
   calc
-    (∑ i in s, f i * g i) ≤ ∑ i in s, (f i ^ p / Real.toNNReal p + g i ^ q / Real.toNNReal q) :=
+    ∑ i in s, f i * g i ≤ ∑ i in s, (f i ^ p / Real.toNNReal p + g i ^ q / Real.toNNReal q) :=
       Finset.sum_le_sum fun i _ => young_inequality_real (f i) (g i) hpq
     _ = (∑ i in s, f i ^ p) / Real.toNNReal p + (∑ i in s, g i ^ q) / Real.toNNReal q := by
       rw [sum_add_distrib, sum_div, sum_div]
@@ -336,8 +336,8 @@ private theorem inner_le_Lp_mul_Lp_of_norm_le_one (f g : ι → ℝ≥0) {p q :
     _ = 1 := hpq.inv_add_inv_conj_nnreal
 
 private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q : ℝ}
-    (hpq : p.IsConjugateExponent q) (hf : (∑ i in s, f i ^ p) = 0) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
+    (hpq : p.IsConjugateExponent q) (hf : ∑ i in s, f i ^ p = 0) :
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   simp only [hf, hpq.ne_zero, one_div, sum_eq_zero_iff, zero_rpow, MulZeroClass.zero_mul,
     inv_eq_zero, Ne.def, not_false_iff, le_zero_iff, mul_eq_zero]
   intro i his
@@ -349,12 +349,12 @@ private theorem inner_le_Lp_mul_Lp_of_norm_eq_zero (f g : ι → ℝ≥0) {p q :
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
-  by_cases hF_zero : (∑ i in s, f i ^ p) = 0
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
+  by_cases hF_zero : ∑ i in s, f i ^ p = 0
   · exact inner_le_Lp_mul_Lp_of_norm_eq_zero s f g hpq hF_zero
-  by_cases hG_zero : (∑ i in s, g i ^ q) = 0
+  by_cases hG_zero : ∑ i in s, g i ^ q = 0
   · calc
-      (∑ i in s, f i * g i) = ∑ i in s, g i * f i := by
+      ∑ i in s, f i * g i = ∑ i in s, g i * f i := by
         congr with i
         rw [mul_comm]
       _ ≤ (∑ i in s, g i ^ q) ^ (1 / q) * (∑ i in s, f i ^ p) ^ (1 / p) :=
@@ -384,9 +384,9 @@ functions. For an alternative version, convenient if the infinite sums are alrea
 theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
-      (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
+      ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
   have H₁ : ∀ s : Finset ι,
-      (∑ i in s, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
+      ∑ i in s, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
     intro s
     refine' le_trans (inner_le_Lp_mul_Lq s f g hpq) (mul_le_mul _ _ bot_le bot_le)
     · rw [NNReal.rpow_le_rpow_iff (one_div_pos.mpr hpq.pos)]
@@ -409,7 +409,7 @@ theorem summable_mul_of_Lp_Lq {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConj
 
 theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
     (hf : Summable fun i => f i ^ p) (hg : Summable fun i => g i ^ q) :
-    (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+    ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum hpq hf hg).2
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
 
@@ -450,11 +450,11 @@ theorem rpow_sum_le_const_mul_sum_rpow (f : ι → ℝ≥0) {p : ℝ} (hp : 1 
 /-- The `L_p` seminorm of a vector `f` is the greatest value of the inner product
 `∑ i in s, f i * g i` over functions `g` of `L_q` seminorm less than or equal to one. -/
 theorem isGreatest_Lp (f : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjugateExponent q) :
-    IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' { g | (∑ i in s, g i ^ q) ≤ 1 })
+    IsGreatest ((fun g : ι → ℝ≥0 => ∑ i in s, f i * g i) '' { g | ∑ i in s, g i ^ q ≤ 1 })
       ((∑ i in s, f i ^ p) ^ (1 / p)) := by
   constructor
   · use fun i => f i ^ p / f i / (∑ i in s, f i ^ p) ^ (1 / q)
-    by_cases hf : (∑ i in s, f i ^ p) = 0
+    by_cases hf : ∑ i in s, f i ^ p = 0
     · simp [hf, hpq.ne_zero, hpq.symm.ne_zero]
     · have A : p + q - q ≠ 0 := by simp [hpq.ne_zero]
       have B : ∀ y : ℝ≥0, y * y ^ p / y = y ^ p := by
@@ -554,7 +554,7 @@ variable (f g : ι → ℝ) {p q : ℝ}
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with real-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : IsConjugateExponent p q) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, |f i| ^ p) ^ (1 / p) * (∑ i in s, |g i| ^ q) ^ (1 / q) := by
+    ∑ i in s, f i * g i ≤ (∑ i in s, |f i| ^ p) ^ (1 / p) * (∑ i in s, |g i| ^ q) ^ (1 / q) := by
   have :=
     NNReal.coe_le_coe.2
       (NNReal.inner_le_Lp_mul_Lq s (fun i => ⟨_, abs_nonneg (f i)⟩) (fun i => ⟨_, abs_nonneg (g i)⟩)
@@ -597,7 +597,7 @@ variable {f g}
 with real-valued nonnegative functions. -/
 theorem inner_le_Lp_mul_Lq_of_nonneg (hpq : IsConjugateExponent p q) (hf : ∀ i ∈ s, 0 ≤ f i)
     (hg : ∀ i ∈ s, 0 ≤ g i) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   convert inner_le_Lp_mul_Lq s f g hpq using 3 <;> apply sum_congr rfl <;> intro i hi <;>
     simp only [abs_of_nonneg, hf i hi, hg i hi]
 #align real.inner_le_Lp_mul_Lq_of_nonneg Real.inner_le_Lp_mul_Lq_of_nonneg
@@ -609,7 +609,7 @@ see `inner_le_Lp_mul_Lq_hasSum_of_nonneg`. -/
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
     (Summable fun i => f i * g i) ∧
-      (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
+      ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
   norm_cast at *
@@ -624,7 +624,7 @@ theorem summable_mul_of_Lp_Lq_of_nonneg (hpq : p.IsConjugateExponent q) (hf : 
 
 theorem inner_le_Lp_mul_Lq_tsum_of_nonneg' (hpq : p.IsConjugateExponent q) (hf : ∀ i, 0 ≤ f i)
     (hg : ∀ i, 0 ≤ g i) (hf_sum : Summable fun i => f i ^ p) (hg_sum : Summable fun i => g i ^ q) :
-    (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
+    ∑' i, f i * g i ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) :=
   (inner_le_Lp_mul_Lq_tsum_of_nonneg hpq hf hg hf_sum hg_sum).2
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg' Real.inner_le_Lp_mul_Lq_tsum_of_nonneg'
 
@@ -722,13 +722,13 @@ variable (f g : ι → ℝ≥0∞) {p q : ℝ}
 `L^p` and `L^q` norms when `p` and `q` are conjugate exponents. Version for sums over finite sets,
 with `ℝ≥0∞`-valued functions. -/
 theorem inner_le_Lp_mul_Lq (hpq : p.IsConjugateExponent q) :
-    (∑ i in s, f i * g i) ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
+    ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q) := by
   by_cases H : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0
   · replace H : (∀ i ∈ s, f i = 0) ∨ ∀ i ∈ s, g i = 0
     · simpa [ENNReal.rpow_eq_zero_iff, hpq.pos, hpq.symm.pos, asymm hpq.pos, asymm hpq.symm.pos,
         sum_eq_zero_iff_of_nonneg] using H
     have : ∀ i ∈ s, f i * g i = 0 := fun i hi => by cases' H with H H <;> simp [H i hi]
-    have : (∑ i in s, f i * g i) = ∑ i in s, 0 := sum_congr rfl this
+    have : ∑ i in s, f i * g i = ∑ i in s, 0 := sum_congr rfl this
     simp [this]
   push_neg at H
   by_cases H' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ q) ^ (1 / q) = ⊤

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -299,7 +299,7 @@ theorem young_inequality (a b : ℝ≥0∞) {p q : ℝ} (hpq : p.IsConjugateExpo
   · refine' le_trans le_top (le_of_eq _)
     repeat rw [div_eq_mul_inv]
     cases' h with h h <;> rw [h] <;> simp [h, hpq.pos, hpq.symm.pos]
-  push_neg  at h
+  push_neg at h
   -- if a ≠ ⊤ and b ≠ ⊤, use the nnreal version: nnreal.young_inequality_real
   rw [← coe_toNNReal h.left, ← coe_toNNReal h.right, ← coe_mul, coe_rpow_of_nonneg _ hpq.nonneg,
     coe_rpow_of_nonneg _ hpq.symm.nonneg, ENNReal.ofReal, ENNReal.ofReal, ←
@@ -612,7 +612,7 @@ theorem inner_le_Lp_mul_Lq_tsum_of_nonneg (hpq : p.IsConjugateExponent q) (hf :
       (∑' i, f i * g i) ≤ (∑' i, f i ^ p) ^ (1 / p) * (∑' i, g i ^ q) ^ (1 / q) := by
   lift f to ι → ℝ≥0 using hf
   lift g to ι → ℝ≥0 using hg
-  norm_cast  at *
+  norm_cast at *
   exact NNReal.inner_le_Lp_mul_Lq_tsum hpq hf_sum hg_sum
 #align real.inner_le_Lp_mul_Lq_tsum_of_nonneg Real.inner_le_Lp_mul_Lq_tsum_of_nonneg
 
@@ -705,7 +705,7 @@ theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg :
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast  at hfA hgB
+  norm_cast at hfA hgB
   obtain ⟨C, hC₁, hC₂⟩ := NNReal.Lp_add_le_hasSum hp hfA hgB
   use C
   norm_cast

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -506,7 +506,7 @@ theorem Lp_add_le_tsum {f g : ι → ℝ≥0} {p : ℝ} (hp : 1 ≤ p) (hf : Sum
     refine' le_trans (Lp_add_le s f g hp) (add_le_add _ _) <;>
         rw [NNReal.rpow_le_rpow_iff (one_div_pos.mpr pos)] <;>
       refine' sum_le_tsum _ (fun _ _ => zero_le _) _
-    exacts[hf, hg]
+    exacts [hf, hg]
   have bdd : BddAbove (Set.range fun s => ∑ i in s, (f i + g i) ^ p) := by
     refine' ⟨((∑' i, f i ^ p) ^ (1 / p) + (∑' i, g i ^ p) ^ (1 / p)) ^ p, _⟩
     rintro a ⟨s, rfl⟩

@@ -95,9 +95,7 @@ less than or equal to the sum of the maximum values of the summands.
 
 universe u v
 
-open Finset
-
-open Classical BigOperators NNReal ENNReal
+open Finset Classical BigOperators NNReal ENNReal
 
 set_option linter.uppercaseLean3 false
 
@@ -107,7 +105,7 @@ local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issu
 
 variable {ι : Type u} (s : Finset ι)
 
-section GeomMeanLeArithMean
+section GeomMeanLEArithMean
 
 /-! ### AM-GM inequality -/
 
@@ -244,7 +242,7 @@ theorem geom_mean_le_arith_mean4_weighted {w₁ w₂ w₃ w₄ p₁ p₂ p₃ p
 
 end Real
 
-end GeomMeanLeArithMean
+end GeomMeanLEArithMean
 
 section Young
 
@@ -642,7 +640,7 @@ theorem inner_le_Lp_mul_Lq_hasSum_of_nonneg (hpq : p.IsConjugateExponent q) {A B
   lift g to ι → ℝ≥0 using hg
   lift A to ℝ≥0 using hA
   lift B to ℝ≥0 using hB
-  norm_cast  at hf_sum hg_sum
+  norm_cast at hf_sum hg_sum
   obtain ⟨C, hC, H⟩ := NNReal.inner_le_Lp_mul_Lq_hasSum hpq hf_sum hg_sum
   refine' ⟨C, C.prop, hC, _⟩
   norm_cast

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -380,7 +380,7 @@ theorem inner_le_Lp_mul_Lq (f g : ι → ℝ≥0) {p q : ℝ} (hpq : p.IsConjuga
 #align nnreal.inner_le_Lp_mul_Lq NNReal.inner_le_Lp_mul_Lq
 
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
-`L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
+`L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_hasSum`. -/
 theorem inner_le_Lp_mul_Lq_tsum {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsConjugateExponent q)
@@ -416,7 +416,7 @@ theorem inner_le_Lp_mul_Lq_tsum' {f g : ι → ℝ≥0} {p q : ℝ} (hpq : p.IsC
 #align nnreal.inner_le_Lp_mul_Lq_tsum' NNReal.inner_le_Lp_mul_Lq_tsum'
 
 /-- Hölder inequality: the scalar product of two functions is bounded by the product of their
-`L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `nnreal`-valued
+`L^p` and `L^q` norms when `p` and `q` are conjugate exponents. A version for `NNReal`-valued
 functions. For an alternative version, convenient if the infinite sums are not already expressed as
 `p`-th powers, see `inner_le_Lp_mul_Lq_tsum`.  -/
 theorem inner_le_Lp_mul_Lq_hasSum {f g : ι → ℝ≥0} {A B : ℝ≥0} {p q : ℝ}

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Komyyy <pol_tta@outlook.jp>