data.real.nnreal | Mathlib porting status

feat(measure_theory/order/upper_lower): Order-connected sets in ℝⁿ are measurable (#16976)

Prove that the frontier of an order-connected set in ℝⁿ (with the ∞-metric, but it doesn't actually matter) has measure zero.

As a corollary, antichains in ℝⁿ have measure zero.

Co-authored-by: @JasonKYi

Diff

@@ -822,6 +822,8 @@ lemma nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 lemma coe_to_nnreal_le (x : ℝ) : (to_nnreal x : ℝ) ≤ |x| :=
 max_le (le_abs_self _) (abs_nonneg _)
 
+@[simp] lemma to_nnreal_abs (x : ℝ) : |x|.to_nnreal = x.nnabs := nnreal.coe_injective $ by simp
+
 lemma cast_nat_abs_eq_nnabs_cast (n : ℤ) :
   (n.nat_abs : ℝ≥0) = nnabs n :=
 by { ext, rw [nnreal.coe_nat_cast, int.cast_nat_abs, real.coe_nnabs] }

(last sync)

feat(algebra/order/sub/defs): make has_ordered_sub a Prop (#18810)

has_ordered_sub was incorrectly a Type, because of a Lean 3 bug. This is a backport of mathlib4 [#3436](https://github.com/leanprover-community/mathlib4/pull/3436) .

Co-authored-by: Alex J Best <alex.j.best@gmail.com>

Diff

@@ -568,7 +568,7 @@ lemma sub_def {r p : ℝ≥0} : r - p = real.to_nnreal (r - p) := rfl
 
 lemma coe_sub_def {r p : ℝ≥0} : ↑(r - p) = max (r - p : ℝ) 0 := rfl
 
-noncomputable example : has_ordered_sub ℝ≥0 := by apply_instance
+example : has_ordered_sub ℝ≥0 := by apply_instance
 
 lemma sub_div (a b c : ℝ≥0) : (a - b) / c = a / c - b / c := tsub_div _ _ _

chore(algebra/order/nonneg/*): Separate floor_ring from field (#18596)

Move the archimedean and floor_ring instances out of algebra.order.nonneg.field into a new file algebra.order.nonneg.floor.

Diff

@@ -3,11 +3,12 @@ Copyright (c) 2018 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import order.conditionally_complete_lattice.group
 import algebra.algebra.basic
-import algebra.order.nonneg.field
 import algebra.order.field.canonical.basic
+import algebra.order.nonneg.field
+import algebra.order.nonneg.floor
 import data.real.pointwise
+import order.conditionally_complete_lattice.group
 import tactic.positivity
 
 /-!

chore(data/real/nnreal): drop some lemmas (#18492)

These lemmas are now available for any semifield, so we don't need them.

All these lemmas are @[deprecated] in the Mathlib 4 port and will be removed in the forward-port of this PR.

Diff

@@ -579,12 +579,6 @@ lemma sum_div {ι} (s : finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
   (∑ i in s, f i) / b = ∑ i in s, (f i / b) :=
 finset.sum_div
 
-@[simp] lemma inv_pos {r : ℝ≥0} : 0 < r⁻¹ ↔ 0 < r := inv_pos
-
-lemma div_pos {r p : ℝ≥0} (hr : 0 < r) (hp : 0 < p) : 0 < r / p := div_pos hr hp
-
-lemma div_self_le (r : ℝ≥0) : r / r ≤ 1 := div_self_le_one r
-
 @[simp] lemma inv_le {r p : ℝ≥0} (h : r ≠ 0) : r⁻¹ ≤ p ↔ 1 ≤ r * p :=
 by rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h]
 
@@ -661,36 +655,16 @@ le_of_forall_ge_of_dense $ assume a ha,
   have (a * x⁻¹) * x ≤ y, from h _ this,
   by rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this
 
-lemma div_add_div_same (a b c : ℝ≥0) : a / c + b / c = (a + b) / c := div_add_div_same _ _ _
-
-lemma half_pos {a : ℝ≥0} (h : 0 < a) : 0 < a / 2 := half_pos h
-
-lemma add_halves (a : ℝ≥0) : a / 2 + a / 2 = a := add_halves _
-
 lemma half_le_self (a : ℝ≥0) : a / 2 ≤ a := half_le_self bot_le
 
 lemma half_lt_self {a : ℝ≥0} (h : a ≠ 0) : a / 2 < a := half_lt_self h.bot_lt
 
-lemma two_inv_lt_one : (2⁻¹:ℝ≥0) < 1 := two_inv_lt_one
-
 lemma div_lt_one_of_lt {a b : ℝ≥0} (h : a < b) : a / b < 1 :=
 begin
   rwa [div_lt_iff, one_mul],
   exact ne_of_gt (lt_of_le_of_lt (zero_le _) h)
 end
 
-@[field_simps] lemma div_add_div (a : ℝ≥0) {b : ℝ≥0} (c : ℝ≥0) {d : ℝ≥0}
-  (hb : b ≠ 0) (hd : d ≠ 0) : a / b + c / d = (a * d + b * c) / (b * d) :=
-div_add_div _ _ hb hd
-
-@[field_simps] lemma add_div' (a b c : ℝ≥0) (hc : c ≠ 0) :
-  b + a / c = (b * c + a) / c :=
-add_div' _ _ _ hc
-
-@[field_simps] lemma div_add' (a b c : ℝ≥0) (hc : c ≠ 0) :
-  a / c + b = (a + b * c) / c :=
-div_add' _ _ _ hc
-
 lemma _root_.real.to_nnreal_inv {x : ℝ} :
   real.to_nnreal x⁻¹ = (real.to_nnreal x)⁻¹ :=
 begin
@@ -712,8 +686,6 @@ by rw [div_eq_inv_mul, div_eq_inv_mul, real.to_nnreal_mul (inv_nonneg.2 hy), rea
 lemma inv_lt_one_iff {x : ℝ≥0} (hx : x ≠ 0) : x⁻¹ < 1 ↔ 1 < x :=
 by rwa [← one_div, div_lt_iff hx, one_mul]
 
-lemma inv_lt_one {x : ℝ≥0} (hx : 1 < x) : x⁻¹ < 1 := inv_lt_one hx
-
 lemma zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
 begin
   cases n,
@@ -721,10 +693,8 @@ begin
   { simp [pow_pos hx.bot_lt _] }
 end
 
-lemma inv_lt_inv_iff {x y : ℝ≥0} (hx : x ≠ 0) (hy : y ≠ 0) : y⁻¹ < x⁻¹ ↔ x < y := inv_lt_inv₀ hy hx
-
 lemma inv_lt_inv {x y : ℝ≥0} (hx : x ≠ 0) (h : x < y) : y⁻¹ < x⁻¹ :=
-(inv_lt_inv_iff hx ((bot_le.trans_lt h).ne')).2 h
+inv_lt_inv_of_lt hx.bot_lt h
 
 end inv

dc6c365e

(first ported)

Overall diff

@@ -822,6 +822,8 @@ lemma nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 lemma coe_to_nnreal_le (x : ℝ) : (to_nnreal x : ℝ) ≤ |x| :=
 max_le (le_abs_self _) (abs_nonneg _)
 
+@[simp] lemma to_nnreal_abs (x : ℝ) : |x|.to_nnreal = x.nnabs := nnreal.coe_injective $ by simp
+
 lemma cast_nat_abs_eq_nnabs_cast (n : ℤ) :
   (n.nat_abs : ℝ≥0) = nnabs n :=
 by { ext, rw [nnreal.coe_nat_cast, int.cast_nat_abs, real.coe_nnabs] }

If you forward-port all of these commits, please update the SHA in the file header to b1abe23ae96fef89ad30d9f4362c307f72a55010. Where possible, port just one commit at a time.

If they exist, also link to any forward-port PRs that already forward-ported it.

Do not forward-port a commit from this list without also forward-porting everything below it!

See this wiki page for more information on how to forward-port.

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -434,11 +434,11 @@ theorem coe_nsmul (r : ℝ≥0) (n : ℕ) : ↑(n • r) = n • (r : ℝ) := by
 #align nnreal.nsmul_coe NNReal.coe_nsmul
 -/
 
-#print NNReal.coe_nat_cast /-
+#print NNReal.coe_natCast /-
 @[simp, norm_cast]
-protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
+protected theorem coe_natCast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
   map_natCast toRealHom n
-#align nnreal.coe_nat_cast NNReal.coe_nat_cast
+#align nnreal.coe_nat_cast NNReal.coe_natCast
 -/
 
 noncomputable example : LinearOrder ℝ≥0 := by infer_instance
@@ -485,7 +485,7 @@ theorem Real.toNNReal_coe {r : ℝ≥0} : Real.toNNReal r = r :=
 #print NNReal.mk_natCast /-
 @[simp]
 theorem mk_natCast (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
-  NNReal.eq (NNReal.coe_nat_cast n).symm
+  NNReal.eq (NNReal.coe_natCast n).symm
 #align nnreal.mk_coe_nat NNReal.mk_natCast
 -/
 
@@ -1428,7 +1428,7 @@ theorem toNNReal_abs (x : ℝ) : |x|.toNNReal = x.nnabs :=
 
 #print Real.cast_natAbs_eq_nnabs_cast /-
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by ext;
-  rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs]
+  rw [NNReal.coe_natCast, Int.cast_natAbs, Real.coe_nnabs]
 #align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_cast
 -/

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -482,11 +482,11 @@ theorem Real.toNNReal_coe {r : ℝ≥0} : Real.toNNReal r = r :=
 #align real.to_nnreal_coe Real.toNNReal_coe
 -/
 
-#print NNReal.mk_coe_nat /-
+#print NNReal.mk_natCast /-
 @[simp]
-theorem mk_coe_nat (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
+theorem mk_natCast (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
   NNReal.eq (NNReal.coe_nat_cast n).symm
-#align nnreal.mk_coe_nat NNReal.mk_coe_nat
+#align nnreal.mk_coe_nat NNReal.mk_natCast
 -/
 
 #print NNReal.toNNReal_coe_nat /-

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -1419,10 +1419,12 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 #align real.coe_to_nnreal_le Real.coe_toNNReal_le
 -/
 
+#print Real.toNNReal_abs /-
 @[simp]
 theorem toNNReal_abs (x : ℝ) : |x|.toNNReal = x.nnabs :=
   NNReal.coe_injective <| by simp
 #align real.to_nnreal_abs Real.toNNReal_abs
+-/
 
 #print Real.cast_natAbs_eq_nnabs_cast /-
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by ext;

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -947,7 +947,7 @@ theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   by
   obtain ⟨n, hn, h'n⟩ : ∃ n : ℤ, (y : ℝ) ^ n ≤ x ∧ (x : ℝ) < y ^ (n + 1) :=
     exists_mem_Ico_zpow (bot_lt_iff_ne_bot.mpr hx) hy
-  rw [← NNReal.coe_zpow] at hn h'n 
+  rw [← NNReal.coe_zpow] at hn h'n
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ico_zpow NNReal.exists_mem_Ico_zpow
 -/
@@ -958,7 +958,7 @@ theorem exists_mem_Ioc_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   by
   obtain ⟨n, hn, h'n⟩ : ∃ n : ℤ, (y : ℝ) ^ n < x ∧ (x : ℝ) ≤ y ^ (n + 1) :=
     exists_mem_Ioc_zpow (bot_lt_iff_ne_bot.mpr hx) hy
-  rw [← NNReal.coe_zpow] at hn h'n 
+  rw [← NNReal.coe_zpow] at hn h'n
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ioc_zpow NNReal.exists_mem_Ioc_zpow
 -/
@@ -1142,7 +1142,7 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
     have hx' : x⁻¹ ≠ 0 := by rwa [(· ≠ ·), inv_eq_zero]
     have : a * x⁻¹ < 1 := by rwa [← lt_inv_iff_mul_lt hx', inv_inv]
     have : a * x⁻¹ * x ≤ y := h _ this
-    rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this 
+    rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this
 #align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_le
 -/
 
@@ -1236,7 +1236,7 @@ theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y
 #print NNReal.sSup_of_not_bddAbove /-
 theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 :=
   by
-  rw [← bdd_above_coe] at hs 
+  rw [← bdd_above_coe] at hs
   rw [← NNReal.coe_inj, coe_Sup]
   exact Sup_of_not_bdd_above hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
@@ -1353,8 +1353,8 @@ theorem preimage_coe_nnreal_real (h : s.OrdConnected) : (coe ⁻¹' s : Set ℝ
 
 #print Set.OrdConnected.image_coe_nnreal_real /-
 theorem image_coe_nnreal_real (h : t.OrdConnected) : (coe '' t : Set ℝ).OrdConnected :=
-  ⟨ball_image_iff.2 fun x hx =>
-      ball_image_iff.2 fun y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
+  ⟨forall_mem_image.2 fun x hx =>
+      forall_mem_image.2 fun y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
 #align set.ord_connected.image_coe_nnreal_real Set.OrdConnected.image_coe_nnreal_real
 -/
 
@@ -1363,10 +1363,10 @@ theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConne
   by
   refine' ⟨ball_image_iff.2 fun x hx => ball_image_iff.2 fun y hy z hz => _⟩
   cases' le_total y 0 with hy₀ hy₀
-  · rw [mem_Icc, Real.toNNReal_of_nonpos hy₀, nonpos_iff_eq_zero] at hz 
+  · rw [mem_Icc, Real.toNNReal_of_nonpos hy₀, nonpos_iff_eq_zero] at hz
     exact ⟨y, hy, (to_nnreal_of_nonpos hy₀).trans hz.2.symm⟩
   · lift y to ℝ≥0 using hy₀
-    rw [to_nnreal_coe] at hz 
+    rw [to_nnreal_coe] at hz
     exact ⟨z, h.out hx hy ⟨to_nnreal_le_iff_le_coe.1 hz.1, hz.2⟩, to_nnreal_coe⟩
 #align set.ord_connected.image_real_to_nnreal Set.OrdConnected.image_real_toNNReal
 -/

bump to nightly-2024-02-14-08

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

b742255f

Diff

@@ -187,11 +187,11 @@ protected theorem coe_injective : Function.Injective (coe : ℝ≥0 → ℝ) :=
 #align nnreal.coe_injective NNReal.coe_injective
 -/
 
-#print NNReal.coe_eq /-
+#print NNReal.coe_inj /-
 @[simp, norm_cast]
-protected theorem coe_eq {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) = r₂ ↔ r₁ = r₂ :=
+protected theorem coe_inj {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) = r₂ ↔ r₁ = r₂ :=
   NNReal.coe_injective.eq_iff
-#align nnreal.coe_eq NNReal.coe_eq
+#align nnreal.coe_eq NNReal.coe_inj
 -/
 
 #print NNReal.coe_zero /-
@@ -253,17 +253,21 @@ protected theorem coe_sub {r₁ r₂ : ℝ≥0} (h : r₂ ≤ r₁) : ((r₁ - r
 #align nnreal.coe_sub NNReal.coe_sub
 -/
 
+/- warning: nnreal.coe_eq_zero clashes with coe_eq_zero -> NNReal.coe_eq_zero
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_eq_zero NNReal.coe_eq_zeroₓ'. -/
 #print NNReal.coe_eq_zero /-
 @[simp, norm_cast]
 protected theorem coe_eq_zero (r : ℝ≥0) : ↑r = (0 : ℝ) ↔ r = 0 := by
-  rw [← NNReal.coe_zero, NNReal.coe_eq]
+  rw [← NNReal.coe_zero, NNReal.coe_inj]
 #align nnreal.coe_eq_zero NNReal.coe_eq_zero
 -/
 
+/- warning: nnreal.coe_eq_one clashes with coe_inj_one -> NNReal.coe_eq_one
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_eq_one NNReal.coe_eq_oneₓ'. -/
 #print NNReal.coe_eq_one /-
 @[simp, norm_cast]
 protected theorem coe_eq_one (r : ℝ≥0) : ↑r = (1 : ℝ) ↔ r = 1 := by
-  rw [← NNReal.coe_one, NNReal.coe_eq]
+  rw [← NNReal.coe_one, NNReal.coe_inj]
 #align nnreal.coe_eq_one NNReal.coe_eq_one
 -/
 
@@ -404,7 +408,7 @@ theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a)
 theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∑ a in s, f a) = ∑ a in s, Real.toNNReal (f a) :=
   by
-  rw [← NNReal.coe_eq, NNReal.coe_sum, Real.coe_toNNReal _ (Finset.sum_nonneg hf)]
+  rw [← NNReal.coe_inj, NNReal.coe_sum, Real.coe_toNNReal _ (Finset.sum_nonneg hf)]
   exact Finset.sum_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonneg
 -/
@@ -420,7 +424,7 @@ theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a
 theorem Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∏ a in s, f a) = ∏ a in s, Real.toNNReal (f a) :=
   by
-  rw [← NNReal.coe_eq, NNReal.coe_prod, Real.coe_toNNReal _ (Finset.prod_nonneg hf)]
+  rw [← NNReal.coe_inj, NNReal.coe_prod, Real.coe_toNNReal _ (Finset.prod_nonneg hf)]
   exact Finset.prod_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonneg
 -/
@@ -782,7 +786,7 @@ theorem toNNReal_le_toNNReal_iff {r p : ℝ} (hp : 0 ≤ p) :
 #print Real.toNNReal_eq_toNNReal_iff /-
 @[simp]
 theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
-    Real.toNNReal r = Real.toNNReal p ↔ r = p := by simp [← NNReal.coe_eq, coe_to_nnreal, hr, hp]
+    Real.toNNReal r = Real.toNNReal p ↔ r = p := by simp [← NNReal.coe_inj, coe_to_nnreal, hr, hp]
 #align real.to_nnreal_eq_to_nnreal_iff Real.toNNReal_eq_toNNReal_iff
 -/
 
@@ -887,7 +891,7 @@ theorem toNNReal_bit1 {r : ℝ} (hr : 0 ≤ r) : Real.toNNReal (bit1 r) = bit1 (
 
 #print Real.toNNReal_pow /-
 theorem toNNReal_pow {x : ℝ} (hx : 0 ≤ x) (n : ℕ) : (x ^ n).toNNReal = x.toNNReal ^ n := by
-  rw [← NNReal.coe_eq, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),
+  rw [← NNReal.coe_inj, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),
     Real.coe_toNNReal x hx]
 #align real.to_nnreal_pow Real.toNNReal_pow
 -/
@@ -1233,7 +1237,7 @@ theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y
 theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 :=
   by
   rw [← bdd_above_coe] at hs 
-  rw [← NNReal.coe_eq, coe_Sup]
+  rw [← NNReal.coe_inj, coe_Sup]
   exact Sup_of_not_bdd_above hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
 -/
@@ -1245,7 +1249,7 @@ theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
 -/
 
 #print NNReal.iInf_empty /-
-theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw [← NNReal.coe_eq, coe_infi];
+theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw [← NNReal.coe_inj, coe_infi];
   exact Real.iInf_of_isEmpty _
 #align nnreal.infi_empty NNReal.iInf_empty
 -/
@@ -1253,14 +1257,14 @@ theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw
 #print NNReal.iInf_const_zero /-
 @[simp]
 theorem iInf_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 := by
-  rw [← NNReal.coe_eq, coe_infi]; exact Real.ciInf_const_zero
+  rw [← NNReal.coe_inj, coe_infi]; exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero
 -/
 
 #print NNReal.iInf_mul /-
 theorem iInf_mul (f : ι → ℝ≥0) (a : ℝ≥0) : iInf f * a = ⨅ i, f i * a :=
   by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, coe_infi, coe_infi]
+  rw [← NNReal.coe_inj, NNReal.coe_mul, coe_infi, coe_infi]
   exact Real.iInf_mul_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.infi_mul NNReal.iInf_mul
 -/
@@ -1274,7 +1278,7 @@ theorem mul_iInf (f : ι → ℝ≥0) (a : ℝ≥0) : a * iInf f = ⨅ i, a * f
 #print NNReal.mul_iSup /-
 theorem mul_iSup (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i :=
   by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
+  rw [← NNReal.coe_inj, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
   exact Real.mul_iSup_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.mul_supr NNReal.mul_iSup
 -/

bump to nightly-2024-02-05-08

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

516c6ec2

Diff

@@ -1246,7 +1246,7 @@ theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
 
 #print NNReal.iInf_empty /-
 theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw [← NNReal.coe_eq, coe_infi];
-  exact Real.ciInf_empty _
+  exact Real.iInf_of_isEmpty _
 #align nnreal.infi_empty NNReal.iInf_empty
 -/

bump to nightly-2024-01-13-06

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

31733180

Diff

@@ -995,11 +995,13 @@ end Sub
 
 section Inv
 
-#print NNReal.sum_div /-
+/- warning: nnreal.sum_div clashes with finset.sum_div -> Finset.sum_div
+Case conversion may be inaccurate. Consider using '#align nnreal.sum_div Finset.sum_divₓ'. -/
+#print Finset.sum_div /-
 theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
     (∑ i in s, f i) / b = ∑ i in s, f i / b :=
   Finset.sum_div
-#align nnreal.sum_div NNReal.sum_div
+#align nnreal.sum_div Finset.sum_div
 -/
 
 #print NNReal.inv_le /-

bump to nightly-2023-11-11-06

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

55354f59

Diff

@@ -631,19 +631,19 @@ example : Archimedean ℝ≥0 := by infer_instance
 #print NNReal.covariant_add /-
 -- TODO: why are these three instances necessary? why aren't they inferred?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
-  OrderedAddCommMonoid.to_covariantClass_left ℝ≥0
+  OrderedAddCommMonoid.toCovariantClassLeft ℝ≥0
 #align nnreal.covariant_add NNReal.covariant_add
 -/
 
 #print NNReal.contravariant_add /-
 instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· < ·) :=
-  OrderedCancelAddCommMonoid.to_contravariantClass_left ℝ≥0
+  OrderedCancelAddCommMonoid.toContravariantClassLeft ℝ≥0
 #align nnreal.contravariant_add NNReal.contravariant_add
 -/
 
 #print NNReal.covariant_mul /-
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
-  OrderedCommMonoid.to_covariantClass_left ℝ≥0
+  OrderedCommMonoid.toCovariantClassLeft ℝ≥0
 #align nnreal.covariant_mul NNReal.covariant_mul
 -/

bump to nightly-2023-10-17-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

6655af51

Diff

@@ -11,7 +11,7 @@ import Data.Real.Pointwise
 import Order.ConditionallyCompleteLattice.Group
 import Tactic.Positivity
 
-#align_import data.real.nnreal from "leanprover-community/mathlib"@"de29c328903507bb7aff506af9135f4bdaf1849c"
+#align_import data.real.nnreal from "leanprover-community/mathlib"@"b1abe23ae96fef89ad30d9f4362c307f72a55010"
 
 /-!
 # Nonnegative real numbers
@@ -1413,6 +1413,11 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 #align real.coe_to_nnreal_le Real.coe_toNNReal_le
 -/
 
+@[simp]
+theorem toNNReal_abs (x : ℝ) : |x|.toNNReal = x.nnabs :=
+  NNReal.coe_injective <| by simp
+#align real.to_nnreal_abs Real.toNNReal_abs
+
 #print Real.cast_natAbs_eq_nnabs_cast /-
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by ext;
   rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs]

bump to nightly-2023-10-07-06

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

d191b687

Diff

@@ -506,7 +506,7 @@ example : OrderBot ℝ≥0 := by infer_instance
 
 example : PartialOrder ℝ≥0 := by infer_instance
 
-noncomputable example : CanonicallyLinearOrderedAddMonoid ℝ≥0 := by infer_instance
+noncomputable example : CanonicallyLinearOrderedAddCommMonoid ℝ≥0 := by infer_instance
 
 noncomputable example : LinearOrderedAddCommMonoid ℝ≥0 := by infer_instance

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,13 +3,13 @@ Copyright (c) 2018 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Algebra.Order.Field.Canonical.Basic
-import Mathbin.Algebra.Order.Nonneg.Field
-import Mathbin.Algebra.Order.Nonneg.Floor
-import Mathbin.Data.Real.Pointwise
-import Mathbin.Order.ConditionallyCompleteLattice.Group
-import Mathbin.Tactic.Positivity
+import Algebra.Algebra.Basic
+import Algebra.Order.Field.Canonical.Basic
+import Algebra.Order.Nonneg.Field
+import Algebra.Order.Nonneg.Floor
+import Data.Real.Pointwise
+import Order.ConditionallyCompleteLattice.Group
+import Tactic.Positivity
 
 #align_import data.real.nnreal from "leanprover-community/mathlib"@"de29c328903507bb7aff506af9135f4bdaf1849c"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit de29c328903507bb7aff506af9135f4bdaf1849c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Basic
 import Mathbin.Algebra.Order.Field.Canonical.Basic
@@ -16,6 +11,8 @@ import Mathbin.Data.Real.Pointwise
 import Mathbin.Order.ConditionallyCompleteLattice.Group
 import Mathbin.Tactic.Positivity
 
+#align_import data.real.nnreal from "leanprover-community/mathlib"@"de29c328903507bb7aff506af9135f4bdaf1849c"
+
 /-!
 # Nonnegative real numbers

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -73,7 +73,6 @@ deriving StrictOrderedSemiring, CommMonoidWithZero, FloorSemiring, CommSemiring,
 #align nnreal NNReal
 -/
 
--- mathport name: nnreal
 scoped[NNReal] notation "ℝ≥0" => NNReal
 
 namespace NNReal
@@ -81,35 +80,49 @@ namespace NNReal
 instance : Coe ℝ≥0 ℝ :=
   ⟨Subtype.val⟩
 
+#print NNReal.val_eq_coe /-
 -- Simp lemma to put back `n.val` into the normal form given by the coercion.
 @[simp]
 theorem val_eq_coe (n : ℝ≥0) : n.val = n :=
   rfl
 #align nnreal.val_eq_coe NNReal.val_eq_coe
+-/
 
+#print NNReal.canLift /-
 instance canLift : CanLift ℝ ℝ≥0 coe fun r => 0 ≤ r :=
   Subtype.canLift _
 #align nnreal.can_lift NNReal.canLift
+-/
 
+#print NNReal.eq /-
 protected theorem eq {n m : ℝ≥0} : (n : ℝ) = (m : ℝ) → n = m :=
   Subtype.eq
 #align nnreal.eq NNReal.eq
+-/
 
+#print NNReal.eq_iff /-
 protected theorem eq_iff {n m : ℝ≥0} : (n : ℝ) = (m : ℝ) ↔ n = m :=
   Iff.intro NNReal.eq (congr_arg coe)
 #align nnreal.eq_iff NNReal.eq_iff
+-/
 
+#print NNReal.ne_iff /-
 theorem ne_iff {x y : ℝ≥0} : (x : ℝ) ≠ (y : ℝ) ↔ x ≠ y :=
   not_congr <| NNReal.eq_iff
 #align nnreal.ne_iff NNReal.ne_iff
+-/
 
+#print NNReal.forall /-
 protected theorem forall {p : ℝ≥0 → Prop} : (∀ x : ℝ≥0, p x) ↔ ∀ (x : ℝ) (hx : 0 ≤ x), p ⟨x, hx⟩ :=
   Subtype.forall
 #align nnreal.forall NNReal.forall
+-/
 
+#print NNReal.exists /-
 protected theorem exists {p : ℝ≥0 → Prop} : (∃ x : ℝ≥0, p x) ↔ ∃ (x : ℝ) (hx : 0 ≤ x), p ⟨x, hx⟩ :=
   Subtype.exists
 #align nnreal.exists NNReal.exists
+-/
 
 #print Real.toNNReal /-
 /-- Reinterpret a real number `r` as a non-negative real number. Returns `0` if `r < 0`. -/
@@ -118,26 +131,36 @@ noncomputable def Real.toNNReal (r : ℝ) : ℝ≥0 :=
 #align real.to_nnreal Real.toNNReal
 -/
 
+#print Real.coe_toNNReal /-
 theorem Real.coe_toNNReal (r : ℝ) (hr : 0 ≤ r) : (Real.toNNReal r : ℝ) = r :=
   max_eq_left hr
 #align real.coe_to_nnreal Real.coe_toNNReal
+-/
 
+#print Real.toNNReal_of_nonneg /-
 theorem Real.toNNReal_of_nonneg {r : ℝ} (hr : 0 ≤ r) : r.toNNReal = ⟨r, hr⟩ := by
   simp_rw [Real.toNNReal, max_eq_left hr]
 #align real.to_nnreal_of_nonneg Real.toNNReal_of_nonneg
+-/
 
+#print Real.le_coe_toNNReal /-
 theorem Real.le_coe_toNNReal (r : ℝ) : r ≤ Real.toNNReal r :=
   le_max_left r 0
 #align real.le_coe_to_nnreal Real.le_coe_toNNReal
+-/
 
+#print NNReal.coe_nonneg /-
 theorem coe_nonneg (r : ℝ≥0) : (0 : ℝ) ≤ r :=
   r.2
 #align nnreal.coe_nonneg NNReal.coe_nonneg
+-/
 
+#print NNReal.coe_mk /-
 @[norm_cast]
 theorem coe_mk (a : ℝ) (ha) : ((⟨a, ha⟩ : ℝ≥0) : ℝ) = a :=
   rfl
 #align nnreal.coe_mk NNReal.coe_mk
+-/
 
 example : Zero ℝ≥0 := by infer_instance
 
@@ -161,38 +184,54 @@ example : Inhabited ℝ≥0 := by infer_instance
 
 example : Nontrivial ℝ≥0 := by infer_instance
 
+#print NNReal.coe_injective /-
 protected theorem coe_injective : Function.Injective (coe : ℝ≥0 → ℝ) :=
   Subtype.coe_injective
 #align nnreal.coe_injective NNReal.coe_injective
+-/
 
+#print NNReal.coe_eq /-
 @[simp, norm_cast]
 protected theorem coe_eq {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) = r₂ ↔ r₁ = r₂ :=
   NNReal.coe_injective.eq_iff
 #align nnreal.coe_eq NNReal.coe_eq
+-/
 
+#print NNReal.coe_zero /-
 protected theorem coe_zero : ((0 : ℝ≥0) : ℝ) = 0 :=
   rfl
 #align nnreal.coe_zero NNReal.coe_zero
+-/
 
+#print NNReal.coe_one /-
 protected theorem coe_one : ((1 : ℝ≥0) : ℝ) = 1 :=
   rfl
 #align nnreal.coe_one NNReal.coe_one
+-/
 
+#print NNReal.coe_add /-
 protected theorem coe_add (r₁ r₂ : ℝ≥0) : ((r₁ + r₂ : ℝ≥0) : ℝ) = r₁ + r₂ :=
   rfl
 #align nnreal.coe_add NNReal.coe_add
+-/
 
+#print NNReal.coe_mul /-
 protected theorem coe_mul (r₁ r₂ : ℝ≥0) : ((r₁ * r₂ : ℝ≥0) : ℝ) = r₁ * r₂ :=
   rfl
 #align nnreal.coe_mul NNReal.coe_mul
+-/
 
+#print NNReal.coe_inv /-
 protected theorem coe_inv (r : ℝ≥0) : ((r⁻¹ : ℝ≥0) : ℝ) = r⁻¹ :=
   rfl
 #align nnreal.coe_inv NNReal.coe_inv
+-/
 
+#print NNReal.coe_div /-
 protected theorem coe_div (r₁ r₂ : ℝ≥0) : ((r₁ / r₂ : ℝ≥0) : ℝ) = r₁ / r₂ :=
   rfl
 #align nnreal.coe_div NNReal.coe_div
+-/
 
 @[simp, norm_cast]
 protected theorem coe_bit0 (r : ℝ≥0) : ((bit0 r : ℝ≥0) : ℝ) = bit0 r :=
@@ -204,27 +243,37 @@ protected theorem coe_bit1 (r : ℝ≥0) : ((bit1 r : ℝ≥0) : ℝ) = bit1 r :
   rfl
 #align nnreal.coe_bit1 NNReal.coe_bit1
 
+#print NNReal.coe_two /-
 protected theorem coe_two : ((2 : ℝ≥0) : ℝ) = 2 :=
   rfl
 #align nnreal.coe_two NNReal.coe_two
+-/
 
+#print NNReal.coe_sub /-
 @[simp, norm_cast]
 protected theorem coe_sub {r₁ r₂ : ℝ≥0} (h : r₂ ≤ r₁) : ((r₁ - r₂ : ℝ≥0) : ℝ) = r₁ - r₂ :=
   max_eq_left <| le_sub_comm.2 <| by simp [show (r₂ : ℝ) ≤ r₁ from h]
 #align nnreal.coe_sub NNReal.coe_sub
+-/
 
+#print NNReal.coe_eq_zero /-
 @[simp, norm_cast]
 protected theorem coe_eq_zero (r : ℝ≥0) : ↑r = (0 : ℝ) ↔ r = 0 := by
   rw [← NNReal.coe_zero, NNReal.coe_eq]
 #align nnreal.coe_eq_zero NNReal.coe_eq_zero
+-/
 
+#print NNReal.coe_eq_one /-
 @[simp, norm_cast]
 protected theorem coe_eq_one (r : ℝ≥0) : ↑r = (1 : ℝ) ↔ r = 1 := by
   rw [← NNReal.coe_one, NNReal.coe_eq]
 #align nnreal.coe_eq_one NNReal.coe_eq_one
+-/
 
+#print NNReal.coe_ne_zero /-
 theorem coe_ne_zero {r : ℝ≥0} : (r : ℝ) ≠ 0 ↔ r ≠ 0 := by norm_cast
 #align nnreal.coe_ne_zero NNReal.coe_ne_zero
+-/
 
 example : CommSemiring ℝ≥0 := by infer_instance
 
@@ -235,10 +284,12 @@ def toRealHom : ℝ≥0 →+* ℝ :=
 #align nnreal.to_real_hom NNReal.toRealHom
 -/
 
+#print NNReal.coe_toRealHom /-
 @[simp]
 theorem coe_toRealHom : ⇑toRealHom = coe :=
   rfl
 #align nnreal.coe_to_real_hom NNReal.coe_toRealHom
+-/
 
 section Actions
 
@@ -246,20 +297,26 @@ section Actions
 instance {M : Type _} [MulAction ℝ M] : MulAction ℝ≥0 M :=
   MulAction.compHom M toRealHom.toMonoidHom
 
+#print NNReal.smul_def /-
 theorem smul_def {M : Type _} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x = (c : ℝ) • x :=
   rfl
 #align nnreal.smul_def NNReal.smul_def
+-/
 
 instance {M N : Type _} [MulAction ℝ M] [MulAction ℝ N] [SMul M N] [IsScalarTower ℝ M N] :
     IsScalarTower ℝ≥0 M N where smul_assoc r := (smul_assoc (r : ℝ) : _)
 
+#print NNReal.smulCommClass_left /-
 instance smulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
     SMulCommClass ℝ≥0 M N where smul_comm r := (smul_comm (r : ℝ) : _)
 #align nnreal.smul_comm_class_left NNReal.smulCommClass_left
+-/
 
+#print NNReal.smulCommClass_right /-
 instance smulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
     SMulCommClass M ℝ≥0 N where smul_comm m r := (smul_comm m (r : ℝ) : _)
 #align nnreal.smul_comm_class_right NNReal.smulCommClass_right
+-/
 
 /-- A `distrib_mul_action` over `ℝ` restricts to a `distrib_mul_action` over `ℝ≥0`. -/
 instance {M : Type _} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction ℝ≥0 M :=
@@ -290,92 +347,126 @@ example : CommMonoidWithZero ℝ≥0 := by infer_instance
 
 noncomputable example : CommGroupWithZero ℝ≥0 := by infer_instance
 
+#print NNReal.coe_indicator /-
 @[simp, norm_cast]
 theorem coe_indicator {α} (s : Set α) (f : α → ℝ≥0) (a : α) :
     ((s.indicator f a : ℝ≥0) : ℝ) = s.indicator (fun x => f x) a :=
   (toRealHom : ℝ≥0 →+ ℝ).map_indicator _ _ _
 #align nnreal.coe_indicator NNReal.coe_indicator
+-/
 
+#print NNReal.coe_pow /-
 @[simp, norm_cast]
 theorem coe_pow (r : ℝ≥0) (n : ℕ) : ((r ^ n : ℝ≥0) : ℝ) = r ^ n :=
   toRealHom.map_pow r n
 #align nnreal.coe_pow NNReal.coe_pow
+-/
 
+#print NNReal.coe_zpow /-
 @[simp, norm_cast]
 theorem coe_zpow (r : ℝ≥0) (n : ℤ) : ((r ^ n : ℝ≥0) : ℝ) = r ^ n := by cases n <;> simp
 #align nnreal.coe_zpow NNReal.coe_zpow
+-/
 
+#print NNReal.coe_list_sum /-
 @[norm_cast]
 theorem coe_list_sum (l : List ℝ≥0) : ((l.Sum : ℝ≥0) : ℝ) = (l.map coe).Sum :=
   toRealHom.map_list_sum l
 #align nnreal.coe_list_sum NNReal.coe_list_sum
+-/
 
+#print NNReal.coe_list_prod /-
 @[norm_cast]
 theorem coe_list_prod (l : List ℝ≥0) : ((l.Prod : ℝ≥0) : ℝ) = (l.map coe).Prod :=
   toRealHom.map_list_prod l
 #align nnreal.coe_list_prod NNReal.coe_list_prod
+-/
 
+#print NNReal.coe_multiset_sum /-
 @[norm_cast]
 theorem coe_multiset_sum (s : Multiset ℝ≥0) : ((s.Sum : ℝ≥0) : ℝ) = (s.map coe).Sum :=
   toRealHom.map_multiset_sum s
 #align nnreal.coe_multiset_sum NNReal.coe_multiset_sum
+-/
 
+#print NNReal.coe_multiset_prod /-
 @[norm_cast]
 theorem coe_multiset_prod (s : Multiset ℝ≥0) : ((s.Prod : ℝ≥0) : ℝ) = (s.map coe).Prod :=
   toRealHom.map_multiset_prod s
 #align nnreal.coe_multiset_prod NNReal.coe_multiset_prod
+-/
 
+#print NNReal.coe_sum /-
 @[norm_cast]
 theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a) = ∑ a in s, (f a : ℝ) :=
   toRealHom.map_sum _ _
 #align nnreal.coe_sum NNReal.coe_sum
+-/
 
+#print Real.toNNReal_sum_of_nonneg /-
 theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∑ a in s, f a) = ∑ a in s, Real.toNNReal (f a) :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_sum, Real.coe_toNNReal _ (Finset.sum_nonneg hf)]
   exact Finset.sum_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonneg
+-/
 
+#print NNReal.coe_prod /-
 @[norm_cast]
 theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a) = ∏ a in s, (f a : ℝ) :=
   toRealHom.map_prod _ _
 #align nnreal.coe_prod NNReal.coe_prod
+-/
 
+#print Real.toNNReal_prod_of_nonneg /-
 theorem Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∏ a in s, f a) = ∏ a in s, Real.toNNReal (f a) :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_prod, Real.coe_toNNReal _ (Finset.prod_nonneg hf)]
   exact Finset.prod_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonneg
+-/
 
+#print NNReal.coe_nsmul /-
 theorem coe_nsmul (r : ℝ≥0) (n : ℕ) : ↑(n • r) = n • (r : ℝ) := by norm_cast
 #align nnreal.nsmul_coe NNReal.coe_nsmul
+-/
 
+#print NNReal.coe_nat_cast /-
 @[simp, norm_cast]
 protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
   map_natCast toRealHom n
 #align nnreal.coe_nat_cast NNReal.coe_nat_cast
+-/
 
 noncomputable example : LinearOrder ℝ≥0 := by infer_instance
 
+#print NNReal.coe_le_coe /-
 @[simp, norm_cast]
 protected theorem coe_le_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) ≤ r₂ ↔ r₁ ≤ r₂ :=
   Iff.rfl
 #align nnreal.coe_le_coe NNReal.coe_le_coe
+-/
 
+#print NNReal.coe_lt_coe /-
 @[simp, norm_cast]
 protected theorem coe_lt_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) < r₂ ↔ r₁ < r₂ :=
   Iff.rfl
 #align nnreal.coe_lt_coe NNReal.coe_lt_coe
+-/
 
+#print NNReal.coe_pos /-
 @[simp, norm_cast]
 protected theorem coe_pos {r : ℝ≥0} : (0 : ℝ) < r ↔ 0 < r :=
   Iff.rfl
 #align nnreal.coe_pos NNReal.coe_pos
+-/
 
+#print NNReal.coe_mono /-
 protected theorem coe_mono : Monotone (coe : ℝ≥0 → ℝ) := fun _ _ => NNReal.coe_le_coe.2
 #align nnreal.coe_mono NNReal.coe_mono
+-/
 
 #print Real.toNNReal_mono /-
 protected theorem Real.toNNReal_mono : Monotone Real.toNNReal := fun x y h =>
@@ -383,26 +474,34 @@ protected theorem Real.toNNReal_mono : Monotone Real.toNNReal := fun x y h =>
 #align real.to_nnreal_mono Real.toNNReal_mono
 -/
 
+#print Real.toNNReal_coe /-
 @[simp]
 theorem Real.toNNReal_coe {r : ℝ≥0} : Real.toNNReal r = r :=
   NNReal.eq <| max_eq_left r.2
 #align real.to_nnreal_coe Real.toNNReal_coe
+-/
 
+#print NNReal.mk_coe_nat /-
 @[simp]
 theorem mk_coe_nat (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
   NNReal.eq (NNReal.coe_nat_cast n).symm
 #align nnreal.mk_coe_nat NNReal.mk_coe_nat
+-/
 
+#print NNReal.toNNReal_coe_nat /-
 @[simp]
 theorem toNNReal_coe_nat (n : ℕ) : Real.toNNReal n = n :=
   NNReal.eq <| by simp [Real.coe_toNNReal]
 #align nnreal.to_nnreal_coe_nat NNReal.toNNReal_coe_nat
+-/
 
+#print NNReal.gi /-
 /-- `real.to_nnreal` and `coe : ℝ≥0 → ℝ` form a Galois insertion. -/
 noncomputable def gi : GaloisInsertion Real.toNNReal coe :=
   GaloisInsertion.monotoneIntro NNReal.coe_mono Real.toNNReal_mono Real.le_coe_toNNReal fun _ =>
     Real.toNNReal_coe
 #align nnreal.gi NNReal.gi
+-/
 
 -- note that anything involving the (decidability of the) linear order,
 -- will be noncomputable, everything else should not be.
@@ -436,6 +535,7 @@ example : DenselyOrdered ℝ≥0 := by infer_instance
 
 example : NoMaxOrder ℝ≥0 := by infer_instance
 
+#print NNReal.orderIsoIccZeroCoe /-
 /-- If `a` is a nonnegative real number, then the closed interval `[0, a]` in `ℝ` is order
 isomorphic to the interval `set.Iic a`. -/
 @[simps apply_coe_coe]
@@ -444,19 +544,25 @@ def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a
   toEquiv := Equiv.Set.sep (Set.Ici 0) fun x => x ≤ a
   map_rel_iff' x y := Iff.rfl
 #align nnreal.order_iso_Icc_zero_coe NNReal.orderIsoIccZeroCoe
+-/
 
+#print NNReal.orderIsoIccZeroCoe_symm_apply_coe /-
 @[simp]
 theorem orderIsoIccZeroCoe_symm_apply_coe (a : ℝ≥0) (b : Set.Iic a) :
     ((orderIsoIccZeroCoe a).symm b : ℝ) = b :=
   rfl
 #align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coe
+-/
 
+#print NNReal.coe_image /-
 -- note we need the `@` to make the `has_mem.mem` have a sensible type
 theorem coe_image {s : Set ℝ≥0} :
     coe '' s = {x : ℝ | ∃ h : 0 ≤ x, @Membership.Mem ℝ≥0 _ _ ⟨x, h⟩ s} :=
   Subtype.coe_image
 #align nnreal.coe_image NNReal.coe_image
+-/
 
+#print NNReal.bddAbove_coe /-
 theorem bddAbove_coe {s : Set ℝ≥0} : BddAbove ((coe : ℝ≥0 → ℝ) '' s) ↔ BddAbove s :=
   Iff.intro
     (fun ⟨b, hb⟩ =>
@@ -464,70 +570,94 @@ theorem bddAbove_coe {s : Set ℝ≥0} : BddAbove ((coe : ℝ≥0 → ℝ) '' s)
         show y ≤ max b 0 from le_max_of_le_left <| hb <| Set.mem_image_of_mem _ hys⟩)
     fun ⟨b, hb⟩ => ⟨b, fun y ⟨x, hx, Eq⟩ => Eq ▸ hb hx⟩
 #align nnreal.bdd_above_coe NNReal.bddAbove_coe
+-/
 
+#print NNReal.bddBelow_coe /-
 theorem bddBelow_coe (s : Set ℝ≥0) : BddBelow ((coe : ℝ≥0 → ℝ) '' s) :=
   ⟨0, fun r ⟨q, _, Eq⟩ => Eq ▸ q.2⟩
 #align nnreal.bdd_below_coe NNReal.bddBelow_coe
+-/
 
 noncomputable instance : ConditionallyCompleteLinearOrderBot ℝ≥0 :=
   Nonneg.conditionallyCompleteLinearOrderBot Real.sSup_empty.le
 
+#print NNReal.coe_sSup /-
 @[norm_cast]
 theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup ((coe : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
     @subset_sSup_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
       Real.sSup_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
 #align nnreal.coe_Sup NNReal.coe_sSup
+-/
 
+#print NNReal.coe_iSup /-
 @[norm_cast]
 theorem coe_iSup {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, s i := by
   rw [iSup, iSup, coe_Sup, Set.range_comp]
 #align nnreal.coe_supr NNReal.coe_iSup
+-/
 
+#print NNReal.coe_sInf /-
 @[norm_cast]
 theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf ((coe : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
     @subset_sInf_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
       Real.sInf_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
 #align nnreal.coe_Inf NNReal.coe_sInf
+-/
 
+#print NNReal.sInf_empty /-
 @[simp]
 theorem sInf_empty : sInf (∅ : Set ℝ≥0) = 0 := by
   rw [← NNReal.coe_eq_zero, coe_Inf, Set.image_empty, Real.sInf_empty]
 #align nnreal.Inf_empty NNReal.sInf_empty
+-/
 
+#print NNReal.coe_iInf /-
 @[norm_cast]
 theorem coe_iInf {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, s i := by
   rw [iInf, iInf, coe_Inf, Set.range_comp]
 #align nnreal.coe_infi NNReal.coe_iInf
+-/
 
+#print NNReal.le_iInf_add_iInf /-
 theorem le_iInf_add_iInf {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
     {a : ℝ≥0} (h : ∀ i j, a ≤ f i + g j) : a ≤ (⨅ i, f i) + ⨅ j, g j :=
   by
   rw [← NNReal.coe_le_coe, NNReal.coe_add, coe_infi, coe_infi]
   exact le_ciInf_add_ciInf h
 #align nnreal.le_infi_add_infi NNReal.le_iInf_add_iInf
+-/
 
 example : Archimedean ℝ≥0 := by infer_instance
 
+#print NNReal.covariant_add /-
 -- TODO: why are these three instances necessary? why aren't they inferred?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
   OrderedAddCommMonoid.to_covariantClass_left ℝ≥0
 #align nnreal.covariant_add NNReal.covariant_add
+-/
 
+#print NNReal.contravariant_add /-
 instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· < ·) :=
   OrderedCancelAddCommMonoid.to_contravariantClass_left ℝ≥0
 #align nnreal.contravariant_add NNReal.contravariant_add
+-/
 
+#print NNReal.covariant_mul /-
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
   OrderedCommMonoid.to_covariantClass_left ℝ≥0
 #align nnreal.covariant_mul NNReal.covariant_mul
+-/
 
+#print NNReal.le_of_forall_pos_le_add /-
 -- Why isn't `nnreal.contravariant_add` inferred?
 theorem le_of_forall_pos_le_add {a b : ℝ≥0} (h : ∀ ε, 0 < ε → a ≤ b + ε) : a ≤ b :=
   @le_of_forall_pos_le_add _ _ _ _ _ _ NNReal.contravariant_add _ _ h
 #align nnreal.le_of_forall_pos_le_add NNReal.le_of_forall_pos_le_add
+-/
 
+#print NNReal.lt_iff_exists_rat_btwn /-
 theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
     a < b ↔ ∃ q : ℚ, 0 ≤ q ∧ a < Real.toNNReal q ∧ Real.toNNReal q < b :=
   Iff.intro
@@ -538,47 +668,66 @@ theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
         simp [Real.coe_toNNReal _ this, nnreal.coe_lt_coe.symm, haq, hqb]⟩)
     fun ⟨q, _, haq, hqb⟩ => lt_trans haq hqb
 #align nnreal.lt_iff_exists_rat_btwn NNReal.lt_iff_exists_rat_btwn
+-/
 
+#print NNReal.bot_eq_zero /-
 theorem bot_eq_zero : (⊥ : ℝ≥0) = 0 :=
   rfl
 #align nnreal.bot_eq_zero NNReal.bot_eq_zero
+-/
 
+#print NNReal.mul_sup /-
 theorem mul_sup (a b c : ℝ≥0) : a * (b ⊔ c) = a * b ⊔ a * c :=
   mul_max_of_nonneg _ _ <| zero_le a
 #align nnreal.mul_sup NNReal.mul_sup
+-/
 
+#print NNReal.sup_mul /-
 theorem sup_mul (a b c : ℝ≥0) : (a ⊔ b) * c = a * c ⊔ b * c :=
   max_mul_of_nonneg _ _ <| zero_le c
 #align nnreal.sup_mul NNReal.sup_mul
+-/
 
+#print NNReal.mul_finset_sup /-
 theorem mul_finset_sup {α} (r : ℝ≥0) (s : Finset α) (f : α → ℝ≥0) :
     r * s.sup f = s.sup fun a => r * f a :=
   Finset.comp_sup_eq_sup_comp _ (NNReal.mul_sup r) (MulZeroClass.mul_zero r)
 #align nnreal.mul_finset_sup NNReal.mul_finset_sup
+-/
 
+#print NNReal.finset_sup_mul /-
 theorem finset_sup_mul {α} (s : Finset α) (f : α → ℝ≥0) (r : ℝ≥0) :
     s.sup f * r = s.sup fun a => f a * r :=
   Finset.comp_sup_eq_sup_comp (· * r) (fun x y => NNReal.sup_mul x y r) (MulZeroClass.zero_mul r)
 #align nnreal.finset_sup_mul NNReal.finset_sup_mul
+-/
 
+#print NNReal.finset_sup_div /-
 theorem finset_sup_div {α} {f : α → ℝ≥0} {s : Finset α} (r : ℝ≥0) :
     s.sup f / r = s.sup fun a => f a / r := by simp only [div_eq_inv_mul, mul_finset_sup]
 #align nnreal.finset_sup_div NNReal.finset_sup_div
+-/
 
+#print NNReal.coe_max /-
 @[simp, norm_cast]
 theorem coe_max (x y : ℝ≥0) : ((max x y : ℝ≥0) : ℝ) = max (x : ℝ) (y : ℝ) :=
   NNReal.coe_mono.map_max
 #align nnreal.coe_max NNReal.coe_max
+-/
 
+#print NNReal.coe_min /-
 @[simp, norm_cast]
 theorem coe_min (x y : ℝ≥0) : ((min x y : ℝ≥0) : ℝ) = min (x : ℝ) (y : ℝ) :=
   NNReal.coe_mono.map_min
 #align nnreal.coe_min NNReal.coe_min
+-/
 
+#print NNReal.zero_le_coe /-
 @[simp]
 theorem zero_le_coe {q : ℝ≥0} : 0 ≤ (q : ℝ) :=
   q.2
 #align nnreal.zero_le_coe NNReal.zero_le_coe
+-/
 
 end NNReal
 
@@ -586,95 +735,134 @@ namespace Real
 
 section ToNnreal
 
+#print Real.toNNReal_zero /-
 @[simp]
 theorem toNNReal_zero : Real.toNNReal 0 = 0 := by simp [Real.toNNReal] <;> rfl
 #align real.to_nnreal_zero Real.toNNReal_zero
+-/
 
+#print Real.toNNReal_one /-
 @[simp]
 theorem toNNReal_one : Real.toNNReal 1 = 1 := by
   simp [Real.toNNReal, max_eq_left (zero_le_one : (0 : ℝ) ≤ 1)] <;> rfl
 #align real.to_nnreal_one Real.toNNReal_one
+-/
 
+#print Real.toNNReal_pos /-
 @[simp]
 theorem toNNReal_pos {r : ℝ} : 0 < Real.toNNReal r ↔ 0 < r := by
   simp [Real.toNNReal, nnreal.coe_lt_coe.symm, lt_irrefl]
 #align real.to_nnreal_pos Real.toNNReal_pos
+-/
 
+#print Real.toNNReal_eq_zero /-
 @[simp]
 theorem toNNReal_eq_zero {r : ℝ} : Real.toNNReal r = 0 ↔ r ≤ 0 := by
   simpa [-to_nnreal_pos] using not_iff_not.2 (@to_nnreal_pos r)
 #align real.to_nnreal_eq_zero Real.toNNReal_eq_zero
+-/
 
+#print Real.toNNReal_of_nonpos /-
 theorem toNNReal_of_nonpos {r : ℝ} : r ≤ 0 → Real.toNNReal r = 0 :=
   toNNReal_eq_zero.2
 #align real.to_nnreal_of_nonpos Real.toNNReal_of_nonpos
+-/
 
+#print Real.coe_toNNReal' /-
 @[simp]
 theorem coe_toNNReal' (r : ℝ) : (Real.toNNReal r : ℝ) = max r 0 :=
   rfl
 #align real.coe_to_nnreal' Real.coe_toNNReal'
+-/
 
+#print Real.toNNReal_le_toNNReal_iff /-
 @[simp]
 theorem toNNReal_le_toNNReal_iff {r p : ℝ} (hp : 0 ≤ p) :
     Real.toNNReal r ≤ Real.toNNReal p ↔ r ≤ p := by simp [nnreal.coe_le_coe.symm, Real.toNNReal, hp]
 #align real.to_nnreal_le_to_nnreal_iff Real.toNNReal_le_toNNReal_iff
+-/
 
+#print Real.toNNReal_eq_toNNReal_iff /-
 @[simp]
 theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal r = Real.toNNReal p ↔ r = p := by simp [← NNReal.coe_eq, coe_to_nnreal, hr, hp]
 #align real.to_nnreal_eq_to_nnreal_iff Real.toNNReal_eq_toNNReal_iff
+-/
 
+#print Real.toNNReal_lt_toNNReal_iff' /-
 @[simp]
 theorem toNNReal_lt_toNNReal_iff' {r p : ℝ} : Real.toNNReal r < Real.toNNReal p ↔ r < p ∧ 0 < p :=
   NNReal.coe_lt_coe.symm.trans max_lt_max_left_iff
 #align real.to_nnreal_lt_to_nnreal_iff' Real.toNNReal_lt_toNNReal_iff'
+-/
 
+#print Real.toNNReal_lt_toNNReal_iff /-
 theorem toNNReal_lt_toNNReal_iff {r p : ℝ} (h : 0 < p) :
     Real.toNNReal r < Real.toNNReal p ↔ r < p :=
   toNNReal_lt_toNNReal_iff'.trans (and_iff_left h)
 #align real.to_nnreal_lt_to_nnreal_iff Real.toNNReal_lt_toNNReal_iff
+-/
 
+#print Real.toNNReal_lt_toNNReal_iff_of_nonneg /-
 theorem toNNReal_lt_toNNReal_iff_of_nonneg {r p : ℝ} (hr : 0 ≤ r) :
     Real.toNNReal r < Real.toNNReal p ↔ r < p :=
   toNNReal_lt_toNNReal_iff'.trans ⟨And.left, fun h => ⟨h, lt_of_le_of_lt hr h⟩⟩
 #align real.to_nnreal_lt_to_nnreal_iff_of_nonneg Real.toNNReal_lt_toNNReal_iff_of_nonneg
+-/
 
+#print Real.toNNReal_add /-
 @[simp]
 theorem toNNReal_add {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal (r + p) = Real.toNNReal r + Real.toNNReal p :=
   NNReal.eq <| by simp [Real.toNNReal, hr, hp, add_nonneg]
 #align real.to_nnreal_add Real.toNNReal_add
+-/
 
+#print Real.toNNReal_add_toNNReal /-
 theorem toNNReal_add_toNNReal {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal r + Real.toNNReal p = Real.toNNReal (r + p) :=
   (Real.toNNReal_add hr hp).symm
 #align real.to_nnreal_add_to_nnreal Real.toNNReal_add_toNNReal
+-/
 
+#print Real.toNNReal_le_toNNReal /-
 theorem toNNReal_le_toNNReal {r p : ℝ} (h : r ≤ p) : Real.toNNReal r ≤ Real.toNNReal p :=
   Real.toNNReal_mono h
 #align real.to_nnreal_le_to_nnreal Real.toNNReal_le_toNNReal
+-/
 
+#print Real.toNNReal_add_le /-
 theorem toNNReal_add_le {r p : ℝ} : Real.toNNReal (r + p) ≤ Real.toNNReal r + Real.toNNReal p :=
   NNReal.coe_le_coe.1 <| max_le (add_le_add (le_max_left _ _) (le_max_left _ _)) NNReal.zero_le_coe
 #align real.to_nnreal_add_le Real.toNNReal_add_le
+-/
 
+#print Real.toNNReal_le_iff_le_coe /-
 theorem toNNReal_le_iff_le_coe {r : ℝ} {p : ℝ≥0} : Real.toNNReal r ≤ p ↔ r ≤ ↑p :=
   NNReal.gi.gc r p
 #align real.to_nnreal_le_iff_le_coe Real.toNNReal_le_iff_le_coe
+-/
 
+#print Real.le_toNNReal_iff_coe_le /-
 theorem le_toNNReal_iff_coe_le {r : ℝ≥0} {p : ℝ} (hp : 0 ≤ p) : r ≤ Real.toNNReal p ↔ ↑r ≤ p := by
   rw [← NNReal.coe_le_coe, Real.coe_toNNReal p hp]
 #align real.le_to_nnreal_iff_coe_le Real.le_toNNReal_iff_coe_le
+-/
 
+#print Real.le_toNNReal_iff_coe_le' /-
 theorem le_toNNReal_iff_coe_le' {r : ℝ≥0} {p : ℝ} (hr : 0 < r) : r ≤ Real.toNNReal p ↔ ↑r ≤ p :=
   (le_or_lt 0 p).elim le_toNNReal_iff_coe_le fun hp => by
     simp only [(hp.trans_le r.coe_nonneg).not_le, to_nnreal_eq_zero.2 hp.le, hr.not_le]
 #align real.le_to_nnreal_iff_coe_le' Real.le_toNNReal_iff_coe_le'
+-/
 
+#print Real.toNNReal_lt_iff_lt_coe /-
 theorem toNNReal_lt_iff_lt_coe {r : ℝ} {p : ℝ≥0} (ha : 0 ≤ r) : Real.toNNReal r < p ↔ r < ↑p := by
   rw [← NNReal.coe_lt_coe, Real.coe_toNNReal r ha]
 #align real.to_nnreal_lt_iff_lt_coe Real.toNNReal_lt_iff_lt_coe
+-/
 
+#print Real.lt_toNNReal_iff_coe_lt /-
 theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔ ↑r < p :=
   by
   cases le_total 0 p
@@ -684,6 +872,7 @@ theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔
     · intro rp; have : ¬p ≤ 0 := not_le_of_lt (lt_of_le_of_lt (NNReal.coe_nonneg _) rp)
       contradiction
 #align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_lt
+-/
 
 @[simp]
 theorem toNNReal_bit0 (r : ℝ) : Real.toNNReal (bit0 r) = bit0 (Real.toNNReal r) :=
@@ -699,10 +888,12 @@ theorem toNNReal_bit1 {r : ℝ} (hr : 0 ≤ r) : Real.toNNReal (bit1 r) = bit1 (
   (Real.toNNReal_add (by simp [hr]) zero_le_one).trans (by simp [bit1])
 #align real.to_nnreal_bit1 Real.toNNReal_bit1
 
+#print Real.toNNReal_pow /-
 theorem toNNReal_pow {x : ℝ} (hx : 0 ≤ x) (n : ℕ) : (x ^ n).toNNReal = x.toNNReal ^ n := by
   rw [← NNReal.coe_eq, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),
     Real.coe_toNNReal x hx]
 #align real.to_nnreal_pow Real.toNNReal_pow
+-/
 
 end ToNnreal
 
@@ -714,10 +905,13 @@ namespace NNReal
 
 section Mul
 
+#print NNReal.mul_eq_mul_left /-
 theorem mul_eq_mul_left {a b c : ℝ≥0} (h : a ≠ 0) : a * b = a * c ↔ b = c := by
   rw [mul_eq_mul_left_iff, or_iff_left h]
 #align nnreal.mul_eq_mul_left NNReal.mul_eq_mul_left
+-/
 
+#print Real.toNNReal_mul /-
 theorem Real.toNNReal_mul {p q : ℝ} (hp : 0 ≤ p) :
     Real.toNNReal (p * q) = Real.toNNReal p * Real.toNNReal q :=
   by
@@ -727,6 +921,7 @@ theorem Real.toNNReal_mul {p q : ℝ} (hp : 0 ≤ p) :
   · have hpq := mul_nonpos_of_nonneg_of_nonpos hp hq
     rw [to_nnreal_eq_zero.2 hq, to_nnreal_eq_zero.2 hpq, MulZeroClass.mul_zero]
 #align real.to_nnreal_mul Real.toNNReal_mul
+-/
 
 end Mul
 
@@ -738,11 +933,14 @@ theorem pow_antitone_exp {a : ℝ≥0} (m n : ℕ) (mn : m ≤ n) (a1 : a ≤ 1)
 #align nnreal.pow_antitone_exp NNReal.pow_antitone_exp
 -/
 
+#print NNReal.exists_pow_lt_of_lt_one /-
 theorem exists_pow_lt_of_lt_one {a b : ℝ≥0} (ha : 0 < a) (hb : b < 1) : ∃ n : ℕ, b ^ n < a := by
   simpa only [← coe_pow, NNReal.coe_lt_coe] using
     exists_pow_lt_of_lt_one (NNReal.coe_pos.2 ha) (NNReal.coe_lt_coe.2 hb)
 #align nnreal.exists_pow_lt_of_lt_one NNReal.exists_pow_lt_of_lt_one
+-/
 
+#print NNReal.exists_mem_Ico_zpow /-
 theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 < y) :
     ∃ n : ℤ, x ∈ Set.Ico (y ^ n) (y ^ (n + 1)) :=
   by
@@ -751,7 +949,9 @@ theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   rw [← NNReal.coe_zpow] at hn h'n 
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ico_zpow NNReal.exists_mem_Ico_zpow
+-/
 
+#print NNReal.exists_mem_Ioc_zpow /-
 theorem exists_mem_Ioc_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 < y) :
     ∃ n : ℤ, x ∈ Set.Ioc (y ^ n) (y ^ (n + 1)) :=
   by
@@ -760,6 +960,7 @@ theorem exists_mem_Ioc_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   rw [← NNReal.coe_zpow] at hn h'n 
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ioc_zpow NNReal.exists_mem_Ioc_zpow
+-/
 
 end Pow
 
@@ -773,104 +974,146 @@ typeclass. For lemmas about subtraction and addition see lemmas
 about `has_ordered_sub` in the file `algebra.order.sub`. See also `mul_tsub` and `tsub_mul`. -/
 
 
+#print NNReal.sub_def /-
 theorem sub_def {r p : ℝ≥0} : r - p = Real.toNNReal (r - p) :=
   rfl
 #align nnreal.sub_def NNReal.sub_def
+-/
 
+#print NNReal.coe_sub_def /-
 theorem coe_sub_def {r p : ℝ≥0} : ↑(r - p) = max (r - p : ℝ) 0 :=
   rfl
 #align nnreal.coe_sub_def NNReal.coe_sub_def
+-/
 
 example : OrderedSub ℝ≥0 := by infer_instance
 
+#print NNReal.sub_div /-
 theorem sub_div (a b c : ℝ≥0) : (a - b) / c = a / c - b / c :=
   tsub_div _ _ _
 #align nnreal.sub_div NNReal.sub_div
+-/
 
 end Sub
 
 section Inv
 
+#print NNReal.sum_div /-
 theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
     (∑ i in s, f i) / b = ∑ i in s, f i / b :=
   Finset.sum_div
 #align nnreal.sum_div NNReal.sum_div
+-/
 
+#print NNReal.inv_le /-
 @[simp]
 theorem inv_le {r p : ℝ≥0} (h : r ≠ 0) : r⁻¹ ≤ p ↔ 1 ≤ r * p := by
   rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h]
 #align nnreal.inv_le NNReal.inv_le
+-/
 
+#print NNReal.inv_le_of_le_mul /-
 theorem inv_le_of_le_mul {r p : ℝ≥0} (h : 1 ≤ r * p) : r⁻¹ ≤ p := by
   by_cases r = 0 <;> simp [*, inv_le]
 #align nnreal.inv_le_of_le_mul NNReal.inv_le_of_le_mul
+-/
 
+#print NNReal.le_inv_iff_mul_le /-
 @[simp]
 theorem le_inv_iff_mul_le {r p : ℝ≥0} (h : p ≠ 0) : r ≤ p⁻¹ ↔ r * p ≤ 1 := by
   rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h, mul_comm]
 #align nnreal.le_inv_iff_mul_le NNReal.le_inv_iff_mul_le
+-/
 
+#print NNReal.lt_inv_iff_mul_lt /-
 @[simp]
 theorem lt_inv_iff_mul_lt {r p : ℝ≥0} (h : p ≠ 0) : r < p⁻¹ ↔ r * p < 1 := by
   rw [← mul_lt_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h, mul_comm]
 #align nnreal.lt_inv_iff_mul_lt NNReal.lt_inv_iff_mul_lt
+-/
 
+#print NNReal.mul_le_iff_le_inv /-
 theorem mul_le_iff_le_inv {a b r : ℝ≥0} (hr : r ≠ 0) : r * a ≤ b ↔ a ≤ r⁻¹ * b :=
   by
   have : 0 < r := lt_of_le_of_ne (zero_le r) hr.symm
   rw [← mul_le_mul_left (inv_pos.mpr this), ← mul_assoc, inv_mul_cancel hr, one_mul]
 #align nnreal.mul_le_iff_le_inv NNReal.mul_le_iff_le_inv
+-/
 
+#print NNReal.le_div_iff_mul_le /-
 theorem le_div_iff_mul_le {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ a * r ≤ b :=
   le_div_iff₀ hr
 #align nnreal.le_div_iff_mul_le NNReal.le_div_iff_mul_le
+-/
 
+#print NNReal.div_le_iff /-
 theorem div_le_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a / r ≤ b ↔ a ≤ b * r :=
   div_le_iff₀ hr
 #align nnreal.div_le_iff NNReal.div_le_iff
+-/
 
+#print NNReal.div_le_iff' /-
 theorem div_le_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a / r ≤ b ↔ a ≤ r * b :=
   @div_le_iff' ℝ _ a r b <| pos_iff_ne_zero.2 hr
 #align nnreal.div_le_iff' NNReal.div_le_iff'
+-/
 
+#print NNReal.div_le_of_le_mul /-
 theorem div_le_of_le_mul {a b c : ℝ≥0} (h : a ≤ b * c) : a / c ≤ b :=
   if h0 : c = 0 then by simp [h0] else (div_le_iff h0).2 h
 #align nnreal.div_le_of_le_mul NNReal.div_le_of_le_mul
+-/
 
+#print NNReal.div_le_of_le_mul' /-
 theorem div_le_of_le_mul' {a b c : ℝ≥0} (h : a ≤ b * c) : a / b ≤ c :=
   div_le_of_le_mul <| mul_comm b c ▸ h
 #align nnreal.div_le_of_le_mul' NNReal.div_le_of_le_mul'
+-/
 
+#print NNReal.le_div_iff /-
 theorem le_div_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ a * r ≤ b :=
   @le_div_iff ℝ _ a b r <| pos_iff_ne_zero.2 hr
 #align nnreal.le_div_iff NNReal.le_div_iff
+-/
 
+#print NNReal.le_div_iff' /-
 theorem le_div_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ r * a ≤ b :=
   @le_div_iff' ℝ _ a b r <| pos_iff_ne_zero.2 hr
 #align nnreal.le_div_iff' NNReal.le_div_iff'
+-/
 
+#print NNReal.div_lt_iff /-
 theorem div_lt_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a / r < b ↔ a < b * r :=
   lt_iff_lt_of_le_iff_le (le_div_iff hr)
 #align nnreal.div_lt_iff NNReal.div_lt_iff
+-/
 
+#print NNReal.div_lt_iff' /-
 theorem div_lt_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a / r < b ↔ a < r * b :=
   lt_iff_lt_of_le_iff_le (le_div_iff' hr)
 #align nnreal.div_lt_iff' NNReal.div_lt_iff'
+-/
 
+#print NNReal.lt_div_iff /-
 theorem lt_div_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a < b / r ↔ a * r < b :=
   lt_iff_lt_of_le_iff_le (div_le_iff hr)
 #align nnreal.lt_div_iff NNReal.lt_div_iff
+-/
 
+#print NNReal.lt_div_iff' /-
 theorem lt_div_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a < b / r ↔ r * a < b :=
   lt_iff_lt_of_le_iff_le (div_le_iff' hr)
 #align nnreal.lt_div_iff' NNReal.lt_div_iff'
+-/
 
+#print NNReal.mul_lt_of_lt_div /-
 theorem mul_lt_of_lt_div {a b r : ℝ≥0} (h : a < b / r) : a * r < b :=
   by
   refine' (lt_div_iff fun hr => False.elim _).1 h
   subst r
   simpa using h
 #align nnreal.mul_lt_of_lt_div NNReal.mul_lt_of_lt_div
+-/
 
 theorem div_le_div_left_of_le {a b c : ℝ≥0} (b0 : 0 < b) (c0 : 0 < c) (cb : c ≤ b) :
     a / b ≤ a / c := by
@@ -881,11 +1124,14 @@ theorem div_le_div_left_of_le {a b c : ℝ≥0} (b0 : 0 < b) (c0 : 0 < c) (cb :
     exact (div_le_div_left a0 b0 c0).mpr cb
 #align nnreal.div_le_div_left_of_le NNReal.div_le_div_left_of_leₓ
 
+#print NNReal.div_le_div_left /-
 theorem div_le_div_left {a b c : ℝ≥0} (a0 : 0 < a) (b0 : 0 < b) (c0 : 0 < c) :
     a / b ≤ a / c ↔ c ≤ b :=
   div_le_div_left a0 b0 c0
 #align nnreal.div_le_div_left NNReal.div_le_div_left
+-/
 
+#print NNReal.le_of_forall_lt_one_mul_le /-
 theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y) : x ≤ y :=
   le_of_forall_ge_of_dense fun a ha =>
     by
@@ -895,21 +1141,29 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
     have : a * x⁻¹ * x ≤ y := h _ this
     rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this 
 #align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_le
+-/
 
+#print NNReal.half_le_self /-
 theorem half_le_self (a : ℝ≥0) : a / 2 ≤ a :=
   half_le_self bot_le
 #align nnreal.half_le_self NNReal.half_le_self
+-/
 
+#print NNReal.half_lt_self /-
 theorem half_lt_self {a : ℝ≥0} (h : a ≠ 0) : a / 2 < a :=
   half_lt_self h.bot_lt
 #align nnreal.half_lt_self NNReal.half_lt_self
+-/
 
+#print NNReal.div_lt_one_of_lt /-
 theorem div_lt_one_of_lt {a b : ℝ≥0} (h : a < b) : a / b < 1 :=
   by
   rwa [div_lt_iff, one_mul]
   exact ne_of_gt (lt_of_le_of_lt (zero_le _) h)
 #align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_lt
+-/
 
+#print Real.toNNReal_inv /-
 theorem Real.toNNReal_inv {x : ℝ} : Real.toNNReal x⁻¹ = (Real.toNNReal x)⁻¹ :=
   by
   by_cases hx : 0 ≤ x
@@ -918,38 +1172,51 @@ theorem Real.toNNReal_inv {x : ℝ} : Real.toNNReal x⁻¹ = (Real.toNNReal x)
   · have hx' := le_of_not_ge hx
     rw [to_nnreal_eq_zero.mpr hx', inv_zero, to_nnreal_eq_zero.mpr (inv_nonpos.mpr hx')]
 #align real.to_nnreal_inv Real.toNNReal_inv
+-/
 
+#print Real.toNNReal_div /-
 theorem Real.toNNReal_div {x y : ℝ} (hx : 0 ≤ x) :
     Real.toNNReal (x / y) = Real.toNNReal x / Real.toNNReal y := by
   rw [div_eq_mul_inv, div_eq_mul_inv, ← Real.toNNReal_inv, ← Real.toNNReal_mul hx]
 #align real.to_nnreal_div Real.toNNReal_div
+-/
 
+#print Real.toNNReal_div' /-
 theorem Real.toNNReal_div' {x y : ℝ} (hy : 0 ≤ y) :
     Real.toNNReal (x / y) = Real.toNNReal x / Real.toNNReal y := by
   rw [div_eq_inv_mul, div_eq_inv_mul, Real.toNNReal_mul (inv_nonneg.2 hy), Real.toNNReal_inv]
 #align real.to_nnreal_div' Real.toNNReal_div'
+-/
 
+#print NNReal.inv_lt_one_iff /-
 theorem inv_lt_one_iff {x : ℝ≥0} (hx : x ≠ 0) : x⁻¹ < 1 ↔ 1 < x := by
   rwa [← one_div, div_lt_iff hx, one_mul]
 #align nnreal.inv_lt_one_iff NNReal.inv_lt_one_iff
+-/
 
+#print NNReal.zpow_pos /-
 theorem zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
   by
   cases n
   · simp [pow_pos hx.bot_lt _]
   · simp [pow_pos hx.bot_lt _]
 #align nnreal.zpow_pos NNReal.zpow_pos
+-/
 
+#print NNReal.inv_lt_inv /-
 theorem inv_lt_inv {x y : ℝ≥0} (hx : x ≠ 0) (h : x < y) : y⁻¹ < x⁻¹ :=
   inv_lt_inv_of_lt hx.bot_lt h
 #align nnreal.inv_lt_inv NNReal.inv_lt_inv
+-/
 
 end Inv
 
+#print NNReal.abs_eq /-
 @[simp]
 theorem abs_eq (x : ℝ≥0) : |(x : ℝ)| = x :=
   abs_of_nonneg x.property
 #align nnreal.abs_eq NNReal.abs_eq
+-/
 
 section Csupr
 
@@ -957,81 +1224,113 @@ open Set
 
 variable {ι : Sort _} {f : ι → ℝ≥0}
 
+#print NNReal.le_toNNReal_of_coe_le /-
 theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y.toNNReal :=
   (le_toNNReal_iff_coe_le <| x.2.trans h).2 h
 #align nnreal.le_to_nnreal_of_coe_le NNReal.le_toNNReal_of_coe_le
+-/
 
+#print NNReal.sSup_of_not_bddAbove /-
 theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 :=
   by
   rw [← bdd_above_coe] at hs 
   rw [← NNReal.coe_eq, coe_Sup]
   exact Sup_of_not_bdd_above hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
+-/
 
+#print NNReal.iSup_of_not_bddAbove /-
 theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
   sSup_of_not_bddAbove hf
 #align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAbove
+-/
 
+#print NNReal.iInf_empty /-
 theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw [← NNReal.coe_eq, coe_infi];
   exact Real.ciInf_empty _
 #align nnreal.infi_empty NNReal.iInf_empty
+-/
 
+#print NNReal.iInf_const_zero /-
 @[simp]
 theorem iInf_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 := by
   rw [← NNReal.coe_eq, coe_infi]; exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero
+-/
 
+#print NNReal.iInf_mul /-
 theorem iInf_mul (f : ι → ℝ≥0) (a : ℝ≥0) : iInf f * a = ⨅ i, f i * a :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_mul, coe_infi, coe_infi]
   exact Real.iInf_mul_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.infi_mul NNReal.iInf_mul
+-/
 
+#print NNReal.mul_iInf /-
 theorem mul_iInf (f : ι → ℝ≥0) (a : ℝ≥0) : a * iInf f = ⨅ i, a * f i := by
   simpa only [mul_comm] using infi_mul f a
 #align nnreal.mul_infi NNReal.mul_iInf
+-/
 
+#print NNReal.mul_iSup /-
 theorem mul_iSup (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
   exact Real.mul_iSup_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.mul_supr NNReal.mul_iSup
+-/
 
+#print NNReal.iSup_mul /-
 theorem iSup_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a := by
   rw [mul_comm, mul_supr]; simp_rw [mul_comm]
 #align nnreal.supr_mul NNReal.iSup_mul
+-/
 
+#print NNReal.iSup_div /-
 theorem iSup_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i, f i / a := by
   simp only [div_eq_mul_inv, supr_mul]
 #align nnreal.supr_div NNReal.iSup_div
+-/
 
 variable [Nonempty ι]
 
+#print NNReal.le_mul_iInf /-
 theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * iInf h := by
   rw [mul_infi]; exact le_ciInf H
 #align nnreal.le_mul_infi NNReal.le_mul_iInf
+-/
 
+#print NNReal.mul_iSup_le /-
 theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a := by
   rw [mul_supr]; exact ciSup_le H
 #align nnreal.mul_supr_le NNReal.mul_iSup_le
+-/
 
+#print NNReal.le_iInf_mul /-
 theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ iInf g * h := by
   rw [infi_mul]; exact le_ciInf H
 #align nnreal.le_infi_mul NNReal.le_iInf_mul
+-/
 
+#print NNReal.iSup_mul_le /-
 theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a := by
   rw [supr_mul]; exact ciSup_le H
 #align nnreal.supr_mul_le NNReal.iSup_mul_le
+-/
 
+#print NNReal.le_iInf_mul_iInf /-
 theorem le_iInf_mul_iInf {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a ≤ g i * h j) :
     a ≤ iInf g * iInf h :=
   le_iInf_mul fun i => le_mul_iInf <| H i
 #align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInf
+-/
 
+#print NNReal.iSup_mul_iSup_le /-
 theorem iSup_mul_iSup_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
     iSup g * iSup h ≤ a :=
   iSup_mul_le fun i => mul_iSup_le <| H _
 #align nnreal.supr_mul_supr_le NNReal.iSup_mul_iSup_le
+-/
 
 end Csupr
 
@@ -1043,14 +1342,18 @@ namespace OrdConnected
 
 variable {s : Set ℝ} {t : Set ℝ≥0}
 
+#print Set.OrdConnected.preimage_coe_nnreal_real /-
 theorem preimage_coe_nnreal_real (h : s.OrdConnected) : (coe ⁻¹' s : Set ℝ≥0).OrdConnected :=
   h.preimage_mono NNReal.coe_mono
 #align set.ord_connected.preimage_coe_nnreal_real Set.OrdConnected.preimage_coe_nnreal_real
+-/
 
+#print Set.OrdConnected.image_coe_nnreal_real /-
 theorem image_coe_nnreal_real (h : t.OrdConnected) : (coe '' t : Set ℝ).OrdConnected :=
   ⟨ball_image_iff.2 fun x hx =>
       ball_image_iff.2 fun y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
 #align set.ord_connected.image_coe_nnreal_real Set.OrdConnected.image_coe_nnreal_real
+-/
 
 #print Set.OrdConnected.image_real_toNNReal /-
 theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConnected :=
@@ -1088,26 +1391,36 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 #align real.nnabs Real.nnabs
 -/
 
+#print Real.coe_nnabs /-
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
   rfl
 #align real.coe_nnabs Real.coe_nnabs
+-/
 
+#print Real.nnabs_of_nonneg /-
 @[simp]
 theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x := by ext;
   simp [coe_to_nnreal x h, abs_of_nonneg h]
 #align real.nnabs_of_nonneg Real.nnabs_of_nonneg
+-/
 
+#print Real.nnabs_coe /-
 theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 #align real.nnabs_coe Real.nnabs_coe
+-/
 
+#print Real.coe_toNNReal_le /-
 theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
   max_le (le_abs_self _) (abs_nonneg _)
 #align real.coe_to_nnreal_le Real.coe_toNNReal_le
+-/
 
+#print Real.cast_natAbs_eq_nnabs_cast /-
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by ext;
   rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs]
 #align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_cast
+-/
 
 end Real

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -453,7 +453,7 @@ theorem orderIsoIccZeroCoe_symm_apply_coe (a : ℝ≥0) (b : Set.Iic a) :
 
 -- note we need the `@` to make the `has_mem.mem` have a sensible type
 theorem coe_image {s : Set ℝ≥0} :
-    coe '' s = { x : ℝ | ∃ h : 0 ≤ x, @Membership.Mem ℝ≥0 _ _ ⟨x, h⟩ s } :=
+    coe '' s = {x : ℝ | ∃ h : 0 ≤ x, @Membership.Mem ℝ≥0 _ _ ⟨x, h⟩ s} :=
   Subtype.coe_image
 #align nnreal.coe_image NNReal.coe_image

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -64,8 +64,9 @@ open scoped Classical BigOperators
 -- to ensure these instances are computable
 /-- Nonnegative real numbers. -/
 def NNReal :=
-  { r : ℝ // 0 ≤ r }deriving StrictOrderedSemiring, CommMonoidWithZero, FloorSemiring, CommSemiring,
-  Semiring, SemilatticeInf, SemilatticeSup, DistribLattice, DenselyOrdered, OrderBot,
+  { r : ℝ // 0 ≤ r }
+deriving StrictOrderedSemiring, CommMonoidWithZero, FloorSemiring, CommSemiring, Semiring,
+  SemilatticeInf, SemilatticeSup, DistribLattice, DenselyOrdered, OrderBot,
   CanonicallyLinearOrderedSemifield, LinearOrderedCommGroupWithZero, Archimedean,
   LinearOrderedSemiring, OrderedCommSemiring, CanonicallyOrderedCommSemiring, Sub, OrderedSub, Div,
   Inhabited
@@ -106,7 +107,7 @@ protected theorem forall {p : ℝ≥0 → Prop} : (∀ x : ℝ≥0, p x) ↔ ∀
   Subtype.forall
 #align nnreal.forall NNReal.forall
 
-protected theorem exists {p : ℝ≥0 → Prop} : (∃ x : ℝ≥0, p x) ↔ ∃ (x : ℝ)(hx : 0 ≤ x), p ⟨x, hx⟩ :=
+protected theorem exists {p : ℝ≥0 → Prop} : (∃ x : ℝ≥0, p x) ↔ ∃ (x : ℝ) (hx : 0 ≤ x), p ⟨x, hx⟩ :=
   Subtype.exists
 #align nnreal.exists NNReal.exists
 
@@ -679,7 +680,7 @@ theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔
   cases le_total 0 p
   · rw [← NNReal.coe_lt_coe, Real.coe_toNNReal p h]
   · rw [to_nnreal_eq_zero.2 h]; constructor
-    · intro ; have := not_lt_of_le (zero_le r); contradiction
+    · intro; have := not_lt_of_le (zero_le r); contradiction
     · intro rp; have : ¬p ≤ 0 := not_le_of_lt (lt_of_le_of_lt (NNReal.coe_nonneg _) rp)
       contradiction
 #align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_lt
@@ -747,7 +748,7 @@ theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   by
   obtain ⟨n, hn, h'n⟩ : ∃ n : ℤ, (y : ℝ) ^ n ≤ x ∧ (x : ℝ) < y ^ (n + 1) :=
     exists_mem_Ico_zpow (bot_lt_iff_ne_bot.mpr hx) hy
-  rw [← NNReal.coe_zpow] at hn h'n
+  rw [← NNReal.coe_zpow] at hn h'n 
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ico_zpow NNReal.exists_mem_Ico_zpow
 
@@ -756,7 +757,7 @@ theorem exists_mem_Ioc_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   by
   obtain ⟨n, hn, h'n⟩ : ∃ n : ℤ, (y : ℝ) ^ n < x ∧ (x : ℝ) ≤ y ^ (n + 1) :=
     exists_mem_Ioc_zpow (bot_lt_iff_ne_bot.mpr hx) hy
-  rw [← NNReal.coe_zpow] at hn h'n
+  rw [← NNReal.coe_zpow] at hn h'n 
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ioc_zpow NNReal.exists_mem_Ioc_zpow
 
@@ -892,7 +893,7 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
     have hx' : x⁻¹ ≠ 0 := by rwa [(· ≠ ·), inv_eq_zero]
     have : a * x⁻¹ < 1 := by rwa [← lt_inv_iff_mul_lt hx', inv_inv]
     have : a * x⁻¹ * x ≤ y := h _ this
-    rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this
+    rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this 
 #align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_le
 
 theorem half_le_self (a : ℝ≥0) : a / 2 ≤ a :=
@@ -962,7 +963,7 @@ theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y
 
 theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 :=
   by
-  rw [← bdd_above_coe] at hs
+  rw [← bdd_above_coe] at hs 
   rw [← NNReal.coe_eq, coe_Sup]
   exact Sup_of_not_bdd_above hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
@@ -1056,10 +1057,10 @@ theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConne
   by
   refine' ⟨ball_image_iff.2 fun x hx => ball_image_iff.2 fun y hy z hz => _⟩
   cases' le_total y 0 with hy₀ hy₀
-  · rw [mem_Icc, Real.toNNReal_of_nonpos hy₀, nonpos_iff_eq_zero] at hz
+  · rw [mem_Icc, Real.toNNReal_of_nonpos hy₀, nonpos_iff_eq_zero] at hz 
     exact ⟨y, hy, (to_nnreal_of_nonpos hy₀).trans hz.2.symm⟩
   · lift y to ℝ≥0 using hy₀
-    rw [to_nnreal_coe] at hz
+    rw [to_nnreal_coe] at hz 
     exact ⟨z, h.out hx hy ⟨to_nnreal_le_iff_le_coe.1 hz.1, hz.2⟩, to_nnreal_coe⟩
 #align set.ord_connected.image_real_to_nnreal Set.OrdConnected.image_real_toNNReal
 -/

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -193,19 +193,15 @@ protected theorem coe_div (r₁ r₂ : ℝ≥0) : ((r₁ / r₂ : ℝ≥0) : ℝ
   rfl
 #align nnreal.coe_div NNReal.coe_div
 
-/- warning: nnreal.coe_bit0 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_bit0 [anonymous]ₓ'. -/
 @[simp, norm_cast]
-protected theorem [anonymous] (r : ℝ≥0) : ((bit0 r : ℝ≥0) : ℝ) = bit0 r :=
+protected theorem coe_bit0 (r : ℝ≥0) : ((bit0 r : ℝ≥0) : ℝ) = bit0 r :=
   rfl
-#align nnreal.coe_bit0 [anonymous]
+#align nnreal.coe_bit0 NNReal.coe_bit0
 
-/- warning: nnreal.coe_bit1 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_bit1 [anonymous]ₓ'. -/
 @[simp, norm_cast]
-protected theorem [anonymous] (r : ℝ≥0) : ((bit1 r : ℝ≥0) : ℝ) = bit1 r :=
+protected theorem coe_bit1 (r : ℝ≥0) : ((bit1 r : ℝ≥0) : ℝ) = bit1 r :=
   rfl
-#align nnreal.coe_bit1 [anonymous]
+#align nnreal.coe_bit1 NNReal.coe_bit1
 
 protected theorem coe_two : ((2 : ℝ≥0) : ℝ) = 2 :=
   rfl
@@ -688,23 +684,19 @@ theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔
       contradiction
 #align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_lt
 
-/- warning: real.to_nnreal_bit0 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_bit0 [anonymous]ₓ'. -/
 @[simp]
-theorem [anonymous] (r : ℝ) : Real.toNNReal (bit0 r) = bit0 (Real.toNNReal r) :=
+theorem toNNReal_bit0 (r : ℝ) : Real.toNNReal (bit0 r) = bit0 (Real.toNNReal r) :=
   by
   cases' le_total r 0 with hr hr
   · rw [to_nnreal_of_nonpos hr, to_nnreal_of_nonpos, bit0_zero]
     exact add_nonpos hr hr
   · exact to_nnreal_add hr hr
-#align real.to_nnreal_bit0 [anonymous]
+#align real.to_nnreal_bit0 Real.toNNReal_bit0
 
-/- warning: real.to_nnreal_bit1 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_bit1 [anonymous]ₓ'. -/
 @[simp]
-theorem [anonymous] {r : ℝ} (hr : 0 ≤ r) : Real.toNNReal (bit1 r) = bit1 (Real.toNNReal r) :=
+theorem toNNReal_bit1 {r : ℝ} (hr : 0 ≤ r) : Real.toNNReal (bit1 r) = bit1 (Real.toNNReal r) :=
   (Real.toNNReal_add (by simp [hr]) zero_le_one).trans (by simp [bit1])
-#align real.to_nnreal_bit1 [anonymous]
+#align real.to_nnreal_bit1 Real.toNNReal_bit1
 
 theorem toNNReal_pow {x : ℝ} (hx : 0 ≤ x) (n : ℕ) : (x ^ n).toNNReal = x.toNNReal ^ n := by
   rw [← NNReal.coe_eq, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -58,7 +58,7 @@ This file defines `ℝ≥0` as a localized notation for `nnreal`.
 -/
 
 
-open Classical BigOperators
+open scoped Classical BigOperators
 
 #print NNReal /-
 -- to ensure these instances are computable
@@ -739,9 +739,11 @@ end Mul
 
 section Pow
 
+#print NNReal.pow_antitone_exp /-
 theorem pow_antitone_exp {a : ℝ≥0} (m n : ℕ) (mn : m ≤ n) (a1 : a ≤ 1) : a ^ n ≤ a ^ m :=
   pow_le_pow_of_le_one (zero_le a) a1 mn
 #align nnreal.pow_antitone_exp NNReal.pow_antitone_exp
+-/
 
 theorem exists_pow_lt_of_lt_one {a b : ℝ≥0} (ha : 0 < a) (hb : b < 1) : ∃ n : ℕ, b ^ n < a := by
   simpa only [← coe_pow, NNReal.coe_lt_coe] using

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -80,74 +80,32 @@ namespace NNReal
 instance : Coe ℝ≥0 ℝ :=
   ⟨Subtype.val⟩
 
-/- warning: nnreal.val_eq_coe -> NNReal.val_eq_coe is a dubious translation:
-lean 3 declaration is
-  forall (n : NNReal), Eq.{1} Real (Subtype.val.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) n) ((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))) n)
-but is expected to have type
-  forall (n : NNReal), Eq.{1} Real (Subtype.val.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) n) (NNReal.toReal n)
-Case conversion may be inaccurate. Consider using '#align nnreal.val_eq_coe NNReal.val_eq_coeₓ'. -/
 -- Simp lemma to put back `n.val` into the normal form given by the coercion.
 @[simp]
 theorem val_eq_coe (n : ℝ≥0) : n.val = n :=
   rfl
 #align nnreal.val_eq_coe NNReal.val_eq_coe
 
-/- warning: nnreal.can_lift -> NNReal.canLift is a dubious translation:
-lean 3 declaration is
-  CanLift.{1, 1} Real NNReal ((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)))) (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)
-but is expected to have type
-  CanLift.{1, 1} Real NNReal NNReal.toReal (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r)
-Case conversion may be inaccurate. Consider using '#align nnreal.can_lift NNReal.canLiftₓ'. -/
 instance canLift : CanLift ℝ ℝ≥0 coe fun r => 0 ≤ r :=
   Subtype.canLift _
 #align nnreal.can_lift NNReal.canLift
 
-/- warning: nnreal.eq -> NNReal.eq is a dubious translation:
-lean 3 declaration is
-  forall {n : NNReal} {m : NNReal}, (Eq.{1} Real ((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))) n) ((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))) m)) -> (Eq.{1} NNReal n m)
-but is expected to have type
-  forall {n : NNReal} {m : NNReal}, (Eq.{1} Real (NNReal.toReal n) (NNReal.toReal m)) -> (Eq.{1} NNReal n m)
-Case conversion may be inaccurate. Consider using '#align nnreal.eq NNReal.eqₓ'. -/
 protected theorem eq {n m : ℝ≥0} : (n : ℝ) = (m : ℝ) → n = m :=
   Subtype.eq
 #align nnreal.eq NNReal.eq
 
-/- warning: nnreal.eq_iff -> NNReal.eq_iff is a dubious translation:
-lean 3 declaration is
-  forall {n : NNReal} {m : NNReal}, Iff (Eq.{1} Real ((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))) n) ((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))) m)) (Eq.{1} NNReal n m)
-but is expected to have type
-  forall {n : NNReal} {m : NNReal}, Iff (Eq.{1} Real (NNReal.toReal n) (NNReal.toReal m)) (Eq.{1} NNReal n m)
-Case conversion may be inaccurate. Consider using '#align nnreal.eq_iff NNReal.eq_iffₓ'. -/
 protected theorem eq_iff {n m : ℝ≥0} : (n : ℝ) = (m : ℝ) ↔ n = m :=
   Iff.intro NNReal.eq (congr_arg coe)
 #align nnreal.eq_iff NNReal.eq_iff
 
-/- warning: nnreal.ne_iff -> NNReal.ne_iff is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, Iff (Ne.{1} Real ((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))) x) ((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))) y)) (Ne.{1} NNReal x y)
-but is expected to have type
-  forall {x : NNReal} {y : NNReal}, Iff (Ne.{1} Real (NNReal.toReal x) (NNReal.toReal y)) (Ne.{1} NNReal x y)
-Case conversion may be inaccurate. Consider using '#align nnreal.ne_iff NNReal.ne_iffₓ'. -/
 theorem ne_iff {x y : ℝ≥0} : (x : ℝ) ≠ (y : ℝ) ↔ x ≠ y :=
   not_congr <| NNReal.eq_iff
 #align nnreal.ne_iff NNReal.ne_iff
 
-/- warning: nnreal.forall -> NNReal.forall is a dubious translation:
-lean 3 declaration is
-  forall {p : NNReal -> Prop}, Iff (forall (x : NNReal), p x) (forall (x : Real) (hx : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x), p (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) x hx))
-but is expected to have type
-  forall {p : NNReal -> Prop}, Iff (forall (x : NNReal), p x) (forall (x : Real) (hx : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x), p (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) x hx))
-Case conversion may be inaccurate. Consider using '#align nnreal.forall NNReal.forallₓ'. -/
 protected theorem forall {p : ℝ≥0 → Prop} : (∀ x : ℝ≥0, p x) ↔ ∀ (x : ℝ) (hx : 0 ≤ x), p ⟨x, hx⟩ :=
   Subtype.forall
 #align nnreal.forall NNReal.forall
 
-/- warning: nnreal.exists -> NNReal.exists is a dubious translation:
-lean 3 declaration is
-  forall {p : NNReal -> Prop}, Iff (Exists.{1} NNReal (fun (x : NNReal) => p x)) (Exists.{1} Real (fun (x : Real) => Exists.{0} (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) (fun (hx : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) => p (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) x hx))))
-but is expected to have type
-  forall {p : NNReal -> Prop}, Iff (Exists.{1} NNReal (fun (x : NNReal) => p x)) (Exists.{1} Real (fun (x : Real) => Exists.{0} (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) (fun (hx : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) => p (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) x hx))))
-Case conversion may be inaccurate. Consider using '#align nnreal.exists NNReal.existsₓ'. -/
 protected theorem exists {p : ℝ≥0 → Prop} : (∃ x : ℝ≥0, p x) ↔ ∃ (x : ℝ)(hx : 0 ≤ x), p ⟨x, hx⟩ :=
   Subtype.exists
 #align nnreal.exists NNReal.exists
@@ -159,52 +117,22 @@ noncomputable def Real.toNNReal (r : ℝ) : ℝ≥0 :=
 #align real.to_nnreal Real.toNNReal
 -/
 
-/- warning: real.coe_to_nnreal -> Real.coe_toNNReal is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real ((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))) (Real.toNNReal r)) r)
-but is expected to have type
-  forall (r : Real), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} Real (NNReal.toReal (Real.toNNReal r)) r)
-Case conversion may be inaccurate. Consider using '#align real.coe_to_nnreal Real.coe_toNNRealₓ'. -/
 theorem Real.coe_toNNReal (r : ℝ) (hr : 0 ≤ r) : (Real.toNNReal r : ℝ) = r :=
   max_eq_left hr
 #align real.coe_to_nnreal Real.coe_toNNReal
 
-/- warning: real.to_nnreal_of_nonneg -> Real.toNNReal_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} (hr : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r), Eq.{1} NNReal (Real.toNNReal r) (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) r hr)
-but is expected to have type
-  forall {r : Real} (hr : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r), Eq.{1} NNReal (Real.toNNReal r) (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) r hr)
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_of_nonneg Real.toNNReal_of_nonnegₓ'. -/
 theorem Real.toNNReal_of_nonneg {r : ℝ} (hr : 0 ≤ r) : r.toNNReal = ⟨r, hr⟩ := by
   simp_rw [Real.toNNReal, max_eq_left hr]
 #align real.to_nnreal_of_nonneg Real.toNNReal_of_nonneg
 
-/- warning: real.le_coe_to_nnreal -> Real.le_coe_toNNReal is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), LE.le.{0} Real Real.hasLe r ((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))) (Real.toNNReal r))
-but is expected to have type
-  forall (r : Real), LE.le.{0} Real Real.instLEReal r (NNReal.toReal (Real.toNNReal r))
-Case conversion may be inaccurate. Consider using '#align real.le_coe_to_nnreal Real.le_coe_toNNRealₓ'. -/
 theorem Real.le_coe_toNNReal (r : ℝ) : r ≤ Real.toNNReal r :=
   le_max_left r 0
 #align real.le_coe_to_nnreal Real.le_coe_toNNReal
 
-/- warning: nnreal.coe_nonneg -> NNReal.coe_nonneg is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) r)
-but is expected to have type
-  forall (r : NNReal), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal r)
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_nonneg NNReal.coe_nonnegₓ'. -/
 theorem coe_nonneg (r : ℝ≥0) : (0 : ℝ) ≤ r :=
   r.2
 #align nnreal.coe_nonneg NNReal.coe_nonneg
 
-/- warning: nnreal.coe_mk -> NNReal.coe_mk is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (ha : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Subtype.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)) Real (HasLiftT.mk.{1, 1} (Subtype.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)) Real (CoeTCₓ.coe.{1, 1} (Subtype.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)) Real (coeBase.{1, 1} (Subtype.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)) Real (coeSubtype.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r))))) (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) a ha)) a
-but is expected to have type
-  forall (a : Real) (ha : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a), Eq.{1} Real (NNReal.toReal (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) a ha)) a
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_mk NNReal.coe_mkₓ'. -/
 @[norm_cast]
 theorem coe_mk (a : ℝ) (ha) : ((⟨a, ha⟩ : ℝ≥0) : ℝ) = a :=
   rfl
@@ -232,93 +160,40 @@ example : Inhabited ℝ≥0 := by infer_instance
 
 example : Nontrivial ℝ≥0 := by infer_instance
 
-/- warning: nnreal.coe_injective -> NNReal.coe_injective is a dubious translation:
-lean 3 declaration is
-  Function.Injective.{1, 1} NNReal Real ((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))))
-but is expected to have type
-  Function.Injective.{1, 1} NNReal Real NNReal.toReal
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_injective NNReal.coe_injectiveₓ'. -/
 protected theorem coe_injective : Function.Injective (coe : ℝ≥0 → ℝ) :=
   Subtype.coe_injective
 #align nnreal.coe_injective NNReal.coe_injective
 
-/- warning: nnreal.coe_eq -> NNReal.coe_eq is a dubious translation:
-lean 3 declaration is
-  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (Eq.{1} Real ((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))) r₁) ((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))) r₂)) (Eq.{1} NNReal r₁ r₂)
-but is expected to have type
-  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (Eq.{1} Real (NNReal.toReal r₁) (NNReal.toReal r₂)) (Eq.{1} NNReal r₁ r₂)
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_eq NNReal.coe_eqₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_eq {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) = r₂ ↔ r₁ = r₂ :=
   NNReal.coe_injective.eq_iff
 #align nnreal.coe_eq NNReal.coe_eq
 
-/- warning: nnreal.coe_zero -> NNReal.coe_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real ((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))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (NNReal.toReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_zero NNReal.coe_zeroₓ'. -/
 protected theorem coe_zero : ((0 : ℝ≥0) : ℝ) = 0 :=
   rfl
 #align nnreal.coe_zero NNReal.coe_zero
 
-/- warning: nnreal.coe_one -> NNReal.coe_one is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real ((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))) (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)))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
-  Eq.{1} Real (NNReal.toReal (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_one NNReal.coe_oneₓ'. -/
 protected theorem coe_one : ((1 : ℝ≥0) : ℝ) = 1 :=
   rfl
 #align nnreal.coe_one NNReal.coe_one
 
-/- warning: nnreal.coe_add -> NNReal.coe_add is a dubious translation:
-lean 3 declaration is
-  forall (r₁ : NNReal) (r₂ : NNReal), Eq.{1} Real ((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))) (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))))) r₁ r₂)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ((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))) r₁) ((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))) r₂))
-but is expected to have type
-  forall (r₁ : NNReal) (r₂ : NNReal), Eq.{1} Real (NNReal.toReal (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))))) r₁ r₂)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (NNReal.toReal r₁) (NNReal.toReal r₂))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_add NNReal.coe_addₓ'. -/
 protected theorem coe_add (r₁ r₂ : ℝ≥0) : ((r₁ + r₂ : ℝ≥0) : ℝ) = r₁ + r₂ :=
   rfl
 #align nnreal.coe_add NNReal.coe_add
 
-/- warning: nnreal.coe_mul -> NNReal.coe_mul is a dubious translation:
-lean 3 declaration is
-  forall (r₁ : NNReal) (r₂ : NNReal), Eq.{1} Real ((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))) (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))))) r₁ r₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((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))) r₁) ((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))) r₂))
-but is expected to have type
-  forall (r₁ : NNReal) (r₂ : NNReal), Eq.{1} Real (NNReal.toReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r₁ r₂)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal r₁) (NNReal.toReal r₂))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_mul NNReal.coe_mulₓ'. -/
 protected theorem coe_mul (r₁ r₂ : ℝ≥0) : ((r₁ * r₂ : ℝ≥0) : ℝ) = r₁ * r₂ :=
   rfl
 #align nnreal.coe_mul NNReal.coe_mul
 
-/- warning: nnreal.coe_inv -> NNReal.coe_inv is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), Eq.{1} Real ((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))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r)) (Inv.inv.{0} Real Real.hasInv ((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))) r))
-but is expected to have type
-  forall (r : NNReal), Eq.{1} Real (NNReal.toReal (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) r)) (Inv.inv.{0} Real Real.instInvReal (NNReal.toReal r))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_inv NNReal.coe_invₓ'. -/
 protected theorem coe_inv (r : ℝ≥0) : ((r⁻¹ : ℝ≥0) : ℝ) = r⁻¹ :=
   rfl
 #align nnreal.coe_inv NNReal.coe_inv
 
-/- warning: nnreal.coe_div -> NNReal.coe_div is a dubious translation:
-lean 3 declaration is
-  forall (r₁ : NNReal) (r₂ : NNReal), Eq.{1} Real ((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))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) r₁ r₂)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((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))) r₁) ((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))) r₂))
-but is expected to have type
-  forall (r₁ : NNReal) (r₂ : NNReal), Eq.{1} Real (NNReal.toReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) r₁ r₂)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (NNReal.toReal r₁) (NNReal.toReal r₂))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_div NNReal.coe_divₓ'. -/
 protected theorem coe_div (r₁ r₂ : ℝ≥0) : ((r₁ / r₂ : ℝ≥0) : ℝ) = r₁ / r₂ :=
   rfl
 #align nnreal.coe_div NNReal.coe_div
 
 /- warning: nnreal.coe_bit0 clashes with [anonymous] -> [anonymous]
-warning: nnreal.coe_bit0 -> [anonymous] is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), Eq.{1} Real ((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))) (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) r)) (bit0.{0} Real Real.hasAdd ((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))) r))
-but is expected to have type
-  forall {r : Type.{u}} {β : Type.{v}}, (Nat -> r -> β) -> Nat -> (List.{u} r) -> (List.{v} β)
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_bit0 [anonymous]ₓ'. -/
 @[simp, norm_cast]
 protected theorem [anonymous] (r : ℝ≥0) : ((bit0 r : ℝ≥0) : ℝ) = bit0 r :=
@@ -326,66 +201,31 @@ protected theorem [anonymous] (r : ℝ≥0) : ((bit0 r : ℝ≥0) : ℝ) = bit0
 #align nnreal.coe_bit0 [anonymous]
 
 /- warning: nnreal.coe_bit1 clashes with [anonymous] -> [anonymous]
-warning: nnreal.coe_bit1 -> [anonymous] is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), Eq.{1} Real ((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))) (bit1.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) r)) (bit1.{0} Real Real.hasOne Real.hasAdd ((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))) r))
-but is expected to have type
-  forall {r : Type.{u}} {β : Type.{v}}, (Nat -> r -> β) -> Nat -> (List.{u} r) -> (List.{v} β)
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_bit1 [anonymous]ₓ'. -/
 @[simp, norm_cast]
 protected theorem [anonymous] (r : ℝ≥0) : ((bit1 r : ℝ≥0) : ℝ) = bit1 r :=
   rfl
 #align nnreal.coe_bit1 [anonymous]
 
-/- warning: nnreal.coe_two -> NNReal.coe_two is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real ((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))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  Eq.{1} Real (NNReal.toReal (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_two NNReal.coe_twoₓ'. -/
 protected theorem coe_two : ((2 : ℝ≥0) : ℝ) = 2 :=
   rfl
 #align nnreal.coe_two NNReal.coe_two
 
-/- warning: nnreal.coe_sub -> NNReal.coe_sub is a dubious translation:
-lean 3 declaration is
-  forall {r₁ : NNReal} {r₂ : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₂ r₁) -> (Eq.{1} Real ((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))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) r₁ r₂)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) ((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))) r₁) ((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))) r₂)))
-but is expected to have type
-  forall {r₁ : NNReal} {r₂ : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r₂ r₁) -> (Eq.{1} Real (NNReal.toReal (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.instSubNNReal) r₁ r₂)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (NNReal.toReal r₁) (NNReal.toReal r₂)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_sub NNReal.coe_subₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_sub {r₁ r₂ : ℝ≥0} (h : r₂ ≤ r₁) : ((r₁ - r₂ : ℝ≥0) : ℝ) = r₁ - r₂ :=
   max_eq_left <| le_sub_comm.2 <| by simp [show (r₂ : ℝ) ≤ r₁ from h]
 #align nnreal.coe_sub NNReal.coe_sub
 
-/- warning: nnreal.coe_eq_zero -> NNReal.coe_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), Iff (Eq.{1} Real ((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))) r) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
-but is expected to have type
-  forall (r : NNReal), Iff (Eq.{1} Real (NNReal.toReal r) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Eq.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_eq_zero NNReal.coe_eq_zeroₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_eq_zero (r : ℝ≥0) : ↑r = (0 : ℝ) ↔ r = 0 := by
   rw [← NNReal.coe_zero, NNReal.coe_eq]
 #align nnreal.coe_eq_zero NNReal.coe_eq_zero
 
-/- warning: nnreal.coe_eq_one -> NNReal.coe_eq_one is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), Iff (Eq.{1} Real ((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))) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Eq.{1} NNReal r (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))))))))
-but is expected to have type
-  forall (r : NNReal), Iff (Eq.{1} Real (NNReal.toReal r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Eq.{1} NNReal r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_eq_one NNReal.coe_eq_oneₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_eq_one (r : ℝ≥0) : ↑r = (1 : ℝ) ↔ r = 1 := by
   rw [← NNReal.coe_one, NNReal.coe_eq]
 #align nnreal.coe_eq_one NNReal.coe_eq_one
 
-/- warning: nnreal.coe_ne_zero -> NNReal.coe_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {r : NNReal}, Iff (Ne.{1} Real ((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))) r) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
-but is expected to have type
-  forall {r : NNReal}, Iff (Ne.{1} Real (NNReal.toReal r) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_ne_zero NNReal.coe_ne_zeroₓ'. -/
 theorem coe_ne_zero {r : ℝ≥0} : (r : ℝ) ≠ 0 ↔ r ≠ 0 := by norm_cast
 #align nnreal.coe_ne_zero NNReal.coe_ne_zero
 
@@ -398,12 +238,6 @@ def toRealHom : ℝ≥0 →+* ℝ :=
 #align nnreal.to_real_hom NNReal.toRealHom
 -/
 
-/- warning: nnreal.coe_to_real_hom -> NNReal.coe_toRealHom is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) NNReal.toRealHom) NNReal.toReal
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_to_real_hom NNReal.coe_toRealHomₓ'. -/
 @[simp]
 theorem coe_toRealHom : ⇑toRealHom = coe :=
   rfl
@@ -415,12 +249,6 @@ section Actions
 instance {M : Type _} [MulAction ℝ M] : MulAction ℝ≥0 M :=
   MulAction.compHom M toRealHom.toMonoidHom
 
-/- warning: nnreal.smul_def -> NNReal.smul_def is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nnreal.smul_def NNReal.smul_defₓ'. -/
 theorem smul_def {M : Type _} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x = (c : ℝ) • x :=
   rfl
 #align nnreal.smul_def NNReal.smul_def
@@ -428,22 +256,10 @@ theorem smul_def {M : Type _} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x
 instance {M N : Type _} [MulAction ℝ M] [MulAction ℝ N] [SMul M N] [IsScalarTower ℝ M N] :
     IsScalarTower ℝ≥0 M N where smul_assoc r := (smul_assoc (r : ℝ) : _)
 
-/- warning: nnreal.smul_comm_class_left -> NNReal.smulCommClass_left is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.monoid] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{0, u1, u2} Real M N (MulAction.toHasSmul.{0, u2} Real N Real.monoid _inst_1) _inst_2], SMulCommClass.{0, u1, u2} NNReal M N (MulAction.toHasSmul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{u2} N _inst_1)) _inst_2
-but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.instMonoidReal] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{0, u1, u2} Real M N (MulAction.toSMul.{0, u2} Real N Real.instMonoidReal _inst_1) _inst_2], SMulCommClass.{0, u1, u2} NNReal M N (MulAction.toSMul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{u2} N _inst_1)) _inst_2
-Case conversion may be inaccurate. Consider using '#align nnreal.smul_comm_class_left NNReal.smulCommClass_leftₓ'. -/
 instance smulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
     SMulCommClass ℝ≥0 M N where smul_comm r := (smul_comm (r : ℝ) : _)
 #align nnreal.smul_comm_class_left NNReal.smulCommClass_left
 
-/- warning: nnreal.smul_comm_class_right -> NNReal.smulCommClass_right is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.monoid] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{u1, 0, u2} M Real N _inst_2 (MulAction.toHasSmul.{0, u2} Real N Real.monoid _inst_1)], SMulCommClass.{u1, 0, u2} M NNReal N _inst_2 (MulAction.toHasSmul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{u2} N _inst_1))
-but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.instMonoidReal] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{u1, 0, u2} M Real N _inst_2 (MulAction.toSMul.{0, u2} Real N Real.instMonoidReal _inst_1)], SMulCommClass.{u1, 0, u2} M NNReal N _inst_2 (MulAction.toSMul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{u2} N _inst_1))
-Case conversion may be inaccurate. Consider using '#align nnreal.smul_comm_class_right NNReal.smulCommClass_rightₓ'. -/
 instance smulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
     SMulCommClass M ℝ≥0 N where smul_comm m r := (smul_comm m (r : ℝ) : _)
 #align nnreal.smul_comm_class_right NNReal.smulCommClass_right
@@ -477,100 +293,46 @@ example : CommMonoidWithZero ℝ≥0 := by infer_instance
 
 noncomputable example : CommGroupWithZero ℝ≥0 := by infer_instance
 
-/- warning: nnreal.coe_indicator -> NNReal.coe_indicator is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_indicator NNReal.coe_indicatorₓ'. -/
 @[simp, norm_cast]
 theorem coe_indicator {α} (s : Set α) (f : α → ℝ≥0) (a : α) :
     ((s.indicator f a : ℝ≥0) : ℝ) = s.indicator (fun x => f x) a :=
   (toRealHom : ℝ≥0 →+ ℝ).map_indicator _ _ _
 #align nnreal.coe_indicator NNReal.coe_indicator
 
-/- warning: nnreal.coe_pow -> NNReal.coe_pow is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_pow NNReal.coe_powₓ'. -/
 @[simp, norm_cast]
 theorem coe_pow (r : ℝ≥0) (n : ℕ) : ((r ^ n : ℝ≥0) : ℝ) = r ^ n :=
   toRealHom.map_pow r n
 #align nnreal.coe_pow NNReal.coe_pow
 
-/- warning: nnreal.coe_zpow -> NNReal.coe_zpow is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall (r : NNReal) (n : Int), Eq.{1} Real (NNReal.toReal (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) r n)) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.instDivisionRingReal))) (NNReal.toReal r) n)
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_zpow NNReal.coe_zpowₓ'. -/
 @[simp, norm_cast]
 theorem coe_zpow (r : ℝ≥0) (n : ℤ) : ((r ^ n : ℝ≥0) : ℝ) = r ^ n := by cases n <;> simp
 #align nnreal.coe_zpow NNReal.coe_zpow
 
-/- warning: nnreal.coe_list_sum -> NNReal.coe_list_sum is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_list_sum NNReal.coe_list_sumₓ'. -/
 @[norm_cast]
 theorem coe_list_sum (l : List ℝ≥0) : ((l.Sum : ℝ≥0) : ℝ) = (l.map coe).Sum :=
   toRealHom.map_list_sum l
 #align nnreal.coe_list_sum NNReal.coe_list_sum
 
-/- warning: nnreal.coe_list_prod -> NNReal.coe_list_prod is a dubious translation:
-lean 3 declaration is
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-  forall (l : List.{0} NNReal), Eq.{1} Real (NNReal.toReal (List.prod.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) instNNRealOne l)) (List.prod.{0} Real Real.instMulReal Real.instOneReal (List.map.{0, 0} NNReal Real NNReal.toReal l))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_list_prod NNReal.coe_list_prodₓ'. -/
 @[norm_cast]
 theorem coe_list_prod (l : List ℝ≥0) : ((l.Prod : ℝ≥0) : ℝ) = (l.map coe).Prod :=
   toRealHom.map_list_prod l
 #align nnreal.coe_list_prod NNReal.coe_list_prod
 
-/- warning: nnreal.coe_multiset_sum -> NNReal.coe_multiset_sum is a dubious translation:
-lean 3 declaration is
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.sum.{0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s)) (Multiset.sum.{0} Real Real.addCommMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
-but is expected to have type
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.sum.{0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s)) (Multiset.sum.{0} Real Real.instAddCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_multiset_sum NNReal.coe_multiset_sumₓ'. -/
 @[norm_cast]
 theorem coe_multiset_sum (s : Multiset ℝ≥0) : ((s.Sum : ℝ≥0) : ℝ) = (s.map coe).Sum :=
   toRealHom.map_multiset_sum s
 #align nnreal.coe_multiset_sum NNReal.coe_multiset_sum
 
-/- warning: nnreal.coe_multiset_prod -> NNReal.coe_multiset_prod is a dubious translation:
-lean 3 declaration is
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.prod.{0} NNReal (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s)) (Multiset.prod.{0} Real Real.commMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
-but is expected to have type
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.prod.{0} NNReal (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s)) (Multiset.prod.{0} Real Real.instCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_multiset_prod NNReal.coe_multiset_prodₓ'. -/
 @[norm_cast]
 theorem coe_multiset_prod (s : Multiset ℝ≥0) : ((s.Prod : ℝ≥0) : ℝ) = (s.map coe).Prod :=
   toRealHom.map_multiset_prod s
 #align nnreal.coe_multiset_prod NNReal.coe_multiset_prod
 
-/- warning: nnreal.coe_sum -> NNReal.coe_sum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => (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))) (f a)))
-but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_sum NNReal.coe_sumₓ'. -/
 @[norm_cast]
 theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a) = ∑ a in s, (f a : ℝ) :=
   toRealHom.map_sum _ _
 #align nnreal.coe_sum NNReal.coe_sum
 
-/- warning: real.to_nnreal_sum_of_nonneg -> Real.toNNReal_sum_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
-but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonnegₓ'. -/
 theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∑ a in s, f a) = ∑ a in s, Real.toNNReal (f a) :=
   by
@@ -578,23 +340,11 @@ theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf :
   exact Finset.sum_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonneg
 
-/- warning: nnreal.coe_prod -> NNReal.coe_prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.prod.{0, u1} NNReal α (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => (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))) (f a)))
-but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.prod.{0, u1} NNReal α (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_prod NNReal.coe_prodₓ'. -/
 @[norm_cast]
 theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a) = ∏ a in s, (f a : ℝ) :=
   toRealHom.map_prod _ _
 #align nnreal.coe_prod NNReal.coe_prod
 
-/- warning: real.to_nnreal_prod_of_nonneg -> Real.toNNReal_prod_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
-but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s (fun (a : α) => Real.toNNReal (f a))))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonnegₓ'. -/
 theorem Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∏ a in s, f a) = ∏ a in s, Real.toNNReal (f a) :=
   by
@@ -602,21 +352,9 @@ theorem Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf :
   exact Finset.prod_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonneg
 
-/- warning: nnreal.nsmul_coe -> NNReal.coe_nsmul is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall (r : NNReal) (n : Nat), Eq.{1} Real (NNReal.toReal (HSMul.hSMul.{0, 0, 0} Nat NNReal NNReal (instHSMul.{0, 0} Nat NNReal (AddMonoid.SMul.{0} NNReal (AddMonoidWithOne.toAddMonoid.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) n r)) (HSMul.hSMul.{0, 0, 0} Nat Real Real (instHSMul.{0, 0} Nat Real (AddMonoid.SMul.{0} Real Real.instAddMonoidReal)) n (NNReal.toReal r))
-Case conversion may be inaccurate. Consider using '#align nnreal.nsmul_coe NNReal.coe_nsmulₓ'. -/
 theorem coe_nsmul (r : ℝ≥0) (n : ℕ) : ↑(n • r) = n • (r : ℝ) := by norm_cast
 #align nnreal.nsmul_coe NNReal.coe_nsmul
 
-/- warning: nnreal.coe_nat_cast -> NNReal.coe_nat_cast is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall (n : Nat), Eq.{1} Real (NNReal.toReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)) (Nat.cast.{0} Real Real.natCast n)
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_nat_cast NNReal.coe_nat_castₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
   map_natCast toRealHom n
@@ -624,45 +362,21 @@ protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
 
 noncomputable example : LinearOrder ℝ≥0 := by infer_instance
 
-/- warning: nnreal.coe_le_coe -> NNReal.coe_le_coe is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_le_coe NNReal.coe_le_coeₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_le_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) ≤ r₂ ↔ r₁ ≤ r₂ :=
   Iff.rfl
 #align nnreal.coe_le_coe NNReal.coe_le_coe
 
-/- warning: nnreal.coe_lt_coe -> NNReal.coe_lt_coe is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LT.lt.{0} Real Real.instLTReal (NNReal.toReal r₁) (NNReal.toReal r₂)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r₁ r₂)
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_lt_coe NNReal.coe_lt_coeₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_lt_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) < r₂ ↔ r₁ < r₂ :=
   Iff.rfl
 #align nnreal.coe_lt_coe NNReal.coe_lt_coe
 
-/- warning: nnreal.coe_pos -> NNReal.coe_pos is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_pos NNReal.coe_posₓ'. -/
 @[simp, norm_cast]
 protected theorem coe_pos {r : ℝ≥0} : (0 : ℝ) < r ↔ 0 < r :=
   Iff.rfl
 #align nnreal.coe_pos NNReal.coe_pos
 
-/- warning: nnreal.coe_mono -> NNReal.coe_mono is a dubious translation:
-lean 3 declaration is
-  Monotone.{0, 0} NNReal Real (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) Real.preorder ((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))))
-but is expected to have type
-  Monotone.{0, 0} NNReal Real (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) Real.instPreorderReal NNReal.toReal
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_mono NNReal.coe_monoₓ'. -/
 protected theorem coe_mono : Monotone (coe : ℝ≥0 → ℝ) := fun _ _ => NNReal.coe_le_coe.2
 #align nnreal.coe_mono NNReal.coe_mono
 
@@ -672,45 +386,21 @@ protected theorem Real.toNNReal_mono : Monotone Real.toNNReal := fun x y h =>
 #align real.to_nnreal_mono Real.toNNReal_mono
 -/
 
-/- warning: real.to_nnreal_coe -> Real.toNNReal_coe is a dubious translation:
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-  forall {r : NNReal}, Eq.{1} NNReal (Real.toNNReal ((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))) r)) r
-but is expected to have type
-  forall {r : NNReal}, Eq.{1} NNReal (Real.toNNReal (NNReal.toReal r)) r
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_coe Real.toNNReal_coeₓ'. -/
 @[simp]
 theorem Real.toNNReal_coe {r : ℝ≥0} : Real.toNNReal r = r :=
   NNReal.eq <| max_eq_left r.2
 #align real.to_nnreal_coe Real.toNNReal_coe
 
-/- warning: nnreal.mk_coe_nat -> NNReal.mk_coe_nat is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Eq.{1} NNReal (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) ((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))) n) (Nat.cast_nonneg.{0} Real Real.orderedSemiring n)) ((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))))))) n)
-but is expected to have type
-  forall (n : Nat), Eq.{1} NNReal (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) (Nat.cast.{0} Real Real.natCast n) (Nat.cast_nonneg.{0} Real Real.orderedSemiring n)) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)
-Case conversion may be inaccurate. Consider using '#align nnreal.mk_coe_nat NNReal.mk_coe_natₓ'. -/
 @[simp]
 theorem mk_coe_nat (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
   NNReal.eq (NNReal.coe_nat_cast n).symm
 #align nnreal.mk_coe_nat NNReal.mk_coe_nat
 
-/- warning: nnreal.to_nnreal_coe_nat -> NNReal.toNNReal_coe_nat is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Eq.{1} NNReal (Real.toNNReal ((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))) n)) ((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))))))) n)
-but is expected to have type
-  forall (n : Nat), Eq.{1} NNReal (Real.toNNReal (Nat.cast.{0} Real Real.natCast n)) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)
-Case conversion may be inaccurate. Consider using '#align nnreal.to_nnreal_coe_nat NNReal.toNNReal_coe_natₓ'. -/
 @[simp]
 theorem toNNReal_coe_nat (n : ℕ) : Real.toNNReal n = n :=
   NNReal.eq <| by simp [Real.coe_toNNReal]
 #align nnreal.to_nnreal_coe_nat NNReal.toNNReal_coe_nat
 
-/- warning: nnreal.gi -> NNReal.gi is a dubious translation:
-lean 3 declaration is
-  GaloisInsertion.{0, 0} Real NNReal Real.preorder (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) Real.toNNReal ((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))))
-but is expected to have type
-  GaloisInsertion.{0, 0} Real NNReal Real.instPreorderReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) Real.toNNReal NNReal.toReal
-Case conversion may be inaccurate. Consider using '#align nnreal.gi NNReal.giₓ'. -/
 /-- `real.to_nnreal` and `coe : ℝ≥0 → ℝ` form a Galois insertion. -/
 noncomputable def gi : GaloisInsertion Real.toNNReal coe :=
   GaloisInsertion.monotoneIntro NNReal.coe_mono Real.toNNReal_mono Real.le_coe_toNNReal fun _ =>
@@ -749,12 +439,6 @@ example : DenselyOrdered ℝ≥0 := by infer_instance
 
 example : NoMaxOrder ℝ≥0 := by infer_instance
 
-/- warning: nnreal.order_iso_Icc_zero_coe -> NNReal.orderIsoIccZeroCoe is a dubious translation:
-lean 3 declaration is
-  forall (a : NNReal), OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))
-but is expected to have type
-  forall (a : NNReal), OrderIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)))
-Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe NNReal.orderIsoIccZeroCoeₓ'. -/
 /-- If `a` is a nonnegative real number, then the closed interval `[0, a]` in `ℝ` is order
 isomorphic to the interval `set.Iic a`. -/
 @[simps apply_coe_coe]
@@ -764,33 +448,18 @@ def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a
   map_rel_iff' x y := Iff.rfl
 #align nnreal.order_iso_Icc_zero_coe NNReal.orderIsoIccZeroCoe
 
-/- warning: nnreal.order_iso_Icc_zero_coe_symm_apply_coe -> NNReal.orderIsoIccZeroCoe_symm_apply_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coeₓ'. -/
 @[simp]
 theorem orderIsoIccZeroCoe_symm_apply_coe (a : ℝ≥0) (b : Set.Iic a) :
     ((orderIsoIccZeroCoe a).symm b : ℝ) = b :=
   rfl
 #align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coe
 
-/- warning: nnreal.coe_image -> NNReal.coe_image is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} NNReal}, Eq.{1} (Set.{0} Real) (Set.image.{0, 0} NNReal Real ((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)))) s) (setOf.{0} Real (fun (x : Real) => Exists.{0} (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) (fun (h : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) x h) s)))
-but is expected to have type
-  forall {s : Set.{0} NNReal}, Eq.{1} (Set.{0} Real) (Set.image.{0, 0} NNReal Real NNReal.toReal s) (setOf.{0} Real (fun (x : Real) => Exists.{0} (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) (fun (h : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) (Subtype.mk.{1} Real (fun (r : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) x h) s)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_image NNReal.coe_imageₓ'. -/
 -- note we need the `@` to make the `has_mem.mem` have a sensible type
 theorem coe_image {s : Set ℝ≥0} :
     coe '' s = { x : ℝ | ∃ h : 0 ≤ x, @Membership.Mem ℝ≥0 _ _ ⟨x, h⟩ s } :=
   Subtype.coe_image
 #align nnreal.coe_image NNReal.coe_image
 
-/- warning: nnreal.bdd_above_coe -> NNReal.bddAbove_coe is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} NNReal}, Iff (BddAbove.{0} Real Real.preorder (Set.image.{0, 0} NNReal Real ((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)))) s)) (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) s)
-but is expected to have type
-  forall {s : Set.{0} NNReal}, Iff (BddAbove.{0} Real Real.instPreorderReal (Set.image.{0, 0} NNReal Real NNReal.toReal s)) (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) s)
-Case conversion may be inaccurate. Consider using '#align nnreal.bdd_above_coe NNReal.bddAbove_coeₓ'. -/
 theorem bddAbove_coe {s : Set ℝ≥0} : BddAbove ((coe : ℝ≥0 → ℝ) '' s) ↔ BddAbove s :=
   Iff.intro
     (fun ⟨b, hb⟩ =>
@@ -799,12 +468,6 @@ theorem bddAbove_coe {s : Set ℝ≥0} : BddAbove ((coe : ℝ≥0 → ℝ) '' s)
     fun ⟨b, hb⟩ => ⟨b, fun y ⟨x, hx, Eq⟩ => Eq ▸ hb hx⟩
 #align nnreal.bdd_above_coe NNReal.bddAbove_coe
 
-/- warning: nnreal.bdd_below_coe -> NNReal.bddBelow_coe is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} NNReal), BddBelow.{0} Real Real.preorder (Set.image.{0, 0} NNReal Real ((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)))) s)
-but is expected to have type
-  forall (s : Set.{0} NNReal), BddBelow.{0} Real Real.instPreorderReal (Set.image.{0, 0} NNReal Real NNReal.toReal s)
-Case conversion may be inaccurate. Consider using '#align nnreal.bdd_below_coe NNReal.bddBelow_coeₓ'. -/
 theorem bddBelow_coe (s : Set ℝ≥0) : BddBelow ((coe : ℝ≥0 → ℝ) '' s) :=
   ⟨0, fun r ⟨q, _, Eq⟩ => Eq ▸ q.2⟩
 #align nnreal.bdd_below_coe NNReal.bddBelow_coe
@@ -812,12 +475,6 @@ theorem bddBelow_coe (s : Set ℝ≥0) : BddBelow ((coe : ℝ≥0 → ℝ) '' s)
 noncomputable instance : ConditionallyCompleteLinearOrderBot ℝ≥0 :=
   Nonneg.conditionallyCompleteLinearOrderBot Real.sSup_empty.le
 
-/- warning: nnreal.coe_Sup -> NNReal.coe_sSup is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} NNReal), Eq.{1} Real ((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))) (SupSet.sSup.{0} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s)) (SupSet.sSup.{0} Real Real.hasSup (Set.image.{0, 0} NNReal Real ((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)))) s))
-but is expected to have type
-  forall (s : Set.{0} NNReal), Eq.{1} Real (NNReal.toReal (SupSet.sSup.{0} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s)) (SupSet.sSup.{0} Real Real.instSupSetReal (Set.image.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_Sup NNReal.coe_sSupₓ'. -/
 @[norm_cast]
 theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup ((coe : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
@@ -825,23 +482,11 @@ theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup ((coe : ℝ≥0
       Real.sSup_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
 #align nnreal.coe_Sup NNReal.coe_sSup
 
-/- warning: nnreal.coe_supr -> NNReal.coe_iSup is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real ((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))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => s i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => (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))) (s i)))
-but is expected to have type
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real (NNReal.toReal (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => s i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => NNReal.toReal (s i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_supr NNReal.coe_iSupₓ'. -/
 @[norm_cast]
 theorem coe_iSup {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, s i := by
   rw [iSup, iSup, coe_Sup, Set.range_comp]
 #align nnreal.coe_supr NNReal.coe_iSup
 
-/- warning: nnreal.coe_Inf -> NNReal.coe_sInf is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} NNReal), Eq.{1} Real ((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))) (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s)) (InfSet.sInf.{0} Real Real.hasInf (Set.image.{0, 0} NNReal Real ((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)))) s))
-but is expected to have type
-  forall (s : Set.{0} NNReal), Eq.{1} Real (NNReal.toReal (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s)) (InfSet.sInf.{0} Real Real.instInfSetReal (Set.image.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_Inf NNReal.coe_sInfₓ'. -/
 @[norm_cast]
 theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf ((coe : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
@@ -849,34 +494,16 @@ theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf ((coe : ℝ≥0
       Real.sInf_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
 #align nnreal.coe_Inf NNReal.coe_sInf
 
-/- warning: nnreal.Inf_empty -> NNReal.sInf_empty is a dubious translation:
-lean 3 declaration is
-  Eq.{1} NNReal (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) (EmptyCollection.emptyCollection.{0} (Set.{0} NNReal) (Set.hasEmptyc.{0} NNReal))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
-but is expected to have type
-  Eq.{1} NNReal (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) (EmptyCollection.emptyCollection.{0} (Set.{0} NNReal) (Set.instEmptyCollectionSet.{0} NNReal))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.Inf_empty NNReal.sInf_emptyₓ'. -/
 @[simp]
 theorem sInf_empty : sInf (∅ : Set ℝ≥0) = 0 := by
   rw [← NNReal.coe_eq_zero, coe_Inf, Set.image_empty, Real.sInf_empty]
 #align nnreal.Inf_empty NNReal.sInf_empty
 
-/- warning: nnreal.coe_infi -> NNReal.coe_iInf is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real ((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))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => s i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => (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))) (s i)))
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_infi NNReal.coe_iInfₓ'. -/
 @[norm_cast]
 theorem coe_iInf {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, s i := by
   rw [iInf, iInf, coe_Inf, Set.range_comp]
 #align nnreal.coe_infi NNReal.coe_iInf
 
-/- warning: nnreal.le_infi_add_infi -> NNReal.le_iInf_add_iInf is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {ι' : Sort.{u2}} [_inst_1 : Nonempty.{u1} ι] [_inst_2 : Nonempty.{u2} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι' (fun (j : ι') => g j))))
-but is expected to have type
-  forall {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : Nonempty.{u1} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))))) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι' (fun (j : ι') => g j))))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_add_infi NNReal.le_iInf_add_iInfₓ'. -/
 theorem le_iInf_add_iInf {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
     {a : ℝ≥0} (h : ∀ i j, a ≤ f i + g j) : a ≤ (⨅ i, f i) + ⨅ j, g j :=
   by
@@ -886,54 +513,24 @@ theorem le_iInf_add_iInf {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι
 
 example : Archimedean ℝ≥0 := by infer_instance
 
-/- warning: nnreal.covariant_add -> NNReal.covariant_add is a dubious translation:
-lean 3 declaration is
-  CovariantClass.{0, 0} NNReal 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)))))) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
-but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4044 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4046 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4044 x._@.Mathlib.Data.Real.NNReal._hyg.4046) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4059 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4061 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4059 x._@.Mathlib.Data.Real.NNReal._hyg.4061)
-Case conversion may be inaccurate. Consider using '#align nnreal.covariant_add NNReal.covariant_addₓ'. -/
 -- TODO: why are these three instances necessary? why aren't they inferred?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
   OrderedAddCommMonoid.to_covariantClass_left ℝ≥0
 #align nnreal.covariant_add NNReal.covariant_add
 
-/- warning: nnreal.contravariant_add -> NNReal.contravariant_add is a dubious translation:
-lean 3 declaration is
-  ContravariantClass.{0, 0} NNReal 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)))))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
-but is expected to have type
-  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4084 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4086 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4084 x._@.Mathlib.Data.Real.NNReal._hyg.4086) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4099 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4101 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4099 x._@.Mathlib.Data.Real.NNReal._hyg.4101)
-Case conversion may be inaccurate. Consider using '#align nnreal.contravariant_add NNReal.contravariant_addₓ'. -/
 instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· < ·) :=
   OrderedCancelAddCommMonoid.to_contravariantClass_left ℝ≥0
 #align nnreal.contravariant_add NNReal.contravariant_add
 
-/- warning: nnreal.covariant_mul -> NNReal.covariant_mul is a dubious translation:
-lean 3 declaration is
-  CovariantClass.{0, 0} NNReal NNReal (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)))))) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
-but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4124 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4126 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4124 x._@.Mathlib.Data.Real.NNReal._hyg.4126) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4139 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4141 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4139 x._@.Mathlib.Data.Real.NNReal._hyg.4141)
-Case conversion may be inaccurate. Consider using '#align nnreal.covariant_mul NNReal.covariant_mulₓ'. -/
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
   OrderedCommMonoid.to_covariantClass_left ℝ≥0
 #align nnreal.covariant_mul NNReal.covariant_mul
 
-/- warning: nnreal.le_of_forall_pos_le_add -> NNReal.le_of_forall_pos_le_add is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal}, (forall (ε : 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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b ε))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b)
-but is expected to have type
-  forall {a : NNReal} {b : NNReal}, (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))))) b ε))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b)
-Case conversion may be inaccurate. Consider using '#align nnreal.le_of_forall_pos_le_add NNReal.le_of_forall_pos_le_addₓ'. -/
 -- Why isn't `nnreal.contravariant_add` inferred?
 theorem le_of_forall_pos_le_add {a b : ℝ≥0} (h : ∀ ε, 0 < ε → a ≤ b + ε) : a ≤ b :=
   @le_of_forall_pos_le_add _ _ _ _ _ _ NNReal.contravariant_add _ _ h
 #align nnreal.le_of_forall_pos_le_add NNReal.le_of_forall_pos_le_add
 
-/- warning: nnreal.lt_iff_exists_rat_btwn -> NNReal.lt_iff_exists_rat_btwn is a dubious translation:
-lean 3 declaration is
-  forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.hasLe (OfNat.ofNat.{0} Rat 0 (OfNat.mk.{0} Rat 0 (Zero.zero.{0} Rat Rat.hasZero))) q) (And (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q)) b))))
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-  forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.instLERat (OfNat.ofNat.{0} Rat 0 (Rat.instOfNatRat 0)) q) (And (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (Real.toNNReal (Rat.cast.{0} Real Real.ratCast q))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal (Rat.cast.{0} Real Real.ratCast q)) b))))
-Case conversion may be inaccurate. Consider using '#align nnreal.lt_iff_exists_rat_btwn NNReal.lt_iff_exists_rat_btwnₓ'. -/
 theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
     a < b ↔ ∃ q : ℚ, 0 ≤ q ∧ a < Real.toNNReal q ∧ Real.toNNReal q < b :=
   Iff.intro
@@ -945,96 +542,42 @@ theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
     fun ⟨q, _, haq, hqb⟩ => lt_trans haq hqb
 #align nnreal.lt_iff_exists_rat_btwn NNReal.lt_iff_exists_rat_btwn
 
-/- warning: nnreal.bot_eq_zero -> NNReal.bot_eq_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} NNReal (Bot.bot.{0} NNReal (ConditionallyCompleteLinearOrderBot.toHasBot.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
-but is expected to have type
-  Eq.{1} NNReal (Bot.bot.{0} NNReal (ConditionallyCompleteLinearOrderBot.toBot.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.bot_eq_zero NNReal.bot_eq_zeroₓ'. -/
 theorem bot_eq_zero : (⊥ : ℝ≥0) = 0 :=
   rfl
 #align nnreal.bot_eq_zero NNReal.bot_eq_zero
 
-/- warning: nnreal.mul_sup -> NNReal.mul_sup is a dubious translation:
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-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (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 (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) b c)) (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) (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) (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 c))
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-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) b c)) (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_sup NNReal.mul_supₓ'. -/
 theorem mul_sup (a b c : ℝ≥0) : a * (b ⊔ c) = a * b ⊔ a * c :=
   mul_max_of_nonneg _ _ <| zero_le a
 #align nnreal.mul_sup NNReal.mul_sup
 
-/- warning: nnreal.sup_mul -> NNReal.sup_mul is a dubious translation:
-lean 3 declaration is
-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (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))))) (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) a b) c) (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) (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 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))))) b c))
-but is expected to have type
-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) a b) c) (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c))
-Case conversion may be inaccurate. Consider using '#align nnreal.sup_mul NNReal.sup_mulₓ'. -/
 theorem sup_mul (a b c : ℝ≥0) : (a ⊔ b) * c = a * c ⊔ b * c :=
   max_mul_of_nonneg _ _ <| zero_le c
 #align nnreal.sup_mul NNReal.sup_mul
 
-/- warning: nnreal.mul_finset_sup -> NNReal.mul_finset_sup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (r : NNReal) (s : Finset.{u1} α) (f : α -> NNReal), Eq.{1} NNReal (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))))) r (Finset.sup.{0, u1} NNReal α NNReal.semilatticeSup NNReal.orderBot s f)) (Finset.sup.{0, u1} NNReal α NNReal.semilatticeSup NNReal.orderBot s (fun (a : α) => 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))))) r (f a)))
-but is expected to have type
-  forall {α : Type.{u1}} (r : NNReal) (s : Finset.{u1} α) (f : α -> NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r (Finset.sup.{0, u1} NNReal α instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring s f)) (Finset.sup.{0, u1} NNReal α instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring s (fun (a : α) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r (f a)))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_finset_sup NNReal.mul_finset_supₓ'. -/
 theorem mul_finset_sup {α} (r : ℝ≥0) (s : Finset α) (f : α → ℝ≥0) :
     r * s.sup f = s.sup fun a => r * f a :=
   Finset.comp_sup_eq_sup_comp _ (NNReal.mul_sup r) (MulZeroClass.mul_zero r)
 #align nnreal.mul_finset_sup NNReal.mul_finset_sup
 
-/- warning: nnreal.finset_sup_mul -> NNReal.finset_sup_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> NNReal) (r : NNReal), Eq.{1} NNReal (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))))) (Finset.sup.{0, u1} NNReal α NNReal.semilatticeSup NNReal.orderBot s f) r) (Finset.sup.{0, u1} NNReal α NNReal.semilatticeSup NNReal.orderBot s (fun (a : α) => 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 a) r))
-but is expected to have type
-  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> NNReal) (r : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (Finset.sup.{0, u1} NNReal α instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring s f) r) (Finset.sup.{0, u1} NNReal α instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring s (fun (a : α) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f a) r))
-Case conversion may be inaccurate. Consider using '#align nnreal.finset_sup_mul NNReal.finset_sup_mulₓ'. -/
 theorem finset_sup_mul {α} (s : Finset α) (f : α → ℝ≥0) (r : ℝ≥0) :
     s.sup f * r = s.sup fun a => f a * r :=
   Finset.comp_sup_eq_sup_comp (· * r) (fun x y => NNReal.sup_mul x y r) (MulZeroClass.zero_mul r)
 #align nnreal.finset_sup_mul NNReal.finset_sup_mul
 
-/- warning: nnreal.finset_sup_div -> NNReal.finset_sup_div is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : α -> NNReal} {s : Finset.{u1} α} (r : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (Finset.sup.{0, u1} NNReal α NNReal.semilatticeSup NNReal.orderBot s f) r) (Finset.sup.{0, u1} NNReal α NNReal.semilatticeSup NNReal.orderBot s (fun (a : α) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f a) r))
-but is expected to have type
-  forall {α : Type.{u1}} {f : α -> NNReal} {s : Finset.{u1} α} (r : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (Finset.sup.{0, u1} NNReal α instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring s f) r) (Finset.sup.{0, u1} NNReal α instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring s (fun (a : α) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f a) r))
-Case conversion may be inaccurate. Consider using '#align nnreal.finset_sup_div NNReal.finset_sup_divₓ'. -/
 theorem finset_sup_div {α} {f : α → ℝ≥0} {s : Finset α} (r : ℝ≥0) :
     s.sup f / r = s.sup fun a => f a / r := by simp only [div_eq_inv_mul, mul_finset_sup]
 #align nnreal.finset_sup_div NNReal.finset_sup_div
 
-/- warning: nnreal.coe_max -> NNReal.coe_max is a dubious translation:
-lean 3 declaration is
-  forall (x : NNReal) (y : NNReal), Eq.{1} Real ((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))) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) x y)) (LinearOrder.max.{0} Real Real.linearOrder ((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))) x) ((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))) y))
-but is expected to have type
-  forall (x : NNReal) (y : NNReal), Eq.{1} Real (NNReal.toReal (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x y)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (NNReal.toReal x) (NNReal.toReal y))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_max NNReal.coe_maxₓ'. -/
 @[simp, norm_cast]
 theorem coe_max (x y : ℝ≥0) : ((max x y : ℝ≥0) : ℝ) = max (x : ℝ) (y : ℝ) :=
   NNReal.coe_mono.map_max
 #align nnreal.coe_max NNReal.coe_max
 
-/- warning: nnreal.coe_min -> NNReal.coe_min is a dubious translation:
-lean 3 declaration is
-  forall (x : NNReal) (y : NNReal), Eq.{1} Real ((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))) (LinearOrder.min.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) x y)) (LinearOrder.min.{0} Real Real.linearOrder ((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))) x) ((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))) y))
-but is expected to have type
-  forall (x : NNReal) (y : NNReal), Eq.{1} Real (NNReal.toReal (Min.min.{0} NNReal (CanonicallyLinearOrderedSemifield.toMin.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x y)) (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (NNReal.toReal x) (NNReal.toReal y))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_min NNReal.coe_minₓ'. -/
 @[simp, norm_cast]
 theorem coe_min (x y : ℝ≥0) : ((min x y : ℝ≥0) : ℝ) = min (x : ℝ) (y : ℝ) :=
   NNReal.coe_mono.map_min
 #align nnreal.coe_min NNReal.coe_min
 
-/- warning: nnreal.zero_le_coe -> NNReal.zero_le_coe is a dubious translation:
-lean 3 declaration is
-  forall {q : NNReal}, LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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)
-but is expected to have type
-  forall {q : NNReal}, LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal q)
-Case conversion may be inaccurate. Consider using '#align nnreal.zero_le_coe NNReal.zero_le_coeₓ'. -/
 @[simp]
 theorem zero_le_coe {q : ℝ≥0} : 0 ≤ (q : ℝ) :=
   q.2
@@ -1046,215 +589,95 @@ namespace Real
 
 section ToNnreal
 
-/- warning: real.to_nnreal_zero -> Real.toNNReal_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} NNReal (Real.toNNReal (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
-but is expected to have type
-  Eq.{1} NNReal (Real.toNNReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_zero Real.toNNReal_zeroₓ'. -/
 @[simp]
 theorem toNNReal_zero : Real.toNNReal 0 = 0 := by simp [Real.toNNReal] <;> rfl
 #align real.to_nnreal_zero Real.toNNReal_zero
 
-/- warning: real.to_nnreal_one -> Real.toNNReal_one is a dubious translation:
-lean 3 declaration is
-  Eq.{1} NNReal (Real.toNNReal (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (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)))))))
-but is expected to have type
-  Eq.{1} NNReal (Real.toNNReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_one Real.toNNReal_oneₓ'. -/
 @[simp]
 theorem toNNReal_one : Real.toNNReal 1 = 1 := by
   simp [Real.toNNReal, max_eq_left (zero_le_one : (0 : ℝ) ≤ 1)] <;> rfl
 #align real.to_nnreal_one Real.toNNReal_one
 
-/- warning: real.to_nnreal_pos -> Real.toNNReal_pos is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, Iff (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (Real.toNNReal r)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)
-but is expected to have type
-  forall {r : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (Real.toNNReal r)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r)
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_pos Real.toNNReal_posₓ'. -/
 @[simp]
 theorem toNNReal_pos {r : ℝ} : 0 < Real.toNNReal r ↔ 0 < r := by
   simp [Real.toNNReal, nnreal.coe_lt_coe.symm, lt_irrefl]
 #align real.to_nnreal_pos Real.toNNReal_pos
 
-/- warning: real.to_nnreal_eq_zero -> Real.toNNReal_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, Iff (Eq.{1} NNReal (Real.toNNReal r) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {r : Real}, Iff (Eq.{1} NNReal (Real.toNNReal r) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_eq_zero Real.toNNReal_eq_zeroₓ'. -/
 @[simp]
 theorem toNNReal_eq_zero {r : ℝ} : Real.toNNReal r = 0 ↔ r ≤ 0 := by
   simpa [-to_nnreal_pos] using not_iff_not.2 (@to_nnreal_pos r)
 #align real.to_nnreal_eq_zero Real.toNNReal_eq_zero
 
-/- warning: real.to_nnreal_of_nonpos -> Real.toNNReal_of_nonpos is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, (LE.le.{0} Real Real.hasLe r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} NNReal (Real.toNNReal r) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
-but is expected to have type
-  forall {r : Real}, (LE.le.{0} Real Real.instLEReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} NNReal (Real.toNNReal r) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_of_nonpos Real.toNNReal_of_nonposₓ'. -/
 theorem toNNReal_of_nonpos {r : ℝ} : r ≤ 0 → Real.toNNReal r = 0 :=
   toNNReal_eq_zero.2
 #align real.to_nnreal_of_nonpos Real.toNNReal_of_nonpos
 
-/- warning: real.coe_to_nnreal' -> Real.coe_toNNReal' is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Real ((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))) (Real.toNNReal r)) (LinearOrder.max.{0} Real Real.linearOrder r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall (r : Real), Eq.{1} Real (NNReal.toReal (Real.toNNReal r)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align real.coe_to_nnreal' Real.coe_toNNReal'ₓ'. -/
 @[simp]
 theorem coe_toNNReal' (r : ℝ) : (Real.toNNReal r : ℝ) = max r 0 :=
   rfl
 #align real.coe_to_nnreal' Real.coe_toNNReal'
 
-/- warning: real.to_nnreal_le_to_nnreal_iff -> Real.toNNReal_le_toNNReal_iff is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe r p))
-but is expected to have type
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (LE.le.{0} Real Real.instLEReal r p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_le_to_nnreal_iff Real.toNNReal_le_toNNReal_iffₓ'. -/
 @[simp]
 theorem toNNReal_le_toNNReal_iff {r p : ℝ} (hp : 0 ≤ p) :
     Real.toNNReal r ≤ Real.toNNReal p ↔ r ≤ p := by simp [nnreal.coe_le_coe.symm, Real.toNNReal, hp]
 #align real.to_nnreal_le_to_nnreal_iff Real.toNNReal_le_toNNReal_iff
 
-/- warning: real.to_nnreal_eq_to_nnreal_iff -> Real.toNNReal_eq_toNNReal_iff is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (Eq.{1} NNReal (Real.toNNReal r) (Real.toNNReal p)) (Eq.{1} Real r p))
-but is expected to have type
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (Eq.{1} NNReal (Real.toNNReal r) (Real.toNNReal p)) (Eq.{1} Real r p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_eq_to_nnreal_iff Real.toNNReal_eq_toNNReal_iffₓ'. -/
 @[simp]
 theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal r = Real.toNNReal p ↔ r = p := by simp [← NNReal.coe_eq, coe_to_nnreal, hr, hp]
 #align real.to_nnreal_eq_to_nnreal_iff Real.toNNReal_eq_toNNReal_iff
 
-/- warning: real.to_nnreal_lt_to_nnreal_iff' -> Real.toNNReal_lt_toNNReal_iff' is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (And (LT.lt.{0} Real Real.hasLt r p) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p))
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-  forall {r : Real} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (And (LT.lt.{0} Real Real.instLTReal r p) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_to_nnreal_iff' Real.toNNReal_lt_toNNReal_iff'ₓ'. -/
 @[simp]
 theorem toNNReal_lt_toNNReal_iff' {r p : ℝ} : Real.toNNReal r < Real.toNNReal p ↔ r < p ∧ 0 < p :=
   NNReal.coe_lt_coe.symm.trans max_lt_max_left_iff
 #align real.to_nnreal_lt_to_nnreal_iff' Real.toNNReal_lt_toNNReal_iff'
 
-/- warning: real.to_nnreal_lt_to_nnreal_iff -> Real.toNNReal_lt_toNNReal_iff is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt r p))
-but is expected to have type
-  forall {r : Real} {p : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.instLTReal r p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_to_nnreal_iff Real.toNNReal_lt_toNNReal_iffₓ'. -/
 theorem toNNReal_lt_toNNReal_iff {r p : ℝ} (h : 0 < p) :
     Real.toNNReal r < Real.toNNReal p ↔ r < p :=
   toNNReal_lt_toNNReal_iff'.trans (and_iff_left h)
 #align real.to_nnreal_lt_to_nnreal_iff Real.toNNReal_lt_toNNReal_iff
 
-/- warning: real.to_nnreal_lt_to_nnreal_iff_of_nonneg -> Real.toNNReal_lt_toNNReal_iff_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt r p))
-but is expected to have type
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.instLTReal r p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_to_nnreal_iff_of_nonneg Real.toNNReal_lt_toNNReal_iff_of_nonnegₓ'. -/
 theorem toNNReal_lt_toNNReal_iff_of_nonneg {r p : ℝ} (hr : 0 ≤ r) :
     Real.toNNReal r < Real.toNNReal p ↔ r < p :=
   toNNReal_lt_toNNReal_iff'.trans ⟨And.left, fun h => ⟨h, lt_of_le_of_lt hr h⟩⟩
 #align real.to_nnreal_lt_to_nnreal_iff_of_nonneg Real.toNNReal_lt_toNNReal_iff_of_nonneg
 
-/- warning: real.to_nnreal_add -> Real.toNNReal_add is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Eq.{1} NNReal (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r 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))))) (Real.toNNReal r) (Real.toNNReal p)))
-but is expected to have type
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Eq.{1} NNReal (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r 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))))) (Real.toNNReal r) (Real.toNNReal p)))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_add Real.toNNReal_addₓ'. -/
 @[simp]
 theorem toNNReal_add {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal (r + p) = Real.toNNReal r + Real.toNNReal p :=
   NNReal.eq <| by simp [Real.toNNReal, hr, hp, add_nonneg]
 #align real.to_nnreal_add Real.toNNReal_add
 
-/- warning: real.to_nnreal_add_to_nnreal -> Real.toNNReal_add_toNNReal is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) 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))))) (Real.toNNReal r) (Real.toNNReal p)) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r p)))
-but is expected to have type
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) 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))))) (Real.toNNReal r) (Real.toNNReal p)) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r p)))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_add_to_nnreal Real.toNNReal_add_toNNRealₓ'. -/
 theorem toNNReal_add_toNNReal {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal r + Real.toNNReal p = Real.toNNReal (r + p) :=
   (Real.toNNReal_add hr hp).symm
 #align real.to_nnreal_add_to_nnreal Real.toNNReal_add_toNNReal
 
-/- warning: real.to_nnreal_le_to_nnreal -> Real.toNNReal_le_toNNReal is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe r p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p))
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-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal r p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_le_to_nnreal Real.toNNReal_le_toNNRealₓ'. -/
 theorem toNNReal_le_toNNReal {r p : ℝ} (h : r ≤ p) : Real.toNNReal r ≤ Real.toNNReal p :=
   Real.toNNReal_mono h
 #align real.to_nnreal_le_to_nnreal Real.toNNReal_le_toNNReal
 
-/- warning: real.to_nnreal_add_le -> Real.toNNReal_add_le is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r 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))))) (Real.toNNReal r) (Real.toNNReal p))
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-  forall {r : Real} {p : Real}, LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r 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))))) (Real.toNNReal r) (Real.toNNReal p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_add_le Real.toNNReal_add_leₓ'. -/
 theorem toNNReal_add_le {r p : ℝ} : Real.toNNReal (r + p) ≤ Real.toNNReal r + Real.toNNReal p :=
   NNReal.coe_le_coe.1 <| max_le (add_le_add (le_max_left _ _) (le_max_left _ _)) NNReal.zero_le_coe
 #align real.to_nnreal_add_le Real.toNNReal_add_le
 
-/- warning: real.to_nnreal_le_iff_le_coe -> Real.toNNReal_le_iff_le_coe is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) p) (LE.le.{0} Real Real.hasLe r ((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))
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-  forall {r : Real} {p : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) p) (LE.le.{0} Real Real.instLEReal r (NNReal.toReal p))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_le_iff_le_coe Real.toNNReal_le_iff_le_coeₓ'. -/
 theorem toNNReal_le_iff_le_coe {r : ℝ} {p : ℝ≥0} : Real.toNNReal r ≤ p ↔ r ≤ ↑p :=
   NNReal.gi.gc r p
 #align real.to_nnreal_le_iff_le_coe Real.toNNReal_le_iff_le_coe
 
-/- warning: real.le_to_nnreal_iff_coe_le -> Real.le_toNNReal_iff_coe_le is a dubious translation:
-lean 3 declaration is
-  forall {r : NNReal} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe ((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))) r) p))
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-  forall {r : NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Real.toNNReal p)) (LE.le.{0} Real Real.instLEReal (NNReal.toReal r) p))
-Case conversion may be inaccurate. Consider using '#align real.le_to_nnreal_iff_coe_le Real.le_toNNReal_iff_coe_leₓ'. -/
 theorem le_toNNReal_iff_coe_le {r : ℝ≥0} {p : ℝ} (hp : 0 ≤ p) : r ≤ Real.toNNReal p ↔ ↑r ≤ p := by
   rw [← NNReal.coe_le_coe, Real.coe_toNNReal p hp]
 #align real.le_to_nnreal_iff_coe_le Real.le_toNNReal_iff_coe_le
 
-/- warning: real.le_to_nnreal_iff_coe_le' -> Real.le_toNNReal_iff_coe_le' is a dubious translation:
-lean 3 declaration is
-  forall {r : NNReal} {p : Real}, (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe ((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))) r) p))
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-  forall {r : NNReal} {p : Real}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Real.toNNReal p)) (LE.le.{0} Real Real.instLEReal (NNReal.toReal r) p))
-Case conversion may be inaccurate. Consider using '#align real.le_to_nnreal_iff_coe_le' Real.le_toNNReal_iff_coe_le'ₓ'. -/
 theorem le_toNNReal_iff_coe_le' {r : ℝ≥0} {p : ℝ} (hr : 0 < r) : r ≤ Real.toNNReal p ↔ ↑r ≤ p :=
   (le_or_lt 0 p).elim le_toNNReal_iff_coe_le fun hp => by
     simp only [(hp.trans_le r.coe_nonneg).not_le, to_nnreal_eq_zero.2 hp.le, hr.not_le]
 #align real.le_to_nnreal_iff_coe_le' Real.le_toNNReal_iff_coe_le'
 
-/- warning: real.to_nnreal_lt_iff_lt_coe -> Real.toNNReal_lt_iff_lt_coe is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : NNReal}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) p) (LT.lt.{0} Real Real.hasLt r ((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)))
-but is expected to have type
-  forall {r : Real} {p : NNReal}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) p) (LT.lt.{0} Real Real.instLTReal r (NNReal.toReal p)))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_iff_lt_coe Real.toNNReal_lt_iff_lt_coeₓ'. -/
 theorem toNNReal_lt_iff_lt_coe {r : ℝ} {p : ℝ≥0} (ha : 0 ≤ r) : Real.toNNReal r < p ↔ r < ↑p := by
   rw [← NNReal.coe_lt_coe, Real.coe_toNNReal r ha]
 #align real.to_nnreal_lt_iff_lt_coe Real.toNNReal_lt_iff_lt_coe
 
-/- warning: real.lt_to_nnreal_iff_coe_lt -> Real.lt_toNNReal_iff_coe_lt is a dubious translation:
-lean 3 declaration is
-  forall {r : NNReal} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt ((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))) r) p)
-but is expected to have type
-  forall {r : NNReal} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Real.toNNReal p)) (LT.lt.{0} Real Real.instLTReal (NNReal.toReal r) p)
-Case conversion may be inaccurate. Consider using '#align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_ltₓ'. -/
 theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔ ↑r < p :=
   by
   cases le_total 0 p
@@ -1266,11 +689,6 @@ theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔
 #align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_lt
 
 /- warning: real.to_nnreal_bit0 clashes with [anonymous] -> [anonymous]
-warning: real.to_nnreal_bit0 -> [anonymous] is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} NNReal (Real.toNNReal (bit0.{0} Real Real.hasAdd r)) (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (Real.toNNReal r))
-but is expected to have type
-  forall {r : Type.{u}} {β : Type.{v}}, (Nat -> r -> β) -> Nat -> (List.{u} r) -> (List.{v} β)
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_bit0 [anonymous]ₓ'. -/
 @[simp]
 theorem [anonymous] (r : ℝ) : Real.toNNReal (bit0 r) = bit0 (Real.toNNReal r) :=
@@ -1282,23 +700,12 @@ theorem [anonymous] (r : ℝ) : Real.toNNReal (bit0 r) = bit0 (Real.toNNReal r)
 #align real.to_nnreal_bit0 [anonymous]
 
 /- warning: real.to_nnreal_bit1 clashes with [anonymous] -> [anonymous]
-warning: real.to_nnreal_bit1 -> [anonymous] is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} NNReal (Real.toNNReal (bit1.{0} Real Real.hasOne Real.hasAdd r)) (bit1.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (Real.toNNReal r)))
-but is expected to have type
-  forall {r : Type.{u}} {hr : Type.{v}}, (Nat -> r -> hr) -> Nat -> (List.{u} r) -> (List.{v} hr)
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_bit1 [anonymous]ₓ'. -/
 @[simp]
 theorem [anonymous] {r : ℝ} (hr : 0 ≤ r) : Real.toNNReal (bit1 r) = bit1 (Real.toNNReal r) :=
   (Real.toNNReal_add (by simp [hr]) zero_le_one).trans (by simp [bit1])
 #align real.to_nnreal_bit1 [anonymous]
 
-/- warning: real.to_nnreal_pow -> Real.toNNReal_pow is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (forall (n : Nat), Eq.{1} NNReal (Real.toNNReal (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x n)) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (Real.toNNReal x) n))
-but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (forall (n : Nat), Eq.{1} NNReal (Real.toNNReal (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x n)) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (Real.toNNReal x) n))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_pow Real.toNNReal_powₓ'. -/
 theorem toNNReal_pow {x : ℝ} (hx : 0 ≤ x) (n : ℕ) : (x ^ n).toNNReal = x.toNNReal ^ n := by
   rw [← NNReal.coe_eq, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),
     Real.coe_toNNReal x hx]
@@ -1314,22 +721,10 @@ namespace NNReal
 
 section Mul
 
-/- warning: nnreal.mul_eq_mul_left -> NNReal.mul_eq_mul_left is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (Ne.{1} NNReal a (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (Eq.{1} NNReal (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) (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 c)) (Eq.{1} NNReal b c))
-but is expected to have type
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (Ne.{1} NNReal a (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c)) (Eq.{1} NNReal b c))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_eq_mul_left NNReal.mul_eq_mul_leftₓ'. -/
 theorem mul_eq_mul_left {a b c : ℝ≥0} (h : a ≠ 0) : a * b = a * c ↔ b = c := by
   rw [mul_eq_mul_left_iff, or_iff_left h]
 #align nnreal.mul_eq_mul_left NNReal.mul_eq_mul_left
 
-/- warning: real.to_nnreal_mul -> Real.toNNReal_mul is a dubious translation:
-lean 3 declaration is
-  forall {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))) p) -> (Eq.{1} NNReal (Real.toNNReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p q)) (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))))) (Real.toNNReal p) (Real.toNNReal q)))
-but is expected to have type
-  forall {p : Real} {q : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Eq.{1} NNReal (Real.toNNReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p q)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (Real.toNNReal p) (Real.toNNReal q)))
-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_mul Real.toNNReal_mulₓ'. -/
 theorem Real.toNNReal_mul {p q : ℝ} (hp : 0 ≤ p) :
     Real.toNNReal (p * q) = Real.toNNReal p * Real.toNNReal q :=
   by
@@ -1344,33 +739,15 @@ end Mul
 
 section Pow
 
-/- warning: nnreal.pow_antitone_exp -> NNReal.pow_antitone_exp is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} (m : Nat) (n : Nat), (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) a n) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) a m))
-but is expected to have type
-  forall {a : NNReal} (m : Nat) (n : Nat), (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) a n) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) a m))
-Case conversion may be inaccurate. Consider using '#align nnreal.pow_antitone_exp NNReal.pow_antitone_expₓ'. -/
 theorem pow_antitone_exp {a : ℝ≥0} (m n : ℕ) (mn : m ≤ n) (a1 : a ≤ 1) : a ^ n ≤ a ^ m :=
   pow_le_pow_of_le_one (zero_le a) a1 mn
 #align nnreal.pow_antitone_exp NNReal.pow_antitone_exp
 
-/- warning: nnreal.exists_pow_lt_of_lt_one -> NNReal.exists_pow_lt_of_lt_one is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : 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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) a) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) b (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)))))))) -> (Exists.{1} Nat (fun (n : Nat) => LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) b n) a))
-but is expected to have type
-  forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) a) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) b (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Exists.{1} Nat (fun (n : Nat) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) b n) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.exists_pow_lt_of_lt_one NNReal.exists_pow_lt_of_lt_oneₓ'. -/
 theorem exists_pow_lt_of_lt_one {a b : ℝ≥0} (ha : 0 < a) (hb : b < 1) : ∃ n : ℕ, b ^ n < a := by
   simpa only [← coe_pow, NNReal.coe_lt_coe] using
     exists_pow_lt_of_lt_one (NNReal.coe_pos.2 ha) (NNReal.coe_lt_coe.2 hb)
 #align nnreal.exists_pow_lt_of_lt_one NNReal.exists_pow_lt_of_lt_one
 
-/- warning: nnreal.exists_mem_Ico_zpow -> NNReal.exists_mem_Ico_zpow is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (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))))))) y) -> (Exists.{1} Int (fun (n : Int) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Ico.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
-but is expected to have type
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (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)) y) -> (Exists.{1} Int (fun (n : Int) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Ico.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
-Case conversion may be inaccurate. Consider using '#align nnreal.exists_mem_Ico_zpow NNReal.exists_mem_Ico_zpowₓ'. -/
 theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 < y) :
     ∃ n : ℤ, x ∈ Set.Ico (y ^ n) (y ^ (n + 1)) :=
   by
@@ -1380,12 +757,6 @@ theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
   exact ⟨n, hn, h'n⟩
 #align nnreal.exists_mem_Ico_zpow NNReal.exists_mem_Ico_zpow
 
-/- warning: nnreal.exists_mem_Ioc_zpow -> NNReal.exists_mem_Ioc_zpow is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.exists_mem_Ioc_zpow NNReal.exists_mem_Ioc_zpowₓ'. -/
 theorem exists_mem_Ioc_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 < y) :
     ∃ n : ℤ, x ∈ Set.Ioc (y ^ n) (y ^ (n + 1)) :=
   by
@@ -1407,34 +778,16 @@ typeclass. For lemmas about subtraction and addition see lemmas
 about `has_ordered_sub` in the file `algebra.order.sub`. See also `mul_tsub` and `tsub_mul`. -/
 
 
-/- warning: nnreal.sub_def -> NNReal.sub_def is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.sub_def NNReal.sub_defₓ'. -/
 theorem sub_def {r p : ℝ≥0} : r - p = Real.toNNReal (r - p) :=
   rfl
 #align nnreal.sub_def NNReal.sub_def
 
-/- warning: nnreal.coe_sub_def -> NNReal.coe_sub_def is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.coe_sub_def NNReal.coe_sub_defₓ'. -/
 theorem coe_sub_def {r p : ℝ≥0} : ↑(r - p) = max (r - p : ℝ) 0 :=
   rfl
 #align nnreal.coe_sub_def NNReal.coe_sub_def
 
 example : OrderedSub ℝ≥0 := by infer_instance
 
-/- warning: nnreal.sub_div -> NNReal.sub_div is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.sub_div NNReal.sub_divₓ'. -/
 theorem sub_div (a b c : ℝ≥0) : (a - b) / c = a / c - b / c :=
   tsub_div _ _ _
 #align nnreal.sub_div NNReal.sub_div
@@ -1443,188 +796,80 @@ end Sub
 
 section Inv
 
-/- warning: nnreal.sum_div -> NNReal.sum_div is a dubious translation:
-lean 3 declaration is
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-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) b))
-Case conversion may be inaccurate. Consider using '#align nnreal.sum_div NNReal.sum_divₓ'. -/
 theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
     (∑ i in s, f i) / b = ∑ i in s, f i / b :=
   Finset.sum_div
 #align nnreal.sum_div NNReal.sum_div
 
-/- warning: nnreal.inv_le -> NNReal.inv_le is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.inv_le NNReal.inv_leₓ'. -/
 @[simp]
 theorem inv_le {r p : ℝ≥0} (h : r ≠ 0) : r⁻¹ ≤ p ↔ 1 ≤ r * p := by
   rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h]
 #align nnreal.inv_le NNReal.inv_le
 
-/- warning: nnreal.inv_le_of_le_mul -> NNReal.inv_le_of_le_mul is a dubious translation:
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-  forall {r : NNReal} {p : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{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))))))) (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))))) r p)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) p)
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-Case conversion may be inaccurate. Consider using '#align nnreal.inv_le_of_le_mul NNReal.inv_le_of_le_mulₓ'. -/
 theorem inv_le_of_le_mul {r p : ℝ≥0} (h : 1 ≤ r * p) : r⁻¹ ≤ p := by
   by_cases r = 0 <;> simp [*, inv_le]
 #align nnreal.inv_le_of_le_mul NNReal.inv_le_of_le_mul
 
-/- warning: nnreal.le_inv_iff_mul_le -> NNReal.le_inv_iff_mul_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.le_inv_iff_mul_le NNReal.le_inv_iff_mul_leₓ'. -/
 @[simp]
 theorem le_inv_iff_mul_le {r p : ℝ≥0} (h : p ≠ 0) : r ≤ p⁻¹ ↔ r * p ≤ 1 := by
   rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h, mul_comm]
 #align nnreal.le_inv_iff_mul_le NNReal.le_inv_iff_mul_le
 
-/- warning: nnreal.lt_inv_iff_mul_lt -> NNReal.lt_inv_iff_mul_lt is a dubious translation:
-lean 3 declaration is
-  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) p)) (LT.lt.{0} NNReal (Preorder.toHasLt.{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))))) r p) (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)))))))))
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-  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) p)) (LT.lt.{0} NNReal (Preorder.toLT.{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)) r p) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))))
-Case conversion may be inaccurate. Consider using '#align nnreal.lt_inv_iff_mul_lt NNReal.lt_inv_iff_mul_ltₓ'. -/
 @[simp]
 theorem lt_inv_iff_mul_lt {r p : ℝ≥0} (h : p ≠ 0) : r < p⁻¹ ↔ r * p < 1 := by
   rw [← mul_lt_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h, mul_comm]
 #align nnreal.lt_inv_iff_mul_lt NNReal.lt_inv_iff_mul_lt
 
-/- warning: nnreal.mul_le_iff_le_inv -> NNReal.mul_le_iff_le_inv is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (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))))) r a) b) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) b)))
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (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)) r a) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) r) b)))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_le_iff_le_inv NNReal.mul_le_iff_le_invₓ'. -/
 theorem mul_le_iff_le_inv {a b r : ℝ≥0} (hr : r ≠ 0) : r * a ≤ b ↔ a ≤ r⁻¹ * b :=
   by
   have : 0 < r := lt_of_le_of_ne (zero_le r) hr.symm
   rw [← mul_le_mul_left (inv_pos.mpr this), ← mul_assoc, inv_mul_cancel hr, one_mul]
 #align nnreal.mul_le_iff_le_inv NNReal.mul_le_iff_le_inv
 
-/- warning: nnreal.le_div_iff_mul_le -> NNReal.le_div_iff_mul_le is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (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 r) b))
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (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 r) b))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_div_iff_mul_le NNReal.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ a * r ≤ b :=
   le_div_iff₀ hr
 #align nnreal.le_div_iff_mul_le NNReal.le_div_iff_mul_le
 
-/- warning: nnreal.div_le_iff -> NNReal.div_le_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b r)))
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a r) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b r)))
-Case conversion may be inaccurate. Consider using '#align nnreal.div_le_iff NNReal.div_le_iffₓ'. -/
 theorem div_le_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a / r ≤ b ↔ a ≤ b * r :=
   div_le_iff₀ hr
 #align nnreal.div_le_iff NNReal.div_le_iff
 
-/- warning: nnreal.div_le_iff' -> NNReal.div_le_iff' is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) r b)))
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a r) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r b)))
-Case conversion may be inaccurate. Consider using '#align nnreal.div_le_iff' NNReal.div_le_iff'ₓ'. -/
 theorem div_le_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a / r ≤ b ↔ a ≤ r * b :=
   @div_le_iff' ℝ _ a r b <| pos_iff_ne_zero.2 hr
 #align nnreal.div_le_iff' NNReal.div_le_iff'
 
-/- warning: nnreal.div_le_of_le_mul -> NNReal.div_le_of_le_mul is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b c)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a c) b)
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-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a c) b)
-Case conversion may be inaccurate. Consider using '#align nnreal.div_le_of_le_mul NNReal.div_le_of_le_mulₓ'. -/
 theorem div_le_of_le_mul {a b c : ℝ≥0} (h : a ≤ b * c) : a / c ≤ b :=
   if h0 : c = 0 then by simp [h0] else (div_le_iff h0).2 h
 #align nnreal.div_le_of_le_mul NNReal.div_le_of_le_mul
 
-/- warning: nnreal.div_le_of_le_mul' -> NNReal.div_le_of_le_mul' is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b c)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) c)
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-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a b) c)
-Case conversion may be inaccurate. Consider using '#align nnreal.div_le_of_le_mul' NNReal.div_le_of_le_mul'ₓ'. -/
 theorem div_le_of_le_mul' {a b c : ℝ≥0} (h : a ≤ b * c) : a / b ≤ c :=
   div_le_of_le_mul <| mul_comm b c ▸ h
 #align nnreal.div_le_of_le_mul' NNReal.div_le_of_le_mul'
 
-/- warning: nnreal.le_div_iff -> NNReal.le_div_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (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 r) b))
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (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 r) b))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_div_iff NNReal.le_div_iffₓ'. -/
 theorem le_div_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ a * r ≤ b :=
   @le_div_iff ℝ _ a b r <| pos_iff_ne_zero.2 hr
 #align nnreal.le_div_iff NNReal.le_div_iff
 
-/- warning: nnreal.le_div_iff' -> NNReal.le_div_iff' is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.le_div_iff' NNReal.le_div_iff'ₓ'. -/
 theorem le_div_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ r * a ≤ b :=
   @le_div_iff' ℝ _ a b r <| pos_iff_ne_zero.2 hr
 #align nnreal.le_div_iff' NNReal.le_div_iff'
 
-/- warning: nnreal.div_lt_iff -> NNReal.div_lt_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.div_lt_iff NNReal.div_lt_iffₓ'. -/
 theorem div_lt_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a / r < b ↔ a < b * r :=
   lt_iff_lt_of_le_iff_le (le_div_iff hr)
 #align nnreal.div_lt_iff NNReal.div_lt_iff
 
-/- warning: nnreal.div_lt_iff' -> NNReal.div_lt_iff' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.div_lt_iff' NNReal.div_lt_iff'ₓ'. -/
 theorem div_lt_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a / r < b ↔ a < r * b :=
   lt_iff_lt_of_le_iff_le (le_div_iff' hr)
 #align nnreal.div_lt_iff' NNReal.div_lt_iff'
 
-/- warning: nnreal.lt_div_iff -> NNReal.lt_div_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.lt_div_iff NNReal.lt_div_iffₓ'. -/
 theorem lt_div_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a < b / r ↔ a * r < b :=
   lt_iff_lt_of_le_iff_le (div_le_iff hr)
 #align nnreal.lt_div_iff NNReal.lt_div_iff
 
-/- warning: nnreal.lt_div_iff' -> NNReal.lt_div_iff' is a dubious translation:
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (LT.lt.{0} NNReal (Preorder.toLT.{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)) r a) b))
-Case conversion may be inaccurate. Consider using '#align nnreal.lt_div_iff' NNReal.lt_div_iff'ₓ'. -/
 theorem lt_div_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a < b / r ↔ r * a < b :=
   lt_iff_lt_of_le_iff_le (div_le_iff' hr)
 #align nnreal.lt_div_iff' NNReal.lt_div_iff'
 
-/- warning: nnreal.mul_lt_of_lt_div -> NNReal.mul_lt_of_lt_div is a dubious translation:
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-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) -> (LT.lt.{0} NNReal (Preorder.toLT.{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 r) b)
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_lt_of_lt_div NNReal.mul_lt_of_lt_divₓ'. -/
 theorem mul_lt_of_lt_div {a b r : ℝ≥0} (h : a < b / r) : a * r < b :=
   by
   refine' (lt_div_iff fun hr => False.elim _).1 h
@@ -1641,23 +886,11 @@ theorem div_le_div_left_of_le {a b c : ℝ≥0} (b0 : 0 < b) (c0 : 0 < c) (cb :
     exact (div_le_div_left a0 b0 c0).mpr cb
 #align nnreal.div_le_div_left_of_le NNReal.div_le_div_left_of_leₓ
 
-/- warning: nnreal.div_le_div_left -> NNReal.div_le_div_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.div_le_div_left NNReal.div_le_div_leftₓ'. -/
 theorem div_le_div_left {a b c : ℝ≥0} (a0 : 0 < a) (b0 : 0 < b) (c0 : 0 < c) :
     a / b ≤ a / c ↔ c ≤ b :=
   div_le_div_left a0 b0 c0
 #align nnreal.div_le_div_left NNReal.div_le_div_left
 
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-Case conversion may be inaccurate. Consider using '#align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_leₓ'. -/
 theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y) : x ≤ y :=
   le_of_forall_ge_of_dense fun a ha =>
     by
@@ -1668,44 +901,20 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
     rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this
 #align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_le
 
-/- warning: nnreal.half_le_self -> NNReal.half_le_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.half_le_self NNReal.half_le_selfₓ'. -/
 theorem half_le_self (a : ℝ≥0) : a / 2 ≤ a :=
   half_le_self bot_le
 #align nnreal.half_le_self NNReal.half_le_self
 
-/- warning: nnreal.half_lt_self -> NNReal.half_lt_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.half_lt_self NNReal.half_lt_selfₓ'. -/
 theorem half_lt_self {a : ℝ≥0} (h : a ≠ 0) : a / 2 < a :=
   half_lt_self h.bot_lt
 #align nnreal.half_lt_self NNReal.half_lt_self
 
-/- warning: nnreal.div_lt_one_of_lt -> NNReal.div_lt_one_of_lt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_ltₓ'. -/
 theorem div_lt_one_of_lt {a b : ℝ≥0} (h : a < b) : a / b < 1 :=
   by
   rwa [div_lt_iff, one_mul]
   exact ne_of_gt (lt_of_le_of_lt (zero_le _) h)
 #align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_lt
 
-/- warning: real.to_nnreal_inv -> Real.toNNReal_inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Eq.{1} NNReal (Real.toNNReal (Inv.inv.{0} Real Real.hasInv x)) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (Real.toNNReal x))
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-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_inv Real.toNNReal_invₓ'. -/
 theorem Real.toNNReal_inv {x : ℝ} : Real.toNNReal x⁻¹ = (Real.toNNReal x)⁻¹ :=
   by
   by_cases hx : 0 ≤ x
@@ -1715,44 +924,20 @@ theorem Real.toNNReal_inv {x : ℝ} : Real.toNNReal x⁻¹ = (Real.toNNReal x)
     rw [to_nnreal_eq_zero.mpr hx', inv_zero, to_nnreal_eq_zero.mpr (inv_nonpos.mpr hx')]
 #align real.to_nnreal_inv Real.toNNReal_inv
 
-/- warning: real.to_nnreal_div -> Real.toNNReal_div is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_div Real.toNNReal_divₓ'. -/
 theorem Real.toNNReal_div {x y : ℝ} (hx : 0 ≤ x) :
     Real.toNNReal (x / y) = Real.toNNReal x / Real.toNNReal y := by
   rw [div_eq_mul_inv, div_eq_mul_inv, ← Real.toNNReal_inv, ← Real.toNNReal_mul hx]
 #align real.to_nnreal_div Real.toNNReal_div
 
-/- warning: real.to_nnreal_div' -> Real.toNNReal_div' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align real.to_nnreal_div' Real.toNNReal_div'ₓ'. -/
 theorem Real.toNNReal_div' {x y : ℝ} (hy : 0 ≤ y) :
     Real.toNNReal (x / y) = Real.toNNReal x / Real.toNNReal y := by
   rw [div_eq_inv_mul, div_eq_inv_mul, Real.toNNReal_mul (inv_nonneg.2 hy), Real.toNNReal_inv]
 #align real.to_nnreal_div' Real.toNNReal_div'
 
-/- warning: nnreal.inv_lt_one_iff -> NNReal.inv_lt_one_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_one_iff NNReal.inv_lt_one_iffₓ'. -/
 theorem inv_lt_one_iff {x : ℝ≥0} (hx : x ≠ 0) : x⁻¹ < 1 ↔ 1 < x := by
   rwa [← one_div, div_lt_iff hx, one_mul]
 #align nnreal.inv_lt_one_iff NNReal.inv_lt_one_iff
 
-/- warning: nnreal.zpow_pos -> NNReal.zpow_pos is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.zpow_pos NNReal.zpow_posₓ'. -/
 theorem zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
   by
   cases n
@@ -1760,24 +945,12 @@ theorem zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
   · simp [pow_pos hx.bot_lt _]
 #align nnreal.zpow_pos NNReal.zpow_pos
 
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-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x y) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) y) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x))
-Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_inv NNReal.inv_lt_invₓ'. -/
 theorem inv_lt_inv {x y : ℝ≥0} (hx : x ≠ 0) (h : x < y) : y⁻¹ < x⁻¹ :=
   inv_lt_inv_of_lt hx.bot_lt h
 #align nnreal.inv_lt_inv NNReal.inv_lt_inv
 
 end Inv
 
-/- warning: nnreal.abs_eq -> NNReal.abs_eq is a dubious translation:
-lean 3 declaration is
-  forall (x : NNReal), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((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))) x)) ((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))) x)
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-  forall (x : NNReal), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (NNReal.toReal x)) (NNReal.toReal x)
-Case conversion may be inaccurate. Consider using '#align nnreal.abs_eq NNReal.abs_eqₓ'. -/
 @[simp]
 theorem abs_eq (x : ℝ≥0) : |(x : ℝ)| = x :=
   abs_of_nonneg x.property
@@ -1789,22 +962,10 @@ open Set
 
 variable {ι : Sort _} {f : ι → ℝ≥0}
 
-/- warning: nnreal.le_to_nnreal_of_coe_le -> NNReal.le_toNNReal_of_coe_le is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal} {y : Real}, (LE.le.{0} Real Real.hasLe ((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))) x) y) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x (Real.toNNReal y))
-but is expected to have type
-  forall {x : NNReal} {y : Real}, (LE.le.{0} Real Real.instLEReal (NNReal.toReal x) y) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x (Real.toNNReal y))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_to_nnreal_of_coe_le NNReal.le_toNNReal_of_coe_leₓ'. -/
 theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y.toNNReal :=
   (le_toNNReal_iff_coe_le <| x.2.trans h).2 h
 #align nnreal.le_to_nnreal_of_coe_le NNReal.le_toNNReal_of_coe_le
 
-/- warning: nnreal.Sup_of_not_bdd_above -> NNReal.sSup_of_not_bddAbove is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAboveₓ'. -/
 theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 :=
   by
   rw [← bdd_above_coe] at hs
@@ -1812,150 +973,66 @@ theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup
   exact Sup_of_not_bdd_above hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
 
-/- warning: nnreal.supr_of_not_bdd_above -> NNReal.iSup_of_not_bddAbove is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {ι : Sort.{u1}} {f : ι -> NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (Set.range.{0, u1} NNReal ι f))) -> (Eq.{1} NNReal (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAboveₓ'. -/
 theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
   sSup_of_not_bddAbove hf
 #align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAbove
 
-/- warning: nnreal.infi_empty -> NNReal.iInf_empty is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
-but is expected to have type
-  forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.infi_empty NNReal.iInf_emptyₓ'. -/
 theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw [← NNReal.coe_eq, coe_infi];
   exact Real.ciInf_empty _
 #align nnreal.infi_empty NNReal.iInf_empty
 
-/- warning: nnreal.infi_const_zero -> NNReal.iInf_const_zero is a dubious translation:
-lean 3 declaration is
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-  forall {α : Sort.{u1}}, Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) α (fun (i : α) => OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.infi_const_zero NNReal.iInf_const_zeroₓ'. -/
 @[simp]
 theorem iInf_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 := by
   rw [← NNReal.coe_eq, coe_infi]; exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero
 
-/- warning: nnreal.infi_mul -> NNReal.iInf_mul is a dubious translation:
-lean 3 declaration is
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-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι f) a) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.infi_mul NNReal.iInf_mulₓ'. -/
 theorem iInf_mul (f : ι → ℝ≥0) (a : ℝ≥0) : iInf f * a = ⨅ i, f i * a :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_mul, coe_infi, coe_infi]
   exact Real.iInf_mul_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.infi_mul NNReal.iInf_mul
 
-/- warning: nnreal.mul_infi -> NNReal.mul_iInf is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nnreal.mul_infi NNReal.mul_iInfₓ'. -/
 theorem mul_iInf (f : ι → ℝ≥0) (a : ℝ≥0) : a * iInf f = ⨅ i, a * f i := by
   simpa only [mul_comm] using infi_mul f a
 #align nnreal.mul_infi NNReal.mul_iInf
 
-/- warning: nnreal.mul_supr -> NNReal.mul_iSup is a dubious translation:
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-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (f i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr NNReal.mul_iSupₓ'. -/
 theorem mul_iSup (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
   exact Real.mul_iSup_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.mul_supr NNReal.mul_iSup
 
-/- warning: nnreal.supr_mul -> NNReal.iSup_mul is a dubious translation:
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-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul NNReal.iSup_mulₓ'. -/
 theorem iSup_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a := by
   rw [mul_comm, mul_supr]; simp_rw [mul_comm]
 #align nnreal.supr_mul NNReal.iSup_mul
 
-/- warning: nnreal.supr_div -> NNReal.iSup_div is a dubious translation:
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-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f i) a))
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-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_div NNReal.iSup_divₓ'. -/
 theorem iSup_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i, f i / a := by
   simp only [div_eq_mul_inv, supr_mul]
 #align nnreal.supr_div NNReal.iSup_div
 
 variable [Nonempty ι]
 
-/- warning: nnreal.le_mul_infi -> NNReal.le_mul_iInf is a dubious translation:
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-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_mul_infi NNReal.le_mul_iInfₓ'. -/
 theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * iInf h := by
   rw [mul_infi]; exact le_ciInf H
 #align nnreal.le_mul_infi NNReal.le_mul_iInf
 
-/- warning: nnreal.mul_supr_le -> NNReal.mul_iSup_le is a dubious translation:
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-  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι), 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 (g ᾰ)) _inst_1) -> (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 (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr_le NNReal.mul_iSup_leₓ'. -/
 theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a := by
   rw [mul_supr]; exact ciSup_le H
 #align nnreal.mul_supr_le NNReal.mul_iSup_le
 
-/- warning: nnreal.le_infi_mul -> NNReal.le_iInf_mul is a dubious translation:
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-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) h))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul NNReal.le_iInf_mulₓ'. -/
 theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ iInf g * h := by
   rw [infi_mul]; exact le_ciInf H
 #align nnreal.le_infi_mul NNReal.le_iInf_mul
 
-/- warning: nnreal.supr_mul_le -> NNReal.iSup_mul_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_le NNReal.iSup_mul_leₓ'. -/
 theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a := by
   rw [supr_mul]; exact ciSup_le H
 #align nnreal.supr_mul_le NNReal.iSup_mul_le
 
-/- warning: nnreal.le_infi_mul_infi -> NNReal.le_iInf_mul_iInf is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
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-Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInfₓ'. -/
 theorem le_iInf_mul_iInf {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a ≤ g i * h j) :
     a ≤ iInf g * iInf h :=
   le_iInf_mul fun i => le_mul_iInf <| H i
 #align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInf
 
-/- warning: nnreal.supr_mul_supr_le -> NNReal.iSup_mul_iSup_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), 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))))) (g i) (h j)) a) -> (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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
-but is expected to have type
-  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι) (j : ι), 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 ᾰ) (g j)) _inst_1) -> (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)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_supr_le NNReal.iSup_mul_iSup_leₓ'. -/
 theorem iSup_mul_iSup_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
     iSup g * iSup h ≤ a :=
   iSup_mul_le fun i => mul_iSup_le <| H _
@@ -1971,22 +1048,10 @@ namespace OrdConnected
 
 variable {s : Set ℝ} {t : Set ℝ≥0}
 
-/- warning: set.ord_connected.preimage_coe_nnreal_real -> Set.OrdConnected.preimage_coe_nnreal_real is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Real}, (Set.OrdConnected.{0} Real Real.preorder s) -> (Set.OrdConnected.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (Set.preimage.{0, 0} NNReal Real ((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)))) s))
-but is expected to have type
-  forall {s : Set.{0} Real}, (Set.OrdConnected.{0} Real Real.instPreorderReal s) -> (Set.OrdConnected.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (Set.preimage.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align set.ord_connected.preimage_coe_nnreal_real Set.OrdConnected.preimage_coe_nnreal_realₓ'. -/
 theorem preimage_coe_nnreal_real (h : s.OrdConnected) : (coe ⁻¹' s : Set ℝ≥0).OrdConnected :=
   h.preimage_mono NNReal.coe_mono
 #align set.ord_connected.preimage_coe_nnreal_real Set.OrdConnected.preimage_coe_nnreal_real
 
-/- warning: set.ord_connected.image_coe_nnreal_real -> Set.OrdConnected.image_coe_nnreal_real is a dubious translation:
-lean 3 declaration is
-  forall {t : Set.{0} NNReal}, (Set.OrdConnected.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) t) -> (Set.OrdConnected.{0} Real Real.preorder (Set.image.{0, 0} NNReal Real ((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)))) t))
-but is expected to have type
-  forall {t : Set.{0} NNReal}, (Set.OrdConnected.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) t) -> (Set.OrdConnected.{0} Real Real.instPreorderReal (Set.image.{0, 0} NNReal Real NNReal.toReal t))
-Case conversion may be inaccurate. Consider using '#align set.ord_connected.image_coe_nnreal_real Set.OrdConnected.image_coe_nnreal_realₓ'. -/
 theorem image_coe_nnreal_real (h : t.OrdConnected) : (coe '' t : Set ℝ).OrdConnected :=
   ⟨ball_image_iff.2 fun x hx =>
       ball_image_iff.2 fun y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
@@ -2028,53 +1093,23 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 #align real.nnabs Real.nnabs
 -/
 
-/- warning: real.coe_nnabs -> Real.coe_nnabs is a dubious translation:
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-  forall (x : Real), Eq.{1} Real ((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))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
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-Case conversion may be inaccurate. Consider using '#align real.coe_nnabs Real.coe_nnabsₓ'. -/
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
   rfl
 #align real.coe_nnabs Real.coe_nnabs
 
-/- warning: real.nnabs_of_nonneg -> Real.nnabs_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x) (Real.toNNReal x))
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-Case conversion may be inaccurate. Consider using '#align real.nnabs_of_nonneg Real.nnabs_of_nonnegₓ'. -/
 @[simp]
 theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x := by ext;
   simp [coe_to_nnreal x h, abs_of_nonneg h]
 #align real.nnabs_of_nonneg Real.nnabs_of_nonneg
 
-/- warning: real.nnabs_coe -> Real.nnabs_coe is a dubious translation:
-lean 3 declaration is
-  forall (x : NNReal), Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((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))) x)) x
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-Case conversion may be inaccurate. Consider using '#align real.nnabs_coe Real.nnabs_coeₓ'. -/
 theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 #align real.nnabs_coe Real.nnabs_coe
 
-/- warning: real.coe_to_nnreal_le -> Real.coe_toNNReal_le is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), LE.le.{0} Real Real.hasLe ((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))) (Real.toNNReal x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
-but is expected to have type
-  forall (x : Real), LE.le.{0} Real Real.instLEReal (NNReal.toReal (Real.toNNReal x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
-Case conversion may be inaccurate. Consider using '#align real.coe_to_nnreal_le Real.coe_toNNReal_leₓ'. -/
 theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
   max_le (le_abs_self _) (abs_nonneg _)
 #align real.coe_to_nnreal_le Real.coe_toNNReal_le
 
-/- warning: real.cast_nat_abs_eq_nnabs_cast -> Real.cast_natAbs_eq_nnabs_cast is a dubious translation:
-lean 3 declaration is
-  forall (n : Int), Eq.{1} NNReal ((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))))))) (Int.natAbs n)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
-but is expected to have type
-  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
-Case conversion may be inaccurate. Consider using '#align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_castₓ'. -/
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by ext;
   rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs]
 #align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_cast

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -1259,13 +1259,9 @@ theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔
   by
   cases le_total 0 p
   · rw [← NNReal.coe_lt_coe, Real.coe_toNNReal p h]
-  · rw [to_nnreal_eq_zero.2 h]
-    constructor
-    · intro
-      have := not_lt_of_le (zero_le r)
-      contradiction
-    · intro rp
-      have : ¬p ≤ 0 := not_le_of_lt (lt_of_le_of_lt (NNReal.coe_nonneg _) rp)
+  · rw [to_nnreal_eq_zero.2 h]; constructor
+    · intro ; have := not_lt_of_le (zero_le r); contradiction
+    · intro rp; have : ¬p ≤ 0 := not_le_of_lt (lt_of_le_of_lt (NNReal.coe_nonneg _) rp)
       contradiction
 #align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_lt
 
@@ -1832,9 +1828,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
 Case conversion may be inaccurate. Consider using '#align nnreal.infi_empty NNReal.iInf_emptyₓ'. -/
-theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 :=
-  by
-  rw [← NNReal.coe_eq, coe_infi]
+theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by rw [← NNReal.coe_eq, coe_infi];
   exact Real.ciInf_empty _
 #align nnreal.infi_empty NNReal.iInf_empty
 
@@ -1845,10 +1839,8 @@ but is expected to have type
   forall {α : Sort.{u1}}, Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) α (fun (i : α) => OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
 Case conversion may be inaccurate. Consider using '#align nnreal.infi_const_zero NNReal.iInf_const_zeroₓ'. -/
 @[simp]
-theorem iInf_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 :=
-  by
-  rw [← NNReal.coe_eq, coe_infi]
-  exact Real.ciInf_const_zero
+theorem iInf_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 := by
+  rw [← NNReal.coe_eq, coe_infi]; exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero
 
 /- warning: nnreal.infi_mul -> NNReal.iInf_mul is a dubious translation:
@@ -1891,10 +1883,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
 Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul NNReal.iSup_mulₓ'. -/
-theorem iSup_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a :=
-  by
-  rw [mul_comm, mul_supr]
-  simp_rw [mul_comm]
+theorem iSup_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a := by
+  rw [mul_comm, mul_supr]; simp_rw [mul_comm]
 #align nnreal.supr_mul NNReal.iSup_mul
 
 /- warning: nnreal.supr_div -> NNReal.iSup_div is a dubious translation:
@@ -1915,10 +1905,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_mul_infi NNReal.le_mul_iInfₓ'. -/
-theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * iInf h :=
-  by
-  rw [mul_infi]
-  exact le_ciInf H
+theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * iInf h := by
+  rw [mul_infi]; exact le_ciInf H
 #align nnreal.le_mul_infi NNReal.le_mul_iInf
 
 /- warning: nnreal.mul_supr_le -> NNReal.mul_iSup_le is a dubious translation:
@@ -1927,10 +1915,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι), 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 (g ᾰ)) _inst_1) -> (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 (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
 Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr_le NNReal.mul_iSup_leₓ'. -/
-theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a :=
-  by
-  rw [mul_supr]
-  exact ciSup_le H
+theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a := by
+  rw [mul_supr]; exact ciSup_le H
 #align nnreal.mul_supr_le NNReal.mul_iSup_le
 
 /- warning: nnreal.le_infi_mul -> NNReal.le_iInf_mul is a dubious translation:
@@ -1939,10 +1925,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) h))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul NNReal.le_iInf_mulₓ'. -/
-theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ iInf g * h :=
-  by
-  rw [infi_mul]
-  exact le_ciInf H
+theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ iInf g * h := by
+  rw [infi_mul]; exact le_ciInf H
 #align nnreal.le_infi_mul NNReal.le_iInf_mul
 
 /- warning: nnreal.supr_mul_le -> NNReal.iSup_mul_le is a dubious translation:
@@ -1951,10 +1935,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : NNReal}, (forall (i : ι), 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 i) g) _inst_1) -> (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)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) g) _inst_1)
 Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_le NNReal.iSup_mul_leₓ'. -/
-theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a :=
-  by
-  rw [supr_mul]
-  exact ciSup_le H
+theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a := by
+  rw [supr_mul]; exact ciSup_le H
 #align nnreal.supr_mul_le NNReal.iSup_mul_le
 
 /- warning: nnreal.le_infi_mul_infi -> NNReal.le_iInf_mul_iInf is a dubious translation:
@@ -2040,15 +2022,9 @@ namespace Real
 @[pp_nodot]
 def nnabs : ℝ →*₀ ℝ≥0 where
   toFun x := ⟨|x|, abs_nonneg x⟩
-  map_zero' := by
-    ext
-    simp
-  map_one' := by
-    ext
-    simp
-  map_mul' x y := by
-    ext
-    simp [abs_mul]
+  map_zero' := by ext; simp
+  map_one' := by ext; simp
+  map_mul' x y := by ext; simp [abs_mul]
 #align real.nnabs Real.nnabs
 -/
 
@@ -2070,9 +2046,7 @@ but is expected to have type
   forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
 Case conversion may be inaccurate. Consider using '#align real.nnabs_of_nonneg Real.nnabs_of_nonnegₓ'. -/
 @[simp]
-theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
-  by
-  ext
+theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x := by ext;
   simp [coe_to_nnreal x h, abs_of_nonneg h]
 #align real.nnabs_of_nonneg Real.nnabs_of_nonneg
 
@@ -2101,9 +2075,7 @@ lean 3 declaration is
 but is expected to have type
   forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
 Case conversion may be inaccurate. Consider using '#align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_castₓ'. -/
-theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n :=
-  by
-  ext
+theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by ext;
   rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs]
 #align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_cast

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -765,10 +765,7 @@ def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a
 #align nnreal.order_iso_Icc_zero_coe NNReal.orderIsoIccZeroCoe
 
 /- warning: nnreal.order_iso_Icc_zero_coe_symm_apply_coe -> NNReal.orderIsoIccZeroCoe_symm_apply_coe is a dubious translation:
-lean 3 declaration is
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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))) a))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))))) (coeFn.{1, 1} (OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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, 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-but is expected to have type
-  forall (a : NNReal) (b : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (fun (_x : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) (NNReal.orderIsoIccZeroCoe a)) b)) (NNReal.toReal (Subtype.val.{1} NNReal (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coeₓ'. -/
 @[simp]
 theorem orderIsoIccZeroCoe_symm_apply_coe (a : ℝ≥0) (b : Set.Iic a) :
@@ -2118,7 +2115,6 @@ open Positivity
 
 private theorem nnreal_coe_pos {r : ℝ≥0} : 0 < r → 0 < (r : ℝ) :=
   NNReal.coe_pos.2
-#align tactic.nnreal_coe_pos tactic.nnreal_coe_pos
 
 /-- Extension for the `positivity` tactic: cast from `ℝ≥0` to `ℝ`. -/
 @[positivity]

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -402,7 +402,7 @@ def toRealHom : ℝ≥0 →+* ℝ :=
 lean 3 declaration is
   Eq.{1} (NNReal -> Real) (coeFn.{1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => NNReal -> Real) (RingHom.hasCoeToFun.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) NNReal.toRealHom) ((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))))
 but is expected to have type
-  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) NNReal.toRealHom) NNReal.toReal
+  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) NNReal.toRealHom) NNReal.toReal
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_to_real_hom NNReal.coe_toRealHomₓ'. -/
 @[simp]
 theorem coe_toRealHom : ⇑toRealHom = coe :=
@@ -768,7 +768,7 @@ def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a
 lean 3 declaration is
   forall (a : NNReal) (b : coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))))) (coeFn.{1, 1} (OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))) (fun (_x : RelIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal 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Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) => (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (RelIso.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) (OrderIso.symm.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (NNReal.orderIsoIccZeroCoe a)) b)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (coeTrans.{1, 1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe) (coeSubtype.{1} NNReal (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))))) b)
 but is expected to have type
-  forall (a : NNReal) (b : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (fun (_x : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) (NNReal.orderIsoIccZeroCoe a)) b)) (NNReal.toReal (Subtype.val.{1} NNReal (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) b))
+  forall (a : NNReal) (b : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (fun (_x : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) (NNReal.orderIsoIccZeroCoe a)) b)) (NNReal.toReal (Subtype.val.{1} NNReal (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coeₓ'. -/
 @[simp]
 theorem orderIsoIccZeroCoe_symm_apply_coe (a : ℝ≥0) (b : Set.Iic a) :
@@ -2059,7 +2059,7 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 lean 3 declaration is
   forall (x : Real), Eq.{1} Real ((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))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
 but is expected to have type
-  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
+  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
 Case conversion may be inaccurate. Consider using '#align real.coe_nnabs Real.coe_nnabsₓ'. -/
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
@@ -2070,7 +2070,7 @@ theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
 lean 3 declaration is
   forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x) (Real.toNNReal x))
 but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
 Case conversion may be inaccurate. Consider using '#align real.nnabs_of_nonneg Real.nnabs_of_nonnegₓ'. -/
 @[simp]
 theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
@@ -2083,7 +2083,7 @@ theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
 lean 3 declaration is
   forall (x : NNReal), Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((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))) x)) x
 but is expected to have type
-  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
+  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
 Case conversion may be inaccurate. Consider using '#align real.nnabs_coe Real.nnabs_coeₓ'. -/
 theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 #align real.nnabs_coe Real.nnabs_coe
@@ -2102,7 +2102,7 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 lean 3 declaration is
   forall (n : Int), Eq.{1} NNReal ((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))))))) (Int.natAbs n)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
+  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
 Case conversion may be inaccurate. Consider using '#align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_castₓ'. -/
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n :=
   by

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -349,7 +349,7 @@ protected theorem coe_two : ((2 : ℝ≥0) : ℝ) = 2 :=
 
 /- warning: nnreal.coe_sub -> NNReal.coe_sub is a dubious translation:
 lean 3 declaration is
-  forall {r₁ : NNReal} {r₂ : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₂ r₁) -> (Eq.{1} Real ((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))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) r₁ r₂)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) ((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))) r₁) ((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))) r₂)))
+  forall {r₁ : NNReal} {r₂ : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₂ r₁) -> (Eq.{1} Real ((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))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) r₁ r₂)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) ((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))) r₁) ((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))) r₂)))
 but is expected to have type
   forall {r₁ : NNReal} {r₂ : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r₂ r₁) -> (Eq.{1} Real (NNReal.toReal (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.instSubNNReal) r₁ r₂)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (NNReal.toReal r₁) (NNReal.toReal r₂)))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_sub NNReal.coe_subₓ'. -/
@@ -626,7 +626,7 @@ noncomputable example : LinearOrder ℝ≥0 := by infer_instance
 
 /- warning: nnreal.coe_le_coe -> NNReal.coe_le_coe is a dubious translation:
 lean 3 declaration is
-  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LE.le.{0} Real Real.hasLe ((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))) r₁) ((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))) r₂)) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₁ r₂)
+  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LE.le.{0} Real Real.hasLe ((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))) r₁) ((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))) r₂)) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₁ r₂)
 but is expected to have type
   forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LE.le.{0} Real Real.instLEReal (NNReal.toReal r₁) (NNReal.toReal r₂)) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r₁ r₂)
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_le_coe NNReal.coe_le_coeₓ'. -/
@@ -637,7 +637,7 @@ protected theorem coe_le_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) ≤ r₂ ↔ r
 
 /- warning: nnreal.coe_lt_coe -> NNReal.coe_lt_coe is a dubious translation:
 lean 3 declaration is
-  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LT.lt.{0} Real Real.hasLt ((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))) r₁) ((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))) r₂)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₁ r₂)
+  forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LT.lt.{0} Real Real.hasLt ((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))) r₁) ((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))) r₂)) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r₁ r₂)
 but is expected to have type
   forall {r₁ : NNReal} {r₂ : NNReal}, Iff (LT.lt.{0} Real Real.instLTReal (NNReal.toReal r₁) (NNReal.toReal r₂)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r₁ r₂)
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_lt_coe NNReal.coe_lt_coeₓ'. -/
@@ -648,7 +648,7 @@ protected theorem coe_lt_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) < r₂ ↔ r
 
 /- warning: nnreal.coe_pos -> NNReal.coe_pos is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) r)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)
+  forall {r : NNReal}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) r)) (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)
 but is expected to have type
   forall {r : NNReal}, Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal r)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r)
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_pos NNReal.coe_posₓ'. -/
@@ -751,7 +751,7 @@ example : NoMaxOrder ℝ≥0 := by infer_instance
 
 /- warning: nnreal.order_iso_Icc_zero_coe -> NNReal.orderIsoIccZeroCoe is a dubious translation:
 lean 3 declaration is
-  forall (a : NNReal), OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))
+  forall (a : NNReal), OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))
 but is expected to have type
   forall (a : NNReal), OrderIso.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)))
 Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe NNReal.orderIsoIccZeroCoeₓ'. -/
@@ -766,7 +766,7 @@ def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a
 
 /- warning: nnreal.order_iso_Icc_zero_coe_symm_apply_coe -> NNReal.orderIsoIccZeroCoe_symm_apply_coe is a dubious translation:
 lean 3 declaration is
-  forall (a : NNReal) (b : coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))))) (coeFn.{1, 1} (OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))) (fun (_x : RelIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) => (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (RelIso.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) (OrderIso.symm.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (NNReal.orderIsoIccZeroCoe a)) b)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (coeTrans.{1, 1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe) (coeSubtype.{1} NNReal (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))))) b)
+  forall (a : NNReal) (b : coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))))) (coeFn.{1, 1} (OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))) (fun (_x : RelIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) => (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (RelIso.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) (OrderIso.symm.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (NNReal.orderIsoIccZeroCoe a)) b)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (coeTrans.{1, 1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe) (coeSubtype.{1} NNReal (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))))) b)
 but is expected to have type
   forall (a : NNReal) (b : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (fun (_x : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) (NNReal.orderIsoIccZeroCoe a)) b)) (NNReal.toReal (Subtype.val.{1} NNReal (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coeₓ'. -/
@@ -876,7 +876,7 @@ theorem coe_iInf {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) =
 
 /- warning: nnreal.le_infi_add_infi -> NNReal.le_iInf_add_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {ι' : Sort.{u2}} [_inst_1 : Nonempty.{u1} ι] [_inst_2 : Nonempty.{u2} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι' (fun (j : ι') => g j))))
+  forall {ι : Sort.{u1}} {ι' : Sort.{u2}} [_inst_1 : Nonempty.{u1} ι] [_inst_2 : Nonempty.{u2} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι' (fun (j : ι') => g j))))
 but is expected to have type
   forall {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : Nonempty.{u1} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))))) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι' (fun (j : ι') => g j))))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_add_infi NNReal.le_iInf_add_iInfₓ'. -/
@@ -891,7 +891,7 @@ example : Archimedean ℝ≥0 := by infer_instance
 
 /- warning: nnreal.covariant_add -> NNReal.covariant_add is a dubious translation:
 lean 3 declaration is
-  CovariantClass.{0, 0} NNReal 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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
+  CovariantClass.{0, 0} NNReal 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)))))) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
   CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4044 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4046 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4044 x._@.Mathlib.Data.Real.NNReal._hyg.4046) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4059 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4061 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4059 x._@.Mathlib.Data.Real.NNReal._hyg.4061)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_add NNReal.covariant_addₓ'. -/
@@ -902,7 +902,7 @@ instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
 
 /- warning: nnreal.contravariant_add -> NNReal.contravariant_add is a dubious translation:
 lean 3 declaration is
-  ContravariantClass.{0, 0} NNReal 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)))))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
+  ContravariantClass.{0, 0} NNReal 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)))))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
   ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4084 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4086 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4084 x._@.Mathlib.Data.Real.NNReal._hyg.4086) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4099 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4101 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4099 x._@.Mathlib.Data.Real.NNReal._hyg.4101)
 Case conversion may be inaccurate. Consider using '#align nnreal.contravariant_add NNReal.contravariant_addₓ'. -/
@@ -912,7 +912,7 @@ instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· <
 
 /- warning: nnreal.covariant_mul -> NNReal.covariant_mul is a dubious translation:
 lean 3 declaration is
-  CovariantClass.{0, 0} NNReal NNReal (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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
+  CovariantClass.{0, 0} NNReal NNReal (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)))))) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
   CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4124 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4126 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4124 x._@.Mathlib.Data.Real.NNReal._hyg.4126) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4139 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4141 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4139 x._@.Mathlib.Data.Real.NNReal._hyg.4141)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_mul NNReal.covariant_mulₓ'. -/
@@ -922,7 +922,7 @@ instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
 
 /- warning: nnreal.le_of_forall_pos_le_add -> NNReal.le_of_forall_pos_le_add is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal}, (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b ε))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b)
+  forall {a : NNReal} {b : NNReal}, (forall (ε : 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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b ε))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b)
 but is expected to have type
   forall {a : NNReal} {b : NNReal}, (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))))) b ε))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b)
 Case conversion may be inaccurate. Consider using '#align nnreal.le_of_forall_pos_le_add NNReal.le_of_forall_pos_le_addₓ'. -/
@@ -933,7 +933,7 @@ theorem le_of_forall_pos_le_add {a b : ℝ≥0} (h : ∀ ε, 0 < ε → a ≤ b
 
 /- warning: nnreal.lt_iff_exists_rat_btwn -> NNReal.lt_iff_exists_rat_btwn is a dubious translation:
 lean 3 declaration is
-  forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.hasLe (OfNat.ofNat.{0} Rat 0 (OfNat.mk.{0} Rat 0 (Zero.zero.{0} Rat Rat.hasZero))) q) (And (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q)) b))))
+  forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.hasLe (OfNat.ofNat.{0} Rat 0 (OfNat.mk.{0} Rat 0 (Zero.zero.{0} Rat Rat.hasZero))) q) (And (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q)) b))))
 but is expected to have type
   forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.instLERat (OfNat.ofNat.{0} Rat 0 (Rat.instOfNatRat 0)) q) (And (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (Real.toNNReal (Rat.cast.{0} Real Real.ratCast q))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal (Rat.cast.{0} Real Real.ratCast q)) b))))
 Case conversion may be inaccurate. Consider using '#align nnreal.lt_iff_exists_rat_btwn NNReal.lt_iff_exists_rat_btwnₓ'. -/
@@ -1072,7 +1072,7 @@ theorem toNNReal_one : Real.toNNReal 1 = 1 := by
 
 /- warning: real.to_nnreal_pos -> Real.toNNReal_pos is a dubious translation:
 lean 3 declaration is
-  forall {r : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (Real.toNNReal r)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)
+  forall {r : Real}, Iff (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (Real.toNNReal r)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r)
 but is expected to have type
   forall {r : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (Real.toNNReal r)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r)
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_pos Real.toNNReal_posₓ'. -/
@@ -1115,7 +1115,7 @@ theorem coe_toNNReal' (r : ℝ) : (Real.toNNReal r : ℝ) = max r 0 :=
 
 /- warning: real.to_nnreal_le_to_nnreal_iff -> Real.toNNReal_le_toNNReal_iff is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe r p))
+  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe r p))
 but is expected to have type
   forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (LE.le.{0} Real Real.instLEReal r p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_le_to_nnreal_iff Real.toNNReal_le_toNNReal_iffₓ'. -/
@@ -1137,7 +1137,7 @@ theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
 
 /- warning: real.to_nnreal_lt_to_nnreal_iff' -> Real.toNNReal_lt_toNNReal_iff' is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (And (LT.lt.{0} Real Real.hasLt r p) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p))
+  forall {r : Real} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (And (LT.lt.{0} Real Real.hasLt r p) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p))
 but is expected to have type
   forall {r : Real} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (And (LT.lt.{0} Real Real.instLTReal r p) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_to_nnreal_iff' Real.toNNReal_lt_toNNReal_iff'ₓ'. -/
@@ -1148,7 +1148,7 @@ theorem toNNReal_lt_toNNReal_iff' {r p : ℝ} : Real.toNNReal r < Real.toNNReal
 
 /- warning: real.to_nnreal_lt_to_nnreal_iff -> Real.toNNReal_lt_toNNReal_iff is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt r p))
+  forall {r : Real} {p : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt r p))
 but is expected to have type
   forall {r : Real} {p : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.instLTReal r p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_to_nnreal_iff Real.toNNReal_lt_toNNReal_iffₓ'. -/
@@ -1159,7 +1159,7 @@ theorem toNNReal_lt_toNNReal_iff {r p : ℝ} (h : 0 < p) :
 
 /- warning: real.to_nnreal_lt_to_nnreal_iff_of_nonneg -> Real.toNNReal_lt_toNNReal_iff_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt r p))
+  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt r p))
 but is expected to have type
   forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p)) (LT.lt.{0} Real Real.instLTReal r p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_to_nnreal_iff_of_nonneg Real.toNNReal_lt_toNNReal_iff_of_nonnegₓ'. -/
@@ -1193,7 +1193,7 @@ theorem toNNReal_add_toNNReal {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
 
 /- warning: real.to_nnreal_le_to_nnreal -> Real.toNNReal_le_toNNReal is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe r p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p))
+  forall {r : Real} {p : Real}, (LE.le.{0} Real Real.hasLe r p) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) (Real.toNNReal p))
 but is expected to have type
   forall {r : Real} {p : Real}, (LE.le.{0} Real Real.instLEReal r p) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) (Real.toNNReal p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_le_to_nnreal Real.toNNReal_le_toNNRealₓ'. -/
@@ -1203,7 +1203,7 @@ theorem toNNReal_le_toNNReal {r p : ℝ} (h : r ≤ p) : Real.toNNReal r ≤ Rea
 
 /- warning: real.to_nnreal_add_le -> Real.toNNReal_add_le is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : Real}, LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r 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))))) (Real.toNNReal r) (Real.toNNReal p))
+  forall {r : Real} {p : Real}, LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r 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))))) (Real.toNNReal r) (Real.toNNReal p))
 but is expected to have type
   forall {r : Real} {p : Real}, LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r 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))))) (Real.toNNReal r) (Real.toNNReal p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_add_le Real.toNNReal_add_leₓ'. -/
@@ -1213,7 +1213,7 @@ theorem toNNReal_add_le {r p : ℝ} : Real.toNNReal (r + p) ≤ Real.toNNReal r
 
 /- warning: real.to_nnreal_le_iff_le_coe -> Real.toNNReal_le_iff_le_coe is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) p) (LE.le.{0} Real Real.hasLe r ((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))
+  forall {r : Real} {p : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) p) (LE.le.{0} Real Real.hasLe r ((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))
 but is expected to have type
   forall {r : Real} {p : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) p) (LE.le.{0} Real Real.instLEReal r (NNReal.toReal p))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_le_iff_le_coe Real.toNNReal_le_iff_le_coeₓ'. -/
@@ -1223,7 +1223,7 @@ theorem toNNReal_le_iff_le_coe {r : ℝ} {p : ℝ≥0} : Real.toNNReal r ≤ p 
 
 /- warning: real.le_to_nnreal_iff_coe_le -> Real.le_toNNReal_iff_coe_le is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe ((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))) r) p))
+  forall {r : NNReal} {p : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe ((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))) r) p))
 but is expected to have type
   forall {r : NNReal} {p : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Real.toNNReal p)) (LE.le.{0} Real Real.instLEReal (NNReal.toReal r) p))
 Case conversion may be inaccurate. Consider using '#align real.le_to_nnreal_iff_coe_le Real.le_toNNReal_iff_coe_leₓ'. -/
@@ -1233,7 +1233,7 @@ theorem le_toNNReal_iff_coe_le {r : ℝ≥0} {p : ℝ} (hp : 0 ≤ p) : r ≤ Re
 
 /- warning: real.le_to_nnreal_iff_coe_le' -> Real.le_toNNReal_iff_coe_le' is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : Real}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe ((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))) r) p))
+  forall {r : NNReal} {p : Real}, (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LE.le.{0} Real Real.hasLe ((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))) r) p))
 but is expected to have type
   forall {r : NNReal} {p : Real}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Real.toNNReal p)) (LE.le.{0} Real Real.instLEReal (NNReal.toReal r) p))
 Case conversion may be inaccurate. Consider using '#align real.le_to_nnreal_iff_coe_le' Real.le_toNNReal_iff_coe_le'ₓ'. -/
@@ -1244,7 +1244,7 @@ theorem le_toNNReal_iff_coe_le' {r : ℝ≥0} {p : ℝ} (hr : 0 < r) : r ≤ Rea
 
 /- warning: real.to_nnreal_lt_iff_lt_coe -> Real.toNNReal_lt_iff_lt_coe is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {p : NNReal}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) p) (LT.lt.{0} Real Real.hasLt r ((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)))
+  forall {r : Real} {p : NNReal}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal r) p) (LT.lt.{0} Real Real.hasLt r ((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)))
 but is expected to have type
   forall {r : Real} {p : NNReal}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal r) p) (LT.lt.{0} Real Real.instLTReal r (NNReal.toReal p)))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_lt_iff_lt_coe Real.toNNReal_lt_iff_lt_coeₓ'. -/
@@ -1254,7 +1254,7 @@ theorem toNNReal_lt_iff_lt_coe {r : ℝ} {p : ℝ≥0} (ha : 0 ≤ r) : Real.toN
 
 /- warning: real.lt_to_nnreal_iff_coe_lt -> Real.lt_toNNReal_iff_coe_lt is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt ((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))) r) p)
+  forall {r : NNReal} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Real.toNNReal p)) (LT.lt.{0} Real Real.hasLt ((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))) r) p)
 but is expected to have type
   forall {r : NNReal} {p : Real}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Real.toNNReal p)) (LT.lt.{0} Real Real.instLTReal (NNReal.toReal r) p)
 Case conversion may be inaccurate. Consider using '#align real.lt_to_nnreal_iff_coe_lt Real.lt_toNNReal_iff_coe_ltₓ'. -/
@@ -1351,15 +1351,19 @@ end Mul
 
 section Pow
 
-#print NNReal.pow_antitone_exp /-
+/- warning: nnreal.pow_antitone_exp -> NNReal.pow_antitone_exp is a dubious translation:
+lean 3 declaration is
+  forall {a : NNReal} (m : Nat) (n : Nat), (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) a n) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) a m))
+but is expected to have type
+  forall {a : NNReal} (m : Nat) (n : Nat), (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) a n) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) a m))
+Case conversion may be inaccurate. Consider using '#align nnreal.pow_antitone_exp NNReal.pow_antitone_expₓ'. -/
 theorem pow_antitone_exp {a : ℝ≥0} (m n : ℕ) (mn : m ≤ n) (a1 : a ≤ 1) : a ^ n ≤ a ^ m :=
   pow_le_pow_of_le_one (zero_le a) a1 mn
 #align nnreal.pow_antitone_exp NNReal.pow_antitone_exp
--/
 
 /- warning: nnreal.exists_pow_lt_of_lt_one -> NNReal.exists_pow_lt_of_lt_one is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) a) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) b (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)))))))) -> (Exists.{1} Nat (fun (n : Nat) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) b n) a))
+  forall {a : NNReal} {b : 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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) a) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) b (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)))))))) -> (Exists.{1} Nat (fun (n : Nat) => LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) b n) a))
 but is expected to have type
   forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) a) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) b (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Exists.{1} Nat (fun (n : Nat) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) b n) a))
 Case conversion may be inaccurate. Consider using '#align nnreal.exists_pow_lt_of_lt_one NNReal.exists_pow_lt_of_lt_oneₓ'. -/
@@ -1370,7 +1374,7 @@ theorem exists_pow_lt_of_lt_one {a b : ℝ≥0} (ha : 0 < a) (hb : b < 1) : ∃
 
 /- warning: nnreal.exists_mem_Ico_zpow -> NNReal.exists_mem_Ico_zpow is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toLT.{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))))))) y) -> (Exists.{1} Int (fun (n : Int) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Ico.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (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))))))) y) -> (Exists.{1} Int (fun (n : Int) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Ico.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
 but is expected to have type
   forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (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)) y) -> (Exists.{1} Int (fun (n : Int) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Ico.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
 Case conversion may be inaccurate. Consider using '#align nnreal.exists_mem_Ico_zpow NNReal.exists_mem_Ico_zpowₓ'. -/
@@ -1385,7 +1389,7 @@ theorem exists_mem_Ico_zpow {x : ℝ≥0} {y : ℝ≥0} (hx : x ≠ 0) (hy : 1 <
 
 /- warning: nnreal.exists_mem_Ioc_zpow -> NNReal.exists_mem_Ioc_zpow is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toLT.{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))))))) y) -> (Exists.{1} Int (fun (n : Int) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Ioc.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (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))))))) y) -> (Exists.{1} Int (fun (n : Int) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Ioc.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
 but is expected to have type
   forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (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)) y) -> (Exists.{1} Int (fun (n : Int) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Ioc.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) y n) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) y (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
 Case conversion may be inaccurate. Consider using '#align nnreal.exists_mem_Ioc_zpow NNReal.exists_mem_Ioc_zpowₓ'. -/
@@ -1459,7 +1463,7 @@ theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
 
 /- warning: nnreal.inv_le -> NNReal.inv_le is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) p) (LE.le.{0} NNReal (Preorder.toLE.{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))))))) (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))))) r p)))
+  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) p) (LE.le.{0} NNReal (Preorder.toHasLe.{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))))))) (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))))) r p)))
 but is expected to have type
   forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) r) p) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r p)))
 Case conversion may be inaccurate. Consider using '#align nnreal.inv_le NNReal.inv_leₓ'. -/
@@ -1470,7 +1474,7 @@ theorem inv_le {r p : ℝ≥0} (h : r ≠ 0) : r⁻¹ ≤ p ↔ 1 ≤ r * p := b
 
 /- warning: nnreal.inv_le_of_le_mul -> NNReal.inv_le_of_le_mul is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{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))))))) (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))))) r p)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) p)
+  forall {r : NNReal} {p : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{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))))))) (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))))) r p)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) p)
 but is expected to have type
   forall {r : NNReal} {p : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r p)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) r) p)
 Case conversion may be inaccurate. Consider using '#align nnreal.inv_le_of_le_mul NNReal.inv_le_of_le_mulₓ'. -/
@@ -1480,7 +1484,7 @@ theorem inv_le_of_le_mul {r p : ℝ≥0} (h : 1 ≤ r * p) : r⁻¹ ≤ p := by
 
 /- warning: nnreal.le_inv_iff_mul_le -> NNReal.le_inv_iff_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) p)) (LE.le.{0} NNReal (Preorder.toLE.{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))))) r p) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))))
+  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) p)) (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))))) r p) (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)))))))))
 but is expected to have type
   forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) p)) (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)) r p) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_inv_iff_mul_le NNReal.le_inv_iff_mul_leₓ'. -/
@@ -1491,7 +1495,7 @@ theorem le_inv_iff_mul_le {r p : ℝ≥0} (h : p ≠ 0) : r ≤ p⁻¹ ↔ r * p
 
 /- warning: nnreal.lt_inv_iff_mul_lt -> NNReal.lt_inv_iff_mul_lt is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) p)) (LT.lt.{0} NNReal (Preorder.toLT.{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))))) r p) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))))
+  forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) p)) (LT.lt.{0} NNReal (Preorder.toHasLt.{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))))) r p) (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)))))))))
 but is expected to have type
   forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal p (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) p)) (LT.lt.{0} NNReal (Preorder.toLT.{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)) r p) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))))
 Case conversion may be inaccurate. Consider using '#align nnreal.lt_inv_iff_mul_lt NNReal.lt_inv_iff_mul_ltₓ'. -/
@@ -1502,7 +1506,7 @@ theorem lt_inv_iff_mul_lt {r p : ℝ≥0} (h : p ≠ 0) : r < p⁻¹ ↔ r * p <
 
 /- warning: nnreal.mul_le_iff_le_inv -> NNReal.mul_le_iff_le_inv is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{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))))) r a) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) b)))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (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))))) r a) b) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) b)))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (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)) r a) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) r) b)))
 Case conversion may be inaccurate. Consider using '#align nnreal.mul_le_iff_le_inv NNReal.mul_le_iff_le_invₓ'. -/
@@ -1514,7 +1518,7 @@ theorem mul_le_iff_le_inv {a b r : ℝ≥0} (hr : r ≠ 0) : r * a ≤ b ↔ a 
 
 /- warning: nnreal.le_div_iff_mul_le -> NNReal.le_div_iff_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LE.le.{0} NNReal (Preorder.toLE.{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 r) b))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (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 r) b))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (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 r) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_div_iff_mul_le NNReal.le_div_iff_mul_leₓ'. -/
@@ -1524,7 +1528,7 @@ theorem le_div_iff_mul_le {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ a *
 
 /- warning: nnreal.div_le_iff -> NNReal.div_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b r)))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b r)))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a r) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b r)))
 Case conversion may be inaccurate. Consider using '#align nnreal.div_le_iff NNReal.div_le_iffₓ'. -/
@@ -1534,7 +1538,7 @@ theorem div_le_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a / r ≤ b ↔ a ≤ b *
 
 /- warning: nnreal.div_le_iff' -> NNReal.div_le_iff' is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) r b)))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) r b)))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a r) b) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r b)))
 Case conversion may be inaccurate. Consider using '#align nnreal.div_le_iff' NNReal.div_le_iff'ₓ'. -/
@@ -1544,7 +1548,7 @@ theorem div_le_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a / r ≤ b ↔ a ≤ r *
 
 /- warning: nnreal.div_le_of_le_mul -> NNReal.div_le_of_le_mul is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b c)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a c) b)
+  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b c)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a c) b)
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a c) b)
 Case conversion may be inaccurate. Consider using '#align nnreal.div_le_of_le_mul NNReal.div_le_of_le_mulₓ'. -/
@@ -1554,7 +1558,7 @@ theorem div_le_of_le_mul {a b c : ℝ≥0} (h : a ≤ b * c) : a / c ≤ b :=
 
 /- warning: nnreal.div_le_of_le_mul' -> NNReal.div_le_of_le_mul' is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b c)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) c)
+  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b c)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) c)
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {c : NNReal}, (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a b) c)
 Case conversion may be inaccurate. Consider using '#align nnreal.div_le_of_le_mul' NNReal.div_le_of_le_mul'ₓ'. -/
@@ -1564,7 +1568,7 @@ theorem div_le_of_le_mul' {a b c : ℝ≥0} (h : a ≤ b * c) : a / b ≤ c :=
 
 /- warning: nnreal.le_div_iff -> NNReal.le_div_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LE.le.{0} NNReal (Preorder.toLE.{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 r) b))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (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 r) b))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (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 r) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_div_iff NNReal.le_div_iffₓ'. -/
@@ -1574,7 +1578,7 @@ theorem le_div_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ a * r ≤
 
 /- warning: nnreal.le_div_iff' -> NNReal.le_div_iff' is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LE.le.{0} NNReal (Preorder.toLE.{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))))) r a) b))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (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))))) r a) b))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (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)) r a) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_div_iff' NNReal.le_div_iff'ₓ'. -/
@@ -1584,7 +1588,7 @@ theorem le_div_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a ≤ b / r ↔ r * a ≤
 
 /- warning: nnreal.div_lt_iff -> NNReal.div_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b r)))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) b r)))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a r) b) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b r)))
 Case conversion may be inaccurate. Consider using '#align nnreal.div_lt_iff NNReal.div_lt_iffₓ'. -/
@@ -1594,7 +1598,7 @@ theorem div_lt_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a / r < b ↔ a < b * r :=
 
 /- warning: nnreal.div_lt_iff' -> NNReal.div_lt_iff' is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) r b)))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a r) b) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) r b)))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a r) b) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) r b)))
 Case conversion may be inaccurate. Consider using '#align nnreal.div_lt_iff' NNReal.div_lt_iff'ₓ'. -/
@@ -1604,7 +1608,7 @@ theorem div_lt_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a / r < b ↔ a < r * b :
 
 /- warning: nnreal.lt_div_iff -> NNReal.lt_div_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LT.lt.{0} NNReal (Preorder.toLT.{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 r) b))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LT.lt.{0} NNReal (Preorder.toHasLt.{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 r) b))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (LT.lt.{0} NNReal (Preorder.toLT.{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 r) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.lt_div_iff NNReal.lt_div_iffₓ'. -/
@@ -1614,7 +1618,7 @@ theorem lt_div_iff {a b r : ℝ≥0} (hr : r ≠ 0) : a < b / r ↔ a * r < b :=
 
 /- warning: nnreal.lt_div_iff' -> NNReal.lt_div_iff' is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LT.lt.{0} NNReal (Preorder.toLT.{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))))) r a) b))
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) (LT.lt.{0} NNReal (Preorder.toHasLt.{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))))) r a) b))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) (LT.lt.{0} NNReal (Preorder.toLT.{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)) r a) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.lt_div_iff' NNReal.lt_div_iff'ₓ'. -/
@@ -1624,7 +1628,7 @@ theorem lt_div_iff' {a b r : ℝ≥0} (hr : r ≠ 0) : a < b / r ↔ r * a < b :
 
 /- warning: nnreal.mul_lt_of_lt_div -> NNReal.mul_lt_of_lt_div is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) -> (LT.lt.{0} NNReal (Preorder.toLT.{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 r) b)
+  forall {a : NNReal} {b : NNReal} {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) b r)) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{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 r) b)
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) b r)) -> (LT.lt.{0} NNReal (Preorder.toLT.{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 r) b)
 Case conversion may be inaccurate. Consider using '#align nnreal.mul_lt_of_lt_div NNReal.mul_lt_of_lt_divₓ'. -/
@@ -1646,7 +1650,7 @@ theorem div_le_div_left_of_le {a b c : ℝ≥0} (b0 : 0 < b) (c0 : 0 < c) (cb :
 
 /- warning: nnreal.div_le_div_left -> NNReal.div_le_div_left is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal} {c : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) a) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) b) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) c) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a c)) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) c b))
+  forall {a : NNReal} {b : NNReal} {c : 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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) a) -> (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) b) -> (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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) c) -> (Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a c)) (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) c b))
 but is expected to have type
   forall {a : NNReal} {b : NNReal} {c : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) a) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) b) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) c) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a b) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a c)) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) c b))
 Case conversion may be inaccurate. Consider using '#align nnreal.div_le_div_left NNReal.div_le_div_leftₓ'. -/
@@ -1657,7 +1661,7 @@ theorem div_le_div_left {a b c : ℝ≥0} (a0 : 0 < a) (b0 : 0 < b) (c0 : 0 < c)
 
 /- warning: nnreal.le_of_forall_lt_one_mul_le -> NNReal.le_of_forall_lt_one_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, (forall (a : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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.toLE.{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 x) y)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x y)
+  forall {x : NNReal} {y : NNReal}, (forall (a : NNReal), (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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 x) y)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x y)
 but is expected to have type
   forall {x : NNReal} {y : NNReal}, (forall (a : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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 x) y)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x y)
 Case conversion may be inaccurate. Consider using '#align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_leₓ'. -/
@@ -1673,7 +1677,7 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
 
 /- warning: nnreal.half_le_self -> NNReal.half_le_self is a dubious translation:
 lean 3 declaration is
-  forall (a : NNReal), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))) a
+  forall (a : NNReal), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))) a
 but is expected to have type
   forall (a : NNReal), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) a
 Case conversion may be inaccurate. Consider using '#align nnreal.half_le_self NNReal.half_le_selfₓ'. -/
@@ -1683,7 +1687,7 @@ theorem half_le_self (a : ℝ≥0) : a / 2 ≤ a :=
 
 /- warning: nnreal.half_lt_self -> NNReal.half_lt_self is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal}, (Ne.{1} NNReal a (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))) a)
+  forall {a : NNReal}, (Ne.{1} NNReal a (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))) a)
 but is expected to have type
   forall {a : NNReal}, (Ne.{1} NNReal a (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) a)
 Case conversion may be inaccurate. Consider using '#align nnreal.half_lt_self NNReal.half_lt_selfₓ'. -/
@@ -1693,7 +1697,7 @@ theorem half_lt_self {a : ℝ≥0} (h : a ≠ 0) : a / 2 < a :=
 
 /- warning: nnreal.div_lt_one_of_lt -> NNReal.div_lt_one_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
+  forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) (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))))))))
 but is expected to have type
   forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a b) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)))
 Case conversion may be inaccurate. Consider using '#align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_ltₓ'. -/
@@ -1742,7 +1746,7 @@ theorem Real.toNNReal_div' {x y : ℝ} (hy : 0 ≤ y) :
 
 /- warning: nnreal.inv_lt_one_iff -> NNReal.inv_lt_one_iff is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x) (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)))))))) (LT.lt.{0} NNReal (Preorder.toLT.{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))))))) x))
+  forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x) (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)))))))) (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))))))) x))
 but is expected to have type
   forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) (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)) x))
 Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_one_iff NNReal.inv_lt_one_iffₓ'. -/
@@ -1752,7 +1756,7 @@ theorem inv_lt_one_iff {x : ℝ≥0} (hx : x ≠ 0) : x⁻¹ < 1 ↔ 1 < x := by
 
 /- warning: nnreal.zpow_pos -> NNReal.zpow_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (n : Int), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) x n))
+  forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (n : Int), 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 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) x n))
 but is expected to have type
   forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (forall (n : Int), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal))))))) x n))
 Case conversion may be inaccurate. Consider using '#align nnreal.zpow_pos NNReal.zpow_posₓ'. -/
@@ -1765,7 +1769,7 @@ theorem zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
 
 /- warning: nnreal.inv_lt_inv -> NNReal.inv_lt_inv is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x y) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) y) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x))
+  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x y) -> (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) y) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x))
 but is expected to have type
   forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x y) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) y) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x))
 Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_inv NNReal.inv_lt_invₓ'. -/
@@ -1794,7 +1798,7 @@ variable {ι : Sort _} {f : ι → ℝ≥0}
 
 /- warning: nnreal.le_to_nnreal_of_coe_le -> NNReal.le_toNNReal_of_coe_le is a dubious translation:
 lean 3 declaration is
-  forall {x : NNReal} {y : Real}, (LE.le.{0} Real Real.hasLe ((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))) x) y) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x (Real.toNNReal y))
+  forall {x : NNReal} {y : Real}, (LE.le.{0} Real Real.hasLe ((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))) x) y) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x (Real.toNNReal y))
 but is expected to have type
   forall {x : NNReal} {y : Real}, (LE.le.{0} Real Real.instLEReal (NNReal.toReal x) y) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x (Real.toNNReal y))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_to_nnreal_of_coe_le NNReal.le_toNNReal_of_coe_leₓ'. -/
@@ -1910,7 +1914,7 @@ variable [Nonempty ι]
 
 /- warning: nnreal.le_mul_infi -> NNReal.le_mul_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (h j))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
 but is expected to have type
   forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_mul_infi NNReal.le_mul_iInfₓ'. -/
@@ -1922,7 +1926,7 @@ theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j,
 
 /- warning: nnreal.mul_supr_le -> NNReal.mul_iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) g (h j)) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) g (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), 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))))) g (h j)) a) -> (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))))) g (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
 but is expected to have type
   forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι), 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 (g ᾰ)) _inst_1) -> (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 (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
 Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr_le NNReal.mul_iSup_leₓ'. -/
@@ -1934,7 +1938,7 @@ theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j,
 
 /- warning: nnreal.le_infi_mul -> NNReal.le_iInf_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h))
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h))
 but is expected to have type
   forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) h))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul NNReal.le_iInf_mulₓ'. -/
@@ -1946,7 +1950,7 @@ theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i,
 
 /- warning: nnreal.supr_mul_le -> NNReal.iSup_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) (g i) h) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h) a)
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), 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))))) (g i) h) a) -> (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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h) a)
 but is expected to have type
   forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : NNReal}, (forall (i : ι), 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 i) g) _inst_1) -> (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)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) g) _inst_1)
 Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_le NNReal.iSup_mul_leₓ'. -/
@@ -1958,7 +1962,7 @@ theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i,
 
 /- warning: nnreal.le_infi_mul_infi -> NNReal.le_iInf_mul_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
 but is expected to have type
   forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
 Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInfₓ'. -/
@@ -1969,7 +1973,7 @@ theorem le_iInf_mul_iInf {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a 
 
 /- warning: nnreal.supr_mul_supr_le -> NNReal.iSup_mul_iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) (g i) (h j)) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), 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))))) (g i) (h j)) a) -> (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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
 but is expected to have type
   forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι) (j : ι), 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 ᾰ) (g j)) _inst_1) -> (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)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
 Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_supr_le NNReal.iSup_mul_iSup_leₓ'. -/

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -813,79 +813,79 @@ theorem bddBelow_coe (s : Set ℝ≥0) : BddBelow ((coe : ℝ≥0 → ℝ) '' s)
 #align nnreal.bdd_below_coe NNReal.bddBelow_coe
 
 noncomputable instance : ConditionallyCompleteLinearOrderBot ℝ≥0 :=
-  Nonneg.conditionallyCompleteLinearOrderBot Real.supₛ_empty.le
+  Nonneg.conditionallyCompleteLinearOrderBot Real.sSup_empty.le
 
-/- warning: nnreal.coe_Sup -> NNReal.coe_supₛ is a dubious translation:
+/- warning: nnreal.coe_Sup -> NNReal.coe_sSup is a dubious translation:
 lean 3 declaration is
-  forall (s : Set.{0} NNReal), Eq.{1} Real ((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))) (SupSet.supₛ.{0} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s)) (SupSet.supₛ.{0} Real Real.hasSup (Set.image.{0, 0} NNReal Real ((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)))) s))
+  forall (s : Set.{0} NNReal), Eq.{1} Real ((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))) (SupSet.sSup.{0} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s)) (SupSet.sSup.{0} Real Real.hasSup (Set.image.{0, 0} NNReal Real ((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)))) s))
 but is expected to have type
-  forall (s : Set.{0} NNReal), Eq.{1} Real (NNReal.toReal (SupSet.supₛ.{0} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s)) (SupSet.supₛ.{0} Real Real.instSupSetReal (Set.image.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_Sup NNReal.coe_supₛₓ'. -/
+  forall (s : Set.{0} NNReal), Eq.{1} Real (NNReal.toReal (SupSet.sSup.{0} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s)) (SupSet.sSup.{0} Real Real.instSupSetReal (Set.image.{0, 0} NNReal Real NNReal.toReal s))
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_Sup NNReal.coe_sSupₓ'. -/
 @[norm_cast]
-theorem coe_supₛ (s : Set ℝ≥0) : (↑(supₛ s) : ℝ) = supₛ ((coe : ℝ≥0 → ℝ) '' s) :=
+theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup ((coe : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
-    @subset_supₛ_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
-      Real.supₛ_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
-#align nnreal.coe_Sup NNReal.coe_supₛ
+    @subset_sSup_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
+      Real.sSup_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
+#align nnreal.coe_Sup NNReal.coe_sSup
 
-/- warning: nnreal.coe_supr -> NNReal.coe_supᵢ is a dubious translation:
+/- warning: nnreal.coe_supr -> NNReal.coe_iSup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real ((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))) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => s i))) (supᵢ.{0, u1} Real Real.hasSup ι (fun (i : ι) => (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))) (s i)))
+  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real ((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))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => s i))) (iSup.{0, u1} Real Real.hasSup ι (fun (i : ι) => (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))) (s i)))
 but is expected to have type
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real (NNReal.toReal (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => s i))) (supᵢ.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => NNReal.toReal (s i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_supr NNReal.coe_supᵢₓ'. -/
+  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real (NNReal.toReal (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => s i))) (iSup.{0, u1} Real Real.instSupSetReal ι (fun (i : ι) => NNReal.toReal (s i)))
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_supr NNReal.coe_iSupₓ'. -/
 @[norm_cast]
-theorem coe_supᵢ {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, s i := by
-  rw [supᵢ, supᵢ, coe_Sup, Set.range_comp]
-#align nnreal.coe_supr NNReal.coe_supᵢ
+theorem coe_iSup {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, s i := by
+  rw [iSup, iSup, coe_Sup, Set.range_comp]
+#align nnreal.coe_supr NNReal.coe_iSup
 
-/- warning: nnreal.coe_Inf -> NNReal.coe_infₛ is a dubious translation:
+/- warning: nnreal.coe_Inf -> NNReal.coe_sInf is a dubious translation:
 lean 3 declaration is
-  forall (s : Set.{0} NNReal), Eq.{1} Real ((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))) (InfSet.infₛ.{0} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s)) (InfSet.infₛ.{0} Real Real.hasInf (Set.image.{0, 0} NNReal Real ((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)))) s))
+  forall (s : Set.{0} NNReal), Eq.{1} Real ((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))) (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s)) (InfSet.sInf.{0} Real Real.hasInf (Set.image.{0, 0} NNReal Real ((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)))) s))
 but is expected to have type
-  forall (s : Set.{0} NNReal), Eq.{1} Real (NNReal.toReal (InfSet.infₛ.{0} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s)) (InfSet.infₛ.{0} Real Real.instInfSetReal (Set.image.{0, 0} NNReal Real NNReal.toReal s))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_Inf NNReal.coe_infₛₓ'. -/
+  forall (s : Set.{0} NNReal), Eq.{1} Real (NNReal.toReal (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s)) (InfSet.sInf.{0} Real Real.instInfSetReal (Set.image.{0, 0} NNReal Real NNReal.toReal s))
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_Inf NNReal.coe_sInfₓ'. -/
 @[norm_cast]
-theorem coe_infₛ (s : Set ℝ≥0) : (↑(infₛ s) : ℝ) = infₛ ((coe : ℝ≥0 → ℝ) '' s) :=
+theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf ((coe : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
-    @subset_infₛ_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
-      Real.infₛ_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
-#align nnreal.coe_Inf NNReal.coe_infₛ
+    @subset_sInf_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
+      Real.sInf_nonneg _ fun y ⟨x, _, hy⟩ => hy ▸ x.2
+#align nnreal.coe_Inf NNReal.coe_sInf
 
-/- warning: nnreal.Inf_empty -> NNReal.infₛ_empty is a dubious translation:
+/- warning: nnreal.Inf_empty -> NNReal.sInf_empty is a dubious translation:
 lean 3 declaration is
-  Eq.{1} NNReal (InfSet.infₛ.{0} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) (EmptyCollection.emptyCollection.{0} (Set.{0} NNReal) (Set.hasEmptyc.{0} NNReal))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
+  Eq.{1} NNReal (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) (EmptyCollection.emptyCollection.{0} (Set.{0} NNReal) (Set.hasEmptyc.{0} NNReal))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
 but is expected to have type
-  Eq.{1} NNReal (InfSet.infₛ.{0} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) (EmptyCollection.emptyCollection.{0} (Set.{0} NNReal) (Set.instEmptyCollectionSet.{0} NNReal))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.Inf_empty NNReal.infₛ_emptyₓ'. -/
+  Eq.{1} NNReal (InfSet.sInf.{0} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) (EmptyCollection.emptyCollection.{0} (Set.{0} NNReal) (Set.instEmptyCollectionSet.{0} NNReal))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
+Case conversion may be inaccurate. Consider using '#align nnreal.Inf_empty NNReal.sInf_emptyₓ'. -/
 @[simp]
-theorem infₛ_empty : infₛ (∅ : Set ℝ≥0) = 0 := by
-  rw [← NNReal.coe_eq_zero, coe_Inf, Set.image_empty, Real.infₛ_empty]
-#align nnreal.Inf_empty NNReal.infₛ_empty
+theorem sInf_empty : sInf (∅ : Set ℝ≥0) = 0 := by
+  rw [← NNReal.coe_eq_zero, coe_Inf, Set.image_empty, Real.sInf_empty]
+#align nnreal.Inf_empty NNReal.sInf_empty
 
-/- warning: nnreal.coe_infi -> NNReal.coe_infᵢ is a dubious translation:
+/- warning: nnreal.coe_infi -> NNReal.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real ((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))) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => s i))) (infᵢ.{0, u1} Real Real.hasInf ι (fun (i : ι) => (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))) (s i)))
+  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real ((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))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => s i))) (iInf.{0, u1} Real Real.hasInf ι (fun (i : ι) => (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))) (s i)))
 but is expected to have type
-  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real (NNReal.toReal (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => s i))) (infᵢ.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => NNReal.toReal (s i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.coe_infi NNReal.coe_infᵢₓ'. -/
+  forall {ι : Sort.{u1}} (s : ι -> NNReal), Eq.{1} Real (NNReal.toReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => s i))) (iInf.{0, u1} Real Real.instInfSetReal ι (fun (i : ι) => NNReal.toReal (s i)))
+Case conversion may be inaccurate. Consider using '#align nnreal.coe_infi NNReal.coe_iInfₓ'. -/
 @[norm_cast]
-theorem coe_infᵢ {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, s i := by
-  rw [infᵢ, infᵢ, coe_Inf, Set.range_comp]
-#align nnreal.coe_infi NNReal.coe_infᵢ
+theorem coe_iInf {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, s i := by
+  rw [iInf, iInf, coe_Inf, Set.range_comp]
+#align nnreal.coe_infi NNReal.coe_iInf
 
-/- warning: nnreal.le_infi_add_infi -> NNReal.le_infᵢ_add_infᵢ is a dubious translation:
+/- warning: nnreal.le_infi_add_infi -> NNReal.le_iInf_add_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {ι' : Sort.{u2}} [_inst_1 : Nonempty.{u1} ι] [_inst_2 : Nonempty.{u2} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (infᵢ.{0, u2} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι' (fun (j : ι') => g j))))
+  forall {ι : Sort.{u1}} {ι' : Sort.{u2}} [_inst_1 : Nonempty.{u1} ι] [_inst_2 : Nonempty.{u2} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι' (fun (j : ι') => g j))))
 but is expected to have type
-  forall {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : Nonempty.{u1} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))))) (infᵢ.{0, u2} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι' (fun (j : ι') => g j))))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_add_infi NNReal.le_infᵢ_add_infᵢₓ'. -/
-theorem le_infᵢ_add_infᵢ {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
+  forall {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : Nonempty.{u1} ι'] {f : ι -> NNReal} {g : ι' -> NNReal} {a : NNReal}, (forall (i : ι) (j : ι'), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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 j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (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))))) (iInf.{0, u2} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι' (fun (j : ι') => g j))))
+Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_add_infi NNReal.le_iInf_add_iInfₓ'. -/
+theorem le_iInf_add_iInf {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
     {a : ℝ≥0} (h : ∀ i j, a ≤ f i + g j) : a ≤ (⨅ i, f i) + ⨅ j, g j :=
   by
   rw [← NNReal.coe_le_coe, NNReal.coe_add, coe_infi, coe_infi]
-  exact le_cinfᵢ_add_cinfᵢ h
-#align nnreal.le_infi_add_infi NNReal.le_infᵢ_add_infᵢ
+  exact le_ciInf_add_ciInf h
+#align nnreal.le_infi_add_infi NNReal.le_iInf_add_iInf
 
 example : Archimedean ℝ≥0 := by infer_instance
 
@@ -1802,181 +1802,181 @@ theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y
   (le_toNNReal_iff_coe_le <| x.2.trans h).2 h
 #align nnreal.le_to_nnreal_of_coe_le NNReal.le_toNNReal_of_coe_le
 
-/- warning: nnreal.Sup_of_not_bdd_above -> NNReal.supₛ_of_not_bddAbove is a dubious translation:
+/- warning: nnreal.Sup_of_not_bdd_above -> NNReal.sSup_of_not_bddAbove is a dubious translation:
 lean 3 declaration is
-  forall {s : Set.{0} NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) s)) -> (Eq.{1} NNReal (SupSet.supₛ.{0} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
+  forall {s : Set.{0} NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) s)) -> (Eq.{1} NNReal (SupSet.sSup.{0} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) s) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
 but is expected to have type
-  forall {s : Set.{0} NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) s)) -> (Eq.{1} NNReal (SupSet.supₛ.{0} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align nnreal.Sup_of_not_bdd_above NNReal.supₛ_of_not_bddAboveₓ'. -/
-theorem supₛ_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.supₛ s = 0 :=
+  forall {s : Set.{0} NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) s)) -> (Eq.{1} NNReal (SupSet.sSup.{0} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) s) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
+Case conversion may be inaccurate. Consider using '#align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAboveₓ'. -/
+theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 :=
   by
   rw [← bdd_above_coe] at hs
   rw [← NNReal.coe_eq, coe_Sup]
   exact Sup_of_not_bdd_above hs
-#align nnreal.Sup_of_not_bdd_above NNReal.supₛ_of_not_bddAbove
+#align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
 
-/- warning: nnreal.supr_of_not_bdd_above -> NNReal.supᵢ_of_not_bddAbove is a dubious translation:
+/- warning: nnreal.supr_of_not_bdd_above -> NNReal.iSup_of_not_bddAbove is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {f : ι -> NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (Set.range.{0, u1} NNReal ι f))) -> (Eq.{1} NNReal (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
+  forall {ι : Sort.{u1}} {f : ι -> NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) (Set.range.{0, u1} NNReal ι f))) -> (Eq.{1} NNReal (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
 but is expected to have type
-  forall {ι : Sort.{u1}} {f : ι -> NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (Set.range.{0, u1} NNReal ι f))) -> (Eq.{1} NNReal (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_of_not_bdd_above NNReal.supᵢ_of_not_bddAboveₓ'. -/
-theorem supᵢ_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
-  supₛ_of_not_bddAbove hf
-#align nnreal.supr_of_not_bdd_above NNReal.supᵢ_of_not_bddAbove
+  forall {ι : Sort.{u1}} {f : ι -> NNReal}, (Not (BddAbove.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) (Set.range.{0, u1} NNReal ι f))) -> (Eq.{1} NNReal (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
+Case conversion may be inaccurate. Consider using '#align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAboveₓ'. -/
+theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
+  sSup_of_not_bddAbove hf
+#align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAbove
 
-/- warning: nnreal.infi_empty -> NNReal.infᵢ_empty is a dubious translation:
+/- warning: nnreal.infi_empty -> NNReal.iInf_empty is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
+  forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
 but is expected to have type
-  forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.infi_empty NNReal.infᵢ_emptyₓ'. -/
-theorem infᵢ_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 :=
+  forall {ι : Sort.{u1}} [_inst_1 : IsEmpty.{u1} ι] (f : ι -> NNReal), Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
+Case conversion may be inaccurate. Consider using '#align nnreal.infi_empty NNReal.iInf_emptyₓ'. -/
+theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 :=
   by
   rw [← NNReal.coe_eq, coe_infi]
-  exact Real.cinfᵢ_empty _
-#align nnreal.infi_empty NNReal.infᵢ_empty
+  exact Real.ciInf_empty _
+#align nnreal.infi_empty NNReal.iInf_empty
 
-/- warning: nnreal.infi_const_zero -> NNReal.infᵢ_const_zero is a dubious translation:
+/- warning: nnreal.infi_const_zero -> NNReal.iInf_const_zero is a dubious translation:
 lean 3 declaration is
-  forall {α : Sort.{u1}}, Eq.{1} NNReal (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) α (fun (i : α) => OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
+  forall {α : Sort.{u1}}, Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) α (fun (i : α) => OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
 but is expected to have type
-  forall {α : Sort.{u1}}, Eq.{1} NNReal (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) α (fun (i : α) => OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
-Case conversion may be inaccurate. Consider using '#align nnreal.infi_const_zero NNReal.infᵢ_const_zeroₓ'. -/
+  forall {α : Sort.{u1}}, Eq.{1} NNReal (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) α (fun (i : α) => OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
+Case conversion may be inaccurate. Consider using '#align nnreal.infi_const_zero NNReal.iInf_const_zeroₓ'. -/
 @[simp]
-theorem infᵢ_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 :=
+theorem iInf_const_zero {α : Sort _} : (⨅ i : α, (0 : ℝ≥0)) = 0 :=
   by
   rw [← NNReal.coe_eq, coe_infi]
-  exact Real.cinfᵢ_const_zero
-#align nnreal.infi_const_zero NNReal.infᵢ_const_zero
+  exact Real.ciInf_const_zero
+#align nnreal.infi_const_zero NNReal.iInf_const_zero
 
-/- warning: nnreal.infi_mul -> NNReal.infᵢ_mul is a dubious translation:
+/- warning: nnreal.infi_mul -> NNReal.iInf_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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))))) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι f) a) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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) a))
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι f) a) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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) a))
 but is expected to have type
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι f) a) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.infi_mul NNReal.infᵢ_mulₓ'. -/
-theorem infᵢ_mul (f : ι → ℝ≥0) (a : ℝ≥0) : infᵢ f * a = ⨅ i, f i * a :=
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι f) a) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
+Case conversion may be inaccurate. Consider using '#align nnreal.infi_mul NNReal.iInf_mulₓ'. -/
+theorem iInf_mul (f : ι → ℝ≥0) (a : ℝ≥0) : iInf f * a = ⨅ i, f i * a :=
   by
   rw [← NNReal.coe_eq, NNReal.coe_mul, coe_infi, coe_infi]
-  exact Real.infᵢ_mul_of_nonneg (NNReal.coe_nonneg _) _
-#align nnreal.infi_mul NNReal.infᵢ_mul
+  exact Real.iInf_mul_of_nonneg (NNReal.coe_nonneg _) _
+#align nnreal.infi_mul NNReal.iInf_mul
 
-/- warning: nnreal.mul_infi -> NNReal.mul_infᵢ is a dubious translation:
+/- warning: nnreal.mul_infi -> NNReal.mul_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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 (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι f)) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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))))) a (f i)))
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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 (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι f)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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))))) a (f i)))
 but is expected to have type
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι f)) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (f i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_infi NNReal.mul_infᵢₓ'. -/
-theorem mul_infᵢ (f : ι → ℝ≥0) (a : ℝ≥0) : a * infᵢ f = ⨅ i, a * f i := by
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι f)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (f i)))
+Case conversion may be inaccurate. Consider using '#align nnreal.mul_infi NNReal.mul_iInfₓ'. -/
+theorem mul_iInf (f : ι → ℝ≥0) (a : ℝ≥0) : a * iInf f = ⨅ i, a * f i := by
   simpa only [mul_comm] using infi_mul f a
-#align nnreal.mul_infi NNReal.mul_infᵢ
+#align nnreal.mul_infi NNReal.mul_iInf
 
-/- warning: nnreal.mul_supr -> NNReal.mul_supᵢ is a dubious translation:
+/- warning: nnreal.mul_supr -> NNReal.mul_iSup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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 (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i))) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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))))) a (f i)))
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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 (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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))))) a (f i)))
 but is expected to have type
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i))) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (f i)))
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr NNReal.mul_supᵢₓ'. -/
-theorem mul_supᵢ (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i :=
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (f i)))
+Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr NNReal.mul_iSupₓ'. -/
+theorem mul_iSup (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i :=
   by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_supᵢ, NNReal.coe_supᵢ]
-  exact Real.mul_supᵢ_of_nonneg (NNReal.coe_nonneg _) _
-#align nnreal.mul_supr NNReal.mul_supᵢ
+  rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
+  exact Real.mul_iSup_of_nonneg (NNReal.coe_nonneg _) _
+#align nnreal.mul_supr NNReal.mul_iSup
 
-/- warning: nnreal.supr_mul -> NNReal.supᵢ_mul is a dubious translation:
+/- warning: nnreal.supr_mul -> NNReal.iSup_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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))))) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) a) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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) a))
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) 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) a))
 but is expected to have type
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul NNReal.supᵢ_mulₓ'. -/
-theorem supᵢ_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a :=
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (f i) a))
+Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul NNReal.iSup_mulₓ'. -/
+theorem iSup_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a :=
   by
   rw [mul_comm, mul_supr]
   simp_rw [mul_comm]
-#align nnreal.supr_mul NNReal.supᵢ_mul
+#align nnreal.supr_mul NNReal.iSup_mul
 
-/- warning: nnreal.supr_div -> NNReal.supᵢ_div is a dubious translation:
+/- warning: nnreal.supr_div -> NNReal.iSup_div is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) a) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f i) a))
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f i) a))
 but is expected to have type
-  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) a))
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_div NNReal.supᵢ_divₓ'. -/
-theorem supᵢ_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i, f i / a := by
+  forall {ι : Sort.{u1}} (f : ι -> NNReal) (a : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => f i)) a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) a))
+Case conversion may be inaccurate. Consider using '#align nnreal.supr_div NNReal.iSup_divₓ'. -/
+theorem iSup_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i, f i / a := by
   simp only [div_eq_mul_inv, supr_mul]
-#align nnreal.supr_div NNReal.supᵢ_div
+#align nnreal.supr_div NNReal.iSup_div
 
 variable [Nonempty ι]
 
-/- warning: nnreal.le_mul_infi -> NNReal.le_mul_infᵢ is a dubious translation:
+/- warning: nnreal.le_mul_infi -> NNReal.le_mul_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
 but is expected to have type
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_mul_infi NNReal.le_mul_infᵢₓ'. -/
-theorem le_mul_infᵢ {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * infᵢ h :=
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) g (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
+Case conversion may be inaccurate. Consider using '#align nnreal.le_mul_infi NNReal.le_mul_iInfₓ'. -/
+theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * iInf h :=
   by
   rw [mul_infi]
-  exact le_cinfᵢ H
-#align nnreal.le_mul_infi NNReal.le_mul_infᵢ
+  exact le_ciInf H
+#align nnreal.le_mul_infi NNReal.le_mul_iInf
 
-/- warning: nnreal.mul_supr_le -> NNReal.mul_supᵢ_le is a dubious translation:
+/- warning: nnreal.mul_supr_le -> NNReal.mul_iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) g (h j)) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) g (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : NNReal} {h : ι -> NNReal}, (forall (j : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) g (h j)) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) g (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
 but is expected to have type
-  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι), 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 (g ᾰ)) _inst_1) -> (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 (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
-Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr_le NNReal.mul_supᵢ_leₓ'. -/
-theorem mul_supᵢ_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * supᵢ h ≤ a :=
+  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι), 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 (g ᾰ)) _inst_1) -> (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 (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
+Case conversion may be inaccurate. Consider using '#align nnreal.mul_supr_le NNReal.mul_iSup_leₓ'. -/
+theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a :=
   by
   rw [mul_supr]
-  exact csupᵢ_le H
-#align nnreal.mul_supr_le NNReal.mul_supᵢ_le
+  exact ciSup_le H
+#align nnreal.mul_supr_le NNReal.mul_iSup_le
 
-/- warning: nnreal.le_infi_mul -> NNReal.le_infᵢ_mul is a dubious translation:
+/- warning: nnreal.le_infi_mul -> NNReal.le_iInf_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h))
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h))
 but is expected to have type
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) h))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul NNReal.le_infᵢ_mulₓ'. -/
-theorem le_infᵢ_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ infᵢ g * h :=
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) h)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) h))
+Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul NNReal.le_iInf_mulₓ'. -/
+theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ iInf g * h :=
   by
   rw [infi_mul]
-  exact le_cinfᵢ H
-#align nnreal.le_infi_mul NNReal.le_infᵢ_mul
+  exact le_ciInf H
+#align nnreal.le_infi_mul NNReal.le_iInf_mul
 
-/- warning: nnreal.supr_mul_le -> NNReal.supᵢ_mul_le is a dubious translation:
+/- warning: nnreal.supr_mul_le -> NNReal.iSup_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) (g i) h) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h) a)
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : NNReal}, (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) (g i) h) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) h) a)
 but is expected to have type
-  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : NNReal}, (forall (i : ι), 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 i) g) _inst_1) -> (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)) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) g) _inst_1)
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_le NNReal.supᵢ_mul_leₓ'. -/
-theorem supᵢ_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : supᵢ g * h ≤ a :=
+  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : NNReal}, (forall (i : ι), 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 i) g) _inst_1) -> (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)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) g) _inst_1)
+Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_le NNReal.iSup_mul_leₓ'. -/
+theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a :=
   by
   rw [supr_mul]
-  exact csupᵢ_le H
-#align nnreal.supr_mul_le NNReal.supᵢ_mul_le
+  exact ciSup_le H
+#align nnreal.supr_mul_le NNReal.iSup_mul_le
 
-/- warning: nnreal.le_infi_mul_infi -> NNReal.le_infᵢ_mul_infᵢ is a dubious translation:
+/- warning: nnreal.le_infi_mul_infi -> NNReal.le_iInf_mul_iInf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (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))))) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toHasInf.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)))
 but is expected to have type
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) (infᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
-Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul_infi NNReal.le_infᵢ_mul_infᵢₓ'. -/
-theorem le_infᵢ_mul_infᵢ {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a ≤ g i * h j) :
-    a ≤ infᵢ g * infᵢ h :=
-  le_infᵢ_mul fun i => le_mul_infᵢ <| H i
-#align nnreal.le_infi_mul_infi NNReal.le_infᵢ_mul_infᵢ
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (g i) (h j))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g) (iInf.{0, u1} NNReal (ConditionallyCompleteLattice.toInfSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι h)))
+Case conversion may be inaccurate. Consider using '#align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInfₓ'. -/
+theorem le_iInf_mul_iInf {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a ≤ g i * h j) :
+    a ≤ iInf g * iInf h :=
+  le_iInf_mul fun i => le_mul_iInf <| H i
+#align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInf
 
-/- warning: nnreal.supr_mul_supr_le -> NNReal.supᵢ_mul_supᵢ_le is a dubious translation:
+/- warning: nnreal.supr_mul_supr_le -> NNReal.iSup_mul_iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) (g i) (h j)) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
+  forall {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] {a : NNReal} {g : ι -> NNReal} {h : ι -> NNReal}, (forall (i : ι) (j : ι), LE.le.{0} NNReal (Preorder.toLE.{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))))) (g i) (h j)) a) -> (LE.le.{0} NNReal (Preorder.toLE.{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))))) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι g) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) ι h)) a)
 but is expected to have type
-  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι) (j : ι), 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 ᾰ) (g j)) _inst_1) -> (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)) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) (supᵢ.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
-Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_supr_le NNReal.supᵢ_mul_supᵢ_leₓ'. -/
-theorem supᵢ_mul_supᵢ_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
-    supᵢ g * supᵢ h ≤ a :=
-  supᵢ_mul_le fun i => mul_supᵢ_le <| H _
-#align nnreal.supr_mul_supr_le NNReal.supᵢ_mul_supᵢ_le
+  forall {ι : Sort.{u1}} {_inst_1 : NNReal} {a : ι -> NNReal} {g : ι -> NNReal}, (forall (ᾰ : ι) (j : ι), 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 ᾰ) (g j)) _inst_1) -> (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)) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι a) (iSup.{0, u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) ι g)) _inst_1)
+Case conversion may be inaccurate. Consider using '#align nnreal.supr_mul_supr_le NNReal.iSup_mul_iSup_leₓ'. -/
+theorem iSup_mul_iSup_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
+    iSup g * iSup h ≤ a :=
+  iSup_mul_le fun i => mul_iSup_le <| H _
+#align nnreal.supr_mul_supr_le NNReal.iSup_mul_iSup_le
 
 end Csupr

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -402,7 +402,7 @@ def toRealHom : ℝ≥0 →+* ℝ :=
 lean 3 declaration is
   Eq.{1} (NNReal -> Real) (coeFn.{1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => NNReal -> Real) (RingHom.hasCoeToFun.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) NNReal.toRealHom) ((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))))
 but is expected to have type
-  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) NNReal.toRealHom) NNReal.toReal
+  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) NNReal.toRealHom) NNReal.toReal
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_to_real_hom NNReal.coe_toRealHomₓ'. -/
 @[simp]
 theorem coe_toRealHom : ⇑toRealHom = coe :=
@@ -893,7 +893,7 @@ example : Archimedean ℝ≥0 := by infer_instance
 lean 3 declaration is
   CovariantClass.{0, 0} NNReal 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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4048 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4050 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4048 x._@.Mathlib.Data.Real.NNReal._hyg.4050) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4063 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4065 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4063 x._@.Mathlib.Data.Real.NNReal._hyg.4065)
+  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4044 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4046 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4044 x._@.Mathlib.Data.Real.NNReal._hyg.4046) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4059 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4061 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4059 x._@.Mathlib.Data.Real.NNReal._hyg.4061)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_add NNReal.covariant_addₓ'. -/
 -- TODO: why are these three instances necessary? why aren't they inferred?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
@@ -904,7 +904,7 @@ instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
 lean 3 declaration is
   ContravariantClass.{0, 0} NNReal 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)))))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4088 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4090 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4088 x._@.Mathlib.Data.Real.NNReal._hyg.4090) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4103 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4105 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4103 x._@.Mathlib.Data.Real.NNReal._hyg.4105)
+  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4084 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4086 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4084 x._@.Mathlib.Data.Real.NNReal._hyg.4086) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4099 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4101 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4099 x._@.Mathlib.Data.Real.NNReal._hyg.4101)
 Case conversion may be inaccurate. Consider using '#align nnreal.contravariant_add NNReal.contravariant_addₓ'. -/
 instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· < ·) :=
   OrderedCancelAddCommMonoid.to_contravariantClass_left ℝ≥0
@@ -914,7 +914,7 @@ instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· <
 lean 3 declaration is
   CovariantClass.{0, 0} NNReal NNReal (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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4128 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4130 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4128 x._@.Mathlib.Data.Real.NNReal._hyg.4130) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4143 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4145 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4143 x._@.Mathlib.Data.Real.NNReal._hyg.4145)
+  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4124 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4126 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4124 x._@.Mathlib.Data.Real.NNReal._hyg.4126) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4139 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4141 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4139 x._@.Mathlib.Data.Real.NNReal._hyg.4141)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_mul NNReal.covariant_mulₓ'. -/
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
   OrderedCommMonoid.to_covariantClass_left ℝ≥0
@@ -2055,7 +2055,7 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 lean 3 declaration is
   forall (x : Real), Eq.{1} Real ((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))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
 but is expected to have type
-  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
+  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
 Case conversion may be inaccurate. Consider using '#align real.coe_nnabs Real.coe_nnabsₓ'. -/
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
@@ -2066,7 +2066,7 @@ theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
 lean 3 declaration is
   forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x) (Real.toNNReal x))
 but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
 Case conversion may be inaccurate. Consider using '#align real.nnabs_of_nonneg Real.nnabs_of_nonnegₓ'. -/
 @[simp]
 theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
@@ -2079,7 +2079,7 @@ theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
 lean 3 declaration is
   forall (x : NNReal), Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((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))) x)) x
 but is expected to have type
-  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
+  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
 Case conversion may be inaccurate. Consider using '#align real.nnabs_coe Real.nnabs_coeₓ'. -/
 theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 #align real.nnabs_coe Real.nnabs_coe
@@ -2098,7 +2098,7 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 lean 3 declaration is
   forall (n : Int), Eq.{1} NNReal ((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))))))) (Int.natAbs n)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
+  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
 Case conversion may be inaccurate. Consider using '#align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_castₓ'. -/
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n :=
   by

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -893,7 +893,7 @@ example : Archimedean ℝ≥0 := by infer_instance
 lean 3 declaration is
   CovariantClass.{0, 0} NNReal 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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4050 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4052 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4050 x._@.Mathlib.Data.Real.NNReal._hyg.4052) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4065 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4067 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4065 x._@.Mathlib.Data.Real.NNReal._hyg.4067)
+  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4048 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4050 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4048 x._@.Mathlib.Data.Real.NNReal._hyg.4050) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4063 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4065 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4063 x._@.Mathlib.Data.Real.NNReal._hyg.4065)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_add NNReal.covariant_addₓ'. -/
 -- TODO: why are these three instances necessary? why aren't they inferred?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
@@ -904,7 +904,7 @@ instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
 lean 3 declaration is
   ContravariantClass.{0, 0} NNReal 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)))))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4090 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4092 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4090 x._@.Mathlib.Data.Real.NNReal._hyg.4092) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4105 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4107 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4105 x._@.Mathlib.Data.Real.NNReal._hyg.4107)
+  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4088 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4090 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4088 x._@.Mathlib.Data.Real.NNReal._hyg.4090) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4103 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4105 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4103 x._@.Mathlib.Data.Real.NNReal._hyg.4105)
 Case conversion may be inaccurate. Consider using '#align nnreal.contravariant_add NNReal.contravariant_addₓ'. -/
 instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· < ·) :=
   OrderedCancelAddCommMonoid.to_contravariantClass_left ℝ≥0
@@ -914,7 +914,7 @@ instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· <
 lean 3 declaration is
   CovariantClass.{0, 0} NNReal NNReal (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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4130 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4132 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4130 x._@.Mathlib.Data.Real.NNReal._hyg.4132) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4145 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4147 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4145 x._@.Mathlib.Data.Real.NNReal._hyg.4147)
+  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4128 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4130 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4128 x._@.Mathlib.Data.Real.NNReal._hyg.4130) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4143 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4145 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4143 x._@.Mathlib.Data.Real.NNReal._hyg.4145)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_mul NNReal.covariant_mulₓ'. -/
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
   OrderedCommMonoid.to_covariantClass_left ℝ≥0

bump to nightly-2023-04-20-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

fbfe5c3e

Diff

@@ -768,7 +768,7 @@ def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a
 lean 3 declaration is
   forall (a : NNReal) (b : coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))))) (coeFn.{1, 1} (OrderIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))))) (fun (_x : RelIso.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) => (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (RelIso.hasCoeToFun.{0, 0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))) (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))))) (OrderIso.symm.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a))) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ((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))) a)))) (Subtype.hasLe.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a))) (NNReal.orderIsoIccZeroCoe a)) b)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) Real (coeTrans.{1, 1, 1} (coeSort.{1, 2} (Set.{0} NNReal) Type (Set.hasCoeToSort.{0} NNReal) (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)) NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe) (coeSubtype.{1} NNReal (fun (x : NNReal) => Membership.Mem.{0, 0} NNReal (Set.{0} NNReal) (Set.hasMem.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))) a)))))) b)
 but is expected to have type
-  forall (a : NNReal) (b : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (fun (_x : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))))) (RelEmbedding.toEmbedding.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) (NNReal.orderIsoIccZeroCoe a)))) b)) (NNReal.toReal (Subtype.val.{1} NNReal (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) b))
+  forall (a : NNReal) (b : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (fun (_x : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) => LE.le.{0} (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) => LE.le.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{0, 0} (Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a))) (Set.Elem.{0} NNReal (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (NNReal.toReal a)))) (Subtype.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a))) (NNReal.orderIsoIccZeroCoe a)) b)) (NNReal.toReal (Subtype.val.{1} NNReal (fun (x : NNReal) => Membership.mem.{0, 0} NNReal (Set.{0} NNReal) (Set.instMembershipSet.{0} NNReal) x (Set.Iic.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring)) a)) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.order_iso_Icc_zero_coe_symm_apply_coe NNReal.orderIsoIccZeroCoe_symm_apply_coeₓ'. -/
 @[simp]
 theorem orderIsoIccZeroCoe_symm_apply_coe (a : ℝ≥0) (b : Set.Iic a) :

bump to nightly-2023-04-16-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b

63127953

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit b3f4f007a962e3787aa0f3b5c7942a1317f7d88e
+! leanprover-community/mathlib commit de29c328903507bb7aff506af9135f4bdaf1849c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1430,7 +1430,7 @@ theorem coe_sub_def {r p : ℝ≥0} : ↑(r - p) = max (r - p : ℝ) 0 :=
   rfl
 #align nnreal.coe_sub_def NNReal.coe_sub_def
 
-noncomputable example : OrderedSub ℝ≥0 := by infer_instance
+example : OrderedSub ℝ≥0 := by infer_instance
 
 /- warning: nnreal.sub_div -> NNReal.sub_div is a dubious translation:
 lean 3 declaration is

bump to nightly-2023-03-17-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

624c906c

Diff

@@ -536,7 +536,7 @@ theorem coe_list_prod (l : List ℝ≥0) : ((l.Prod : ℝ≥0) : ℝ) = (l.map c
 lean 3 declaration is
   forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.sum.{0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s)) (Multiset.sum.{0} Real Real.addCommMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
 but is expected to have type
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.sum.{0} NNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s)) (Multiset.sum.{0} Real Real.instAddCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
+  forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.sum.{0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s)) (Multiset.sum.{0} Real Real.instAddCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_multiset_sum NNReal.coe_multiset_sumₓ'. -/
 @[norm_cast]
 theorem coe_multiset_sum (s : Multiset ℝ≥0) : ((s.Sum : ℝ≥0) : ℝ) = (s.map coe).Sum :=
@@ -547,7 +547,7 @@ theorem coe_multiset_sum (s : Multiset ℝ≥0) : ((s.Sum : ℝ≥0) : ℝ) = (s
 lean 3 declaration is
   forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.prod.{0} NNReal (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s)) (Multiset.prod.{0} Real Real.commMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
 but is expected to have type
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.prod.{0} NNReal (CommSemiring.toCommMonoid.{0} NNReal instNNRealCommSemiring) s)) (Multiset.prod.{0} Real Real.instCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
+  forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.prod.{0} NNReal (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s)) (Multiset.prod.{0} Real Real.instCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_multiset_prod NNReal.coe_multiset_prodₓ'. -/
 @[norm_cast]
 theorem coe_multiset_prod (s : Multiset ℝ≥0) : ((s.Prod : ℝ≥0) : ℝ) = (s.map coe).Prod :=
@@ -558,7 +558,7 @@ theorem coe_multiset_prod (s : Multiset ℝ≥0) : ((s.Prod : ℝ≥0) : ℝ) =
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => (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))) (f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.sum.{0, u1} NNReal α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_sum NNReal.coe_sumₓ'. -/
 @[norm_cast]
 theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a) = ∑ a in s, (f a : ℝ) :=
@@ -569,7 +569,7 @@ theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a)
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (a : α) => Real.toNNReal (f a))))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonnegₓ'. -/
 theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∑ a in s, f a) = ∑ a in s, Real.toNNReal (f a) :=
@@ -582,7 +582,7 @@ theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf :
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.prod.{0, u1} NNReal α (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => (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))) (f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.prod.{0, u1} NNReal α (CommSemiring.toCommMonoid.{0} NNReal instNNRealCommSemiring) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.prod.{0, u1} NNReal α (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_prod NNReal.coe_prodₓ'. -/
 @[norm_cast]
 theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a) = ∏ a in s, (f a : ℝ) :=
@@ -593,7 +593,7 @@ theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (CommSemiring.toCommMonoid.{0} NNReal instNNRealCommSemiring) s (fun (a : α) => Real.toNNReal (f a))))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (LinearOrderedCommMonoid.toCommMonoid.{0} NNReal (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{0} NNReal (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedCommGroupWithZero.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)))) s (fun (a : α) => Real.toNNReal (f a))))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonnegₓ'. -/
 theorem Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∏ a in s, f a) = ∏ a in s, Real.toNNReal (f a) :=
@@ -952,7 +952,7 @@ theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
 lean 3 declaration is
   Eq.{1} NNReal (Bot.bot.{0} NNReal (ConditionallyCompleteLinearOrderBot.toHasBot.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
 but is expected to have type
-  Eq.{1} NNReal (Bot.bot.{0} NNReal (CanonicallyOrderedAddMonoid.toBot.{0} NNReal (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} NNReal instNNRealCanonicallyOrderedCommSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
+  Eq.{1} NNReal (Bot.bot.{0} NNReal (ConditionallyCompleteLinearOrderBot.toBot.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal)) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
 Case conversion may be inaccurate. Consider using '#align nnreal.bot_eq_zero NNReal.bot_eq_zeroₓ'. -/
 theorem bot_eq_zero : (⊥ : ℝ≥0) = 0 :=
   rfl
@@ -1450,7 +1450,7 @@ section Inv
 lean 3 declaration is
   forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f i) b))
 but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (Finset.sum.{0, u1} NNReal ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) b))
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.sum_div NNReal.sum_divₓ'. -/
 theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
     (∑ i in s, f i) / b = ∑ i in s, f i / b :=

bump to nightly-2023-03-17-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

e4251446

Diff

@@ -4,15 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
+! leanprover-community/mathlib commit b3f4f007a962e3787aa0f3b5c7942a1317f7d88e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Order.ConditionallyCompleteLattice.Group
 import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Algebra.Order.Nonneg.Field
 import Mathbin.Algebra.Order.Field.Canonical.Basic
+import Mathbin.Algebra.Order.Nonneg.Field
+import Mathbin.Algebra.Order.Nonneg.Floor
 import Mathbin.Data.Real.Pointwise
+import Mathbin.Order.ConditionallyCompleteLattice.Group
 import Mathbin.Tactic.Positivity
 
 /-!
@@ -533,7 +534,7 @@ theorem coe_list_prod (l : List ℝ≥0) : ((l.Prod : ℝ≥0) : ℝ) = (l.map c
 
 /- warning: nnreal.coe_multiset_sum -> NNReal.coe_multiset_sum is a dubious translation:
 lean 3 declaration is
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.sum.{0} NNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) s)) (Multiset.sum.{0} Real Real.addCommMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
+  forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.sum.{0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s)) (Multiset.sum.{0} Real Real.addCommMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
 but is expected to have type
   forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.sum.{0} NNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s)) (Multiset.sum.{0} Real Real.instAddCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_multiset_sum NNReal.coe_multiset_sumₓ'. -/
@@ -544,7 +545,7 @@ theorem coe_multiset_sum (s : Multiset ℝ≥0) : ((s.Sum : ℝ≥0) : ℝ) = (s
 
 /- warning: nnreal.coe_multiset_prod -> NNReal.coe_multiset_prod is a dubious translation:
 lean 3 declaration is
-  forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.prod.{0} NNReal (CommSemiring.toCommMonoid.{0} NNReal NNReal.commSemiring) s)) (Multiset.prod.{0} Real Real.commMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
+  forall (s : Multiset.{0} NNReal), Eq.{1} Real ((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))) (Multiset.prod.{0} NNReal (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s)) (Multiset.prod.{0} Real Real.commMonoid (Multiset.map.{0, 0} NNReal Real ((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)))) s))
 but is expected to have type
   forall (s : Multiset.{0} NNReal), Eq.{1} Real (NNReal.toReal (Multiset.prod.{0} NNReal (CommSemiring.toCommMonoid.{0} NNReal instNNRealCommSemiring) s)) (Multiset.prod.{0} Real Real.instCommMonoidReal (Multiset.map.{0, 0} NNReal Real NNReal.toReal s))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_multiset_prod NNReal.coe_multiset_prodₓ'. -/
@@ -555,7 +556,7 @@ theorem coe_multiset_prod (s : Multiset ℝ≥0) : ((s.Prod : ℝ≥0) : ℝ) =
 
 /- warning: nnreal.coe_sum -> NNReal.coe_sum is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.sum.{0, u1} NNReal α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => (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))) (f a)))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => (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))) (f a)))
 but is expected to have type
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.sum.{0, u1} NNReal α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (a : α) => f a))) (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_sum NNReal.coe_sumₓ'. -/
@@ -566,7 +567,7 @@ theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a)
 
 /- warning: real.to_nnreal_sum_of_nonneg -> Real.toNNReal_sum_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) s (fun (a : α) => Real.toNNReal (f a))))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
 but is expected to have type
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (a : α) => f a))) (Finset.sum.{0, u1} NNReal α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (a : α) => Real.toNNReal (f a))))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonnegₓ'. -/
@@ -579,7 +580,7 @@ theorem Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ} (hf :
 
 /- warning: nnreal.coe_prod -> NNReal.coe_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.prod.{0, u1} NNReal α (CommSemiring.toCommMonoid.{0} NNReal NNReal.commSemiring) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => (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))) (f a)))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real ((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))) (Finset.prod.{0, u1} NNReal α (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => (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))) (f a)))
 but is expected to have type
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> NNReal}, Eq.{1} Real (NNReal.toReal (Finset.prod.{0, u1} NNReal α (CommSemiring.toCommMonoid.{0} NNReal instNNRealCommSemiring) s (fun (a : α) => f a))) (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => NNReal.toReal (f a)))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_prod NNReal.coe_prodₓ'. -/
@@ -590,7 +591,7 @@ theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a
 
 /- warning: real.to_nnreal_prod_of_nonneg -> Real.toNNReal_prod_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (CommSemiring.toCommMonoid.{0} NNReal NNReal.commSemiring) s (fun (a : α) => Real.toNNReal (f a))))
+  forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.Mem.{u1, u1} α (Finset.{u1} α) (Finset.hasMem.{u1} α) a s) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (OrderedCommMonoid.toCommMonoid.{0} NNReal (CanonicallyOrderedCommSemiring.toOrderedCommMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring)) s (fun (a : α) => Real.toNNReal (f a))))
 but is expected to have type
   forall {α : Type.{u1}} {s : Finset.{u1} α} {f : α -> Real}, (forall (a : α), (Membership.mem.{u1, u1} α (Finset.{u1} α) (Finset.instMembershipFinset.{u1} α) a s) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f a))) -> (Eq.{1} NNReal (Real.toNNReal (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (a : α) => f a))) (Finset.prod.{0, u1} NNReal α (CommSemiring.toCommMonoid.{0} NNReal instNNRealCommSemiring) s (fun (a : α) => Real.toNNReal (f a))))
 Case conversion may be inaccurate. Consider using '#align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonnegₓ'. -/
@@ -949,7 +950,7 @@ theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
 
 /- warning: nnreal.bot_eq_zero -> NNReal.bot_eq_zero is a dubious translation:
 lean 3 declaration is
-  Eq.{1} NNReal (Bot.bot.{0} NNReal (CanonicallyOrderedAddMonoid.toHasBot.{0} NNReal (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} NNReal NNReal.canonicallyOrderedCommSemiring))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
+  Eq.{1} NNReal (Bot.bot.{0} NNReal (ConditionallyCompleteLinearOrderBot.toHasBot.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
 but is expected to have type
   Eq.{1} NNReal (Bot.bot.{0} NNReal (CanonicallyOrderedAddMonoid.toBot.{0} NNReal (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} NNReal instNNRealCanonicallyOrderedCommSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
 Case conversion may be inaccurate. Consider using '#align nnreal.bot_eq_zero NNReal.bot_eq_zeroₓ'. -/
@@ -1011,7 +1012,7 @@ theorem finset_sup_div {α} {f : α → ℝ≥0} {s : Finset α} (r : ℝ≥0) :
 
 /- warning: nnreal.coe_max -> NNReal.coe_max is a dubious translation:
 lean 3 declaration is
-  forall (x : NNReal) (y : NNReal), Eq.{1} Real ((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))) (LinearOrder.max.{0} NNReal (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{0} NNReal (CanonicallyLinearOrderedSemifield.toCanonicallyLinearOrderedAddMonoid.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)) x y)) (LinearOrder.max.{0} Real Real.linearOrder ((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))) x) ((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))) y))
+  forall (x : NNReal) (y : NNReal), Eq.{1} Real ((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))) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) x y)) (LinearOrder.max.{0} Real Real.linearOrder ((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))) x) ((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))) y))
 but is expected to have type
   forall (x : NNReal) (y : NNReal), Eq.{1} Real (NNReal.toReal (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x y)) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (NNReal.toReal x) (NNReal.toReal y))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_max NNReal.coe_maxₓ'. -/
@@ -1022,7 +1023,7 @@ theorem coe_max (x y : ℝ≥0) : ((max x y : ℝ≥0) : ℝ) = max (x : ℝ) (y
 
 /- warning: nnreal.coe_min -> NNReal.coe_min is a dubious translation:
 lean 3 declaration is
-  forall (x : NNReal) (y : NNReal), Eq.{1} Real ((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))) (LinearOrder.min.{0} NNReal (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{0} NNReal (CanonicallyLinearOrderedSemifield.toCanonicallyLinearOrderedAddMonoid.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)) x y)) (LinearOrder.min.{0} Real Real.linearOrder ((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))) x) ((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))) y))
+  forall (x : NNReal) (y : NNReal), Eq.{1} Real ((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))) (LinearOrder.min.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) x y)) (LinearOrder.min.{0} Real Real.linearOrder ((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))) x) ((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))) y))
 but is expected to have type
   forall (x : NNReal) (y : NNReal), Eq.{1} Real (NNReal.toReal (Min.min.{0} NNReal (CanonicallyLinearOrderedSemifield.toMin.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x y)) (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (NNReal.toReal x) (NNReal.toReal y))
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_min NNReal.coe_minₓ'. -/
@@ -1447,7 +1448,7 @@ section Inv
 
 /- warning: nnreal.sum_div -> NNReal.sum_div is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (Finset.sum.{0, u1} NNReal ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f i) b))
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (f i) b))
 but is expected to have type
   forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> NNReal) (b : NNReal), Eq.{1} NNReal (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (Finset.sum.{0, u1} NNReal ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (i : ι) => f i)) b) (Finset.sum.{0, u1} NNReal ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) s (fun (i : ι) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (f i) b))
 Case conversion may be inaccurate. Consider using '#align nnreal.sum_div NNReal.sum_divₓ'. -/

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -401,7 +401,7 @@ def toRealHom : ℝ≥0 →+* ℝ :=
 lean 3 declaration is
   Eq.{1} (NNReal -> Real) (coeFn.{1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => NNReal -> Real) (RingHom.hasCoeToFun.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) NNReal.toRealHom) ((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))))
 but is expected to have type
-  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) NNReal.toRealHom) NNReal.toReal
+  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) NNReal.toRealHom) NNReal.toReal
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_to_real_hom NNReal.coe_toRealHomₓ'. -/
 @[simp]
 theorem coe_toRealHom : ⇑toRealHom = coe :=
@@ -892,7 +892,7 @@ example : Archimedean ℝ≥0 := by infer_instance
 lean 3 declaration is
   CovariantClass.{0, 0} NNReal 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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4047 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4049 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4047 x._@.Mathlib.Data.Real.NNReal._hyg.4049) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4062 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4064 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4062 x._@.Mathlib.Data.Real.NNReal._hyg.4064)
+  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4050 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4052 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4050 x._@.Mathlib.Data.Real.NNReal._hyg.4052) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4065 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4067 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4065 x._@.Mathlib.Data.Real.NNReal._hyg.4067)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_add NNReal.covariant_addₓ'. -/
 -- TODO: why are these three instances necessary? why aren't they inferred?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
@@ -903,7 +903,7 @@ instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) :=
 lean 3 declaration is
   ContravariantClass.{0, 0} NNReal 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)))))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4087 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4089 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4087 x._@.Mathlib.Data.Real.NNReal._hyg.4089) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4102 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4104 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4102 x._@.Mathlib.Data.Real.NNReal._hyg.4104)
+  ContravariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4090 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4092 : 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))))) x._@.Mathlib.Data.Real.NNReal._hyg.4090 x._@.Mathlib.Data.Real.NNReal._hyg.4092) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4105 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4107 : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4105 x._@.Mathlib.Data.Real.NNReal._hyg.4107)
 Case conversion may be inaccurate. Consider using '#align nnreal.contravariant_add NNReal.contravariant_addₓ'. -/
 instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· < ·) :=
   OrderedCancelAddCommMonoid.to_contravariantClass_left ℝ≥0
@@ -913,7 +913,7 @@ instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· <
 lean 3 declaration is
   CovariantClass.{0, 0} NNReal NNReal (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)))))) (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))))
 but is expected to have type
-  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4127 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4129 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4127 x._@.Mathlib.Data.Real.NNReal._hyg.4129) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4142 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4144 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4142 x._@.Mathlib.Data.Real.NNReal._hyg.4144)
+  CovariantClass.{0, 0} NNReal NNReal (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4130 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4132 : NNReal) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) x._@.Mathlib.Data.Real.NNReal._hyg.4130 x._@.Mathlib.Data.Real.NNReal._hyg.4132) (fun (x._@.Mathlib.Data.Real.NNReal._hyg.4145 : NNReal) (x._@.Mathlib.Data.Real.NNReal._hyg.4147 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.Data.Real.NNReal._hyg.4145 x._@.Mathlib.Data.Real.NNReal._hyg.4147)
 Case conversion may be inaccurate. Consider using '#align nnreal.covariant_mul NNReal.covariant_mulₓ'. -/
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) :=
   OrderedCommMonoid.to_covariantClass_left ℝ≥0
@@ -934,7 +934,7 @@ theorem le_of_forall_pos_le_add {a b : ℝ≥0} (h : ∀ ε, 0 < ε → a ≤ b
 lean 3 declaration is
   forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.hasLe (OfNat.ofNat.{0} Rat 0 (OfNat.mk.{0} Rat 0 (Zero.zero.{0} Rat Rat.hasZero))) q) (And (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Real.toNNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q)) b))))
 but is expected to have type
-  forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.instLERat (OfNat.ofNat.{0} Rat 0 (Rat.instOfNatRat 0)) q) (And (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (Real.toNNReal (RatCast.ratCast.{0} Real Real.ratCast q))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal (RatCast.ratCast.{0} Real Real.ratCast q)) b))))
+  forall (a : NNReal) (b : NNReal), Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a b) (Exists.{1} Rat (fun (q : Rat) => And (LE.le.{0} Rat Rat.instLERat (OfNat.ofNat.{0} Rat 0 (Rat.instOfNatRat 0)) q) (And (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) a (Real.toNNReal (Rat.cast.{0} Real Real.ratCast q))) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Real.toNNReal (Rat.cast.{0} Real Real.ratCast q)) b))))
 Case conversion may be inaccurate. Consider using '#align nnreal.lt_iff_exists_rat_btwn NNReal.lt_iff_exists_rat_btwnₓ'. -/
 theorem lt_iff_exists_rat_btwn (a b : ℝ≥0) :
     a < b ↔ ∃ q : ℚ, 0 ≤ q ∧ a < Real.toNNReal q ∧ Real.toNNReal q < b :=
@@ -2054,7 +2054,7 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 lean 3 declaration is
   forall (x : Real), Eq.{1} Real ((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))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
 but is expected to have type
-  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
+  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
 Case conversion may be inaccurate. Consider using '#align real.coe_nnabs Real.coe_nnabsₓ'. -/
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
@@ -2065,7 +2065,7 @@ theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
 lean 3 declaration is
   forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x) (Real.toNNReal x))
 but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
 Case conversion may be inaccurate. Consider using '#align real.nnabs_of_nonneg Real.nnabs_of_nonnegₓ'. -/
 @[simp]
 theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
@@ -2078,7 +2078,7 @@ theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
 lean 3 declaration is
   forall (x : NNReal), Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((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))) x)) x
 but is expected to have type
-  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
+  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
 Case conversion may be inaccurate. Consider using '#align real.nnabs_coe Real.nnabs_coeₓ'. -/
 theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 #align real.nnabs_coe Real.nnabs_coe
@@ -2097,7 +2097,7 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 lean 3 declaration is
   forall (n : Int), Eq.{1} NNReal ((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))))))) (Int.natAbs n)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
+  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
 Case conversion may be inaccurate. Consider using '#align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_castₓ'. -/
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n :=
   by

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -985,7 +985,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align nnreal.mul_finset_sup NNReal.mul_finset_supₓ'. -/
 theorem mul_finset_sup {α} (r : ℝ≥0) (s : Finset α) (f : α → ℝ≥0) :
     r * s.sup f = s.sup fun a => r * f a :=
-  Finset.comp_sup_eq_sup_comp _ (NNReal.mul_sup r) (mul_zero r)
+  Finset.comp_sup_eq_sup_comp _ (NNReal.mul_sup r) (MulZeroClass.mul_zero r)
 #align nnreal.mul_finset_sup NNReal.mul_finset_sup
 
 /- warning: nnreal.finset_sup_mul -> NNReal.finset_sup_mul is a dubious translation:
@@ -996,7 +996,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align nnreal.finset_sup_mul NNReal.finset_sup_mulₓ'. -/
 theorem finset_sup_mul {α} (s : Finset α) (f : α → ℝ≥0) (r : ℝ≥0) :
     s.sup f * r = s.sup fun a => f a * r :=
-  Finset.comp_sup_eq_sup_comp (· * r) (fun x y => NNReal.sup_mul x y r) (zero_mul r)
+  Finset.comp_sup_eq_sup_comp (· * r) (fun x y => NNReal.sup_mul x y r) (MulZeroClass.zero_mul r)
 #align nnreal.finset_sup_mul NNReal.finset_sup_mul
 
 /- warning: nnreal.finset_sup_div -> NNReal.finset_sup_div is a dubious translation:
@@ -1343,7 +1343,7 @@ theorem Real.toNNReal_mul {p q : ℝ} (hp : 0 ≤ p) :
   · apply NNReal.eq
     simp [Real.toNNReal, hp, hq, max_eq_left, mul_nonneg]
   · have hpq := mul_nonpos_of_nonneg_of_nonpos hp hq
-    rw [to_nnreal_eq_zero.2 hq, to_nnreal_eq_zero.2 hpq, mul_zero]
+    rw [to_nnreal_eq_zero.2 hq, to_nnreal_eq_zero.2 hpq, MulZeroClass.mul_zero]
 #align real.to_nnreal_mul Real.toNNReal_mul
 
 end Mul

bump to nightly-2023-03-08-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

10f15343

Diff

@@ -401,7 +401,7 @@ def toRealHom : ℝ≥0 →+* ℝ :=
 lean 3 declaration is
   Eq.{1} (NNReal -> Real) (coeFn.{1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => NNReal -> Real) (RingHom.hasCoeToFun.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) NNReal.toRealHom) ((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))))
 but is expected to have type
-  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) NNReal.toRealHom) NNReal.toReal
+  Eq.{1} (forall (ᾰ : NNReal), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : NNReal) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal (fun (_x : NNReal) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : NNReal) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonUnitalNonAssocSemiring.toMul.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} NNReal Real (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) NNReal.toRealHom) NNReal.toReal
 Case conversion may be inaccurate. Consider using '#align nnreal.coe_to_real_hom NNReal.coe_toRealHomₓ'. -/
 @[simp]
 theorem coe_toRealHom : ⇑toRealHom = coe :=
@@ -2054,7 +2054,7 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 lean 3 declaration is
   forall (x : Real), Eq.{1} Real ((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))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
 but is expected to have type
-  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
+  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
 Case conversion may be inaccurate. Consider using '#align real.coe_nnabs Real.coe_nnabsₓ'. -/
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
@@ -2065,7 +2065,7 @@ theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
 lean 3 declaration is
   forall {x : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x) (Real.toNNReal x))
 but is expected to have type
-  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
+  forall {x : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x) (Real.toNNReal x))
 Case conversion may be inaccurate. Consider using '#align real.nnabs_of_nonneg Real.nnabs_of_nonnegₓ'. -/
 @[simp]
 theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
@@ -2078,7 +2078,7 @@ theorem nnabs_of_nonneg {x : ℝ} (h : 0 ≤ x) : nnabs x = toNNReal x :=
 lean 3 declaration is
   forall (x : NNReal), Eq.{1} NNReal (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((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))) x)) x
 but is expected to have type
-  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
+  forall (x : NNReal), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) (NNReal.toReal x)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (NNReal.toReal x)) x
 Case conversion may be inaccurate. Consider using '#align real.nnabs_coe Real.nnabs_coeₓ'. -/
 theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 #align real.nnabs_coe Real.nnabs_coe
@@ -2097,7 +2097,7 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 lean 3 declaration is
   forall (n : Int), Eq.{1} NNReal ((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))))))) (Int.natAbs n)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
+  forall (n : Int), Eq.{1} NNReal (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (Int.natAbs n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs (Int.cast.{0} Real Real.intCast n))
 Case conversion may be inaccurate. Consider using '#align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_castₓ'. -/
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n :=
   by

bump to nightly-2023-03-02-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

cda909c7

Diff

@@ -427,25 +427,25 @@ theorem smul_def {M : Type _} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x
 instance {M N : Type _} [MulAction ℝ M] [MulAction ℝ N] [SMul M N] [IsScalarTower ℝ M N] :
     IsScalarTower ℝ≥0 M N where smul_assoc r := (smul_assoc (r : ℝ) : _)
 
-/- warning: nnreal.smul_comm_class_left -> NNReal.sMulCommClass_left is a dubious translation:
+/- warning: nnreal.smul_comm_class_left -> NNReal.smulCommClass_left is a dubious translation:
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.monoid] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{0, u1, u2} Real M N (MulAction.toHasSmul.{0, u2} Real N Real.monoid _inst_1) _inst_2], SMulCommClass.{0, u1, u2} NNReal M N (MulAction.toHasSmul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{u2} N _inst_1)) _inst_2
 but is expected to have type
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.instMonoidReal] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{0, u1, u2} Real M N (MulAction.toSMul.{0, u2} Real N Real.instMonoidReal _inst_1) _inst_2], SMulCommClass.{0, u1, u2} NNReal M N (MulAction.toSMul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{u2} N _inst_1)) _inst_2
-Case conversion may be inaccurate. Consider using '#align nnreal.smul_comm_class_left NNReal.sMulCommClass_leftₓ'. -/
-instance sMulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
+Case conversion may be inaccurate. Consider using '#align nnreal.smul_comm_class_left NNReal.smulCommClass_leftₓ'. -/
+instance smulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
     SMulCommClass ℝ≥0 M N where smul_comm r := (smul_comm (r : ℝ) : _)
-#align nnreal.smul_comm_class_left NNReal.sMulCommClass_left
+#align nnreal.smul_comm_class_left NNReal.smulCommClass_left
 
-/- warning: nnreal.smul_comm_class_right -> NNReal.sMulCommClass_right is a dubious translation:
+/- warning: nnreal.smul_comm_class_right -> NNReal.smulCommClass_right is a dubious translation:
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.monoid] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{u1, 0, u2} M Real N _inst_2 (MulAction.toHasSmul.{0, u2} Real N Real.monoid _inst_1)], SMulCommClass.{u1, 0, u2} M NNReal N _inst_2 (MulAction.toHasSmul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)) (NNReal.mulAction.{u2} N _inst_1))
 but is expected to have type
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulAction.{0, u2} Real N Real.instMonoidReal] [_inst_2 : SMul.{u1, u2} M N] [_inst_3 : SMulCommClass.{u1, 0, u2} M Real N _inst_2 (MulAction.toSMul.{0, u2} Real N Real.instMonoidReal _inst_1)], SMulCommClass.{u1, 0, u2} M NNReal N _inst_2 (MulAction.toSMul.{0, u2} NNReal N (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)) (NNReal.instMulActionNNRealToMonoidToMonoidWithZeroInstNNRealSemiring.{u2} N _inst_1))
-Case conversion may be inaccurate. Consider using '#align nnreal.smul_comm_class_right NNReal.sMulCommClass_rightₓ'. -/
-instance sMulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
+Case conversion may be inaccurate. Consider using '#align nnreal.smul_comm_class_right NNReal.smulCommClass_rightₓ'. -/
+instance smulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
     SMulCommClass M ℝ≥0 N where smul_comm m r := (smul_comm m (r : ℝ) : _)
-#align nnreal.smul_comm_class_right NNReal.sMulCommClass_right
+#align nnreal.smul_comm_class_right NNReal.smulCommClass_right
 
 /-- A `distrib_mul_action` over `ℝ` restricts to a `distrib_mul_action` over `ℝ≥0`. -/
 instance {M : Type _} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction ℝ≥0 M :=

bump to nightly-2023-02-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

2097f8af

Diff

@@ -959,9 +959,9 @@ theorem bot_eq_zero : (⊥ : ℝ≥0) = 0 :=
 
 /- warning: nnreal.mul_sup -> NNReal.mul_sup is a dubious translation:
 lean 3 declaration is
-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (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 (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) b c)) (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) (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) (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 c))
+  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (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 (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) b c)) (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) (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) (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 c))
 but is expected to have type
-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal instNNRealSemilatticeSup) b c)) (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal instNNRealSemilatticeSup) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c))
+  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) b c)) (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a b) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c))
 Case conversion may be inaccurate. Consider using '#align nnreal.mul_sup NNReal.mul_supₓ'. -/
 theorem mul_sup (a b c : ℝ≥0) : a * (b ⊔ c) = a * b ⊔ a * c :=
   mul_max_of_nonneg _ _ <| zero_le a
@@ -969,9 +969,9 @@ theorem mul_sup (a b c : ℝ≥0) : a * (b ⊔ c) = a * b ⊔ a * c :=
 
 /- warning: nnreal.sup_mul -> NNReal.sup_mul is a dubious translation:
 lean 3 declaration is
-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (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))))) (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) a b) c) (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) (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 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))))) b c))
+  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (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))))) (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) a b) c) (Sup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal NNReal.semilatticeSup) (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 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))))) b c))
 but is expected to have type
-  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal instNNRealSemilatticeSup) a b) c) (HasSup.sup.{0} NNReal (SemilatticeSup.toHasSup.{0} NNReal instNNRealSemilatticeSup) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c))
+  forall (a : NNReal) (b : NNReal) (c : NNReal), Eq.{1} NNReal (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) a b) c) (Sup.sup.{0} NNReal (SemilatticeSup.toSup.{0} NNReal instNNRealSemilatticeSup) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) a c) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c))
 Case conversion may be inaccurate. Consider using '#align nnreal.sup_mul NNReal.sup_mulₓ'. -/
 theorem sup_mul (a b c : ℝ≥0) : (a ⊔ b) * c = a * c ⊔ b * c :=
   max_mul_of_nonneg _ _ <| zero_le c
@@ -1778,7 +1778,7 @@ end Inv
 lean 3 declaration is
   forall (x : NNReal), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((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))) x)) ((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))) x)
 but is expected to have type
-  forall (x : NNReal), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instHasSupReal) (NNReal.toReal x)) (NNReal.toReal x)
+  forall (x : NNReal), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (NNReal.toReal x)) (NNReal.toReal x)
 Case conversion may be inaccurate. Consider using '#align nnreal.abs_eq NNReal.abs_eqₓ'. -/
 @[simp]
 theorem abs_eq (x : ℝ≥0) : |(x : ℝ)| = x :=
@@ -2054,7 +2054,7 @@ def nnabs : ℝ →*₀ ℝ≥0 where
 lean 3 declaration is
   forall (x : Real), Eq.{1} Real ((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))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (fun (_x : MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) => Real -> NNReal) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
 but is expected to have type
-  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instHasSupReal) x)
+  forall (x : Real), Eq.{1} Real (NNReal.toReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Real) => NNReal) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MulOneClass.toMul.{0} NNReal (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MulZeroOneClass.toMulOneClass.{0} NNReal (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Real NNReal (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toMulZeroOneClass.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)))))) Real.nnabs x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
 Case conversion may be inaccurate. Consider using '#align real.coe_nnabs Real.coe_nnabsₓ'. -/
 @[norm_cast, simp]
 theorem coe_nnabs (x : ℝ) : (nnabs x : ℝ) = |x| :=
@@ -2087,7 +2087,7 @@ theorem nnabs_coe (x : ℝ≥0) : nnabs x = x := by simp
 lean 3 declaration is
   forall (x : Real), LE.le.{0} Real Real.hasLe ((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))) (Real.toNNReal x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
 but is expected to have type
-  forall (x : Real), LE.le.{0} Real Real.instLEReal (NNReal.toReal (Real.toNNReal x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instHasSupReal) x)
+  forall (x : Real), LE.le.{0} Real Real.instLEReal (NNReal.toReal (Real.toNNReal x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
 Case conversion may be inaccurate. Consider using '#align real.coe_to_nnreal_le Real.coe_toNNReal_leₓ'. -/
 theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
   max_le (le_abs_self _) (abs_nonneg _)

bump to nightly-2023-02-25-03

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

39ef98db

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
+! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1456,19 +1456,6 @@ theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
   Finset.sum_div
 #align nnreal.sum_div NNReal.sum_div
 
-@[simp]
-theorem inv_pos {r : ℝ≥0} : 0 < r⁻¹ ↔ 0 < r :=
-  inv_pos
-#align nnreal.inv_pos NNReal.inv_pos
-
-theorem div_pos {r p : ℝ≥0} (hr : 0 < r) (hp : 0 < p) : 0 < r / p :=
-  div_pos hr hp
-#align nnreal.div_pos NNReal.div_pos
-
-theorem div_self_le (r : ℝ≥0) : r / r ≤ 1 :=
-  div_self_le_one r
-#align nnreal.div_self_le NNReal.div_self_le
-
 /- warning: nnreal.inv_le -> NNReal.inv_le is a dubious translation:
 lean 3 declaration is
   forall {r : NNReal} {p : NNReal}, (Ne.{1} NNReal r (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r) p) (LE.le.{0} NNReal (Preorder.toLE.{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))))))) (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))))) r p)))
@@ -1683,18 +1670,6 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
     rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this
 #align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_le
 
-theorem div_add_div_same (a b c : ℝ≥0) : a / c + b / c = (a + b) / c :=
-  div_add_div_same _ _ _
-#align nnreal.div_add_div_same NNReal.div_add_div_same
-
-theorem half_pos {a : ℝ≥0} (h : 0 < a) : 0 < a / 2 :=
-  half_pos h
-#align nnreal.half_pos NNReal.half_pos
-
-theorem add_halves (a : ℝ≥0) : a / 2 + a / 2 = a :=
-  add_halves _
-#align nnreal.add_halves NNReal.add_halves
-
 /- warning: nnreal.half_le_self -> NNReal.half_le_self is a dubious translation:
 lean 3 declaration is
   forall (a : NNReal), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))) a
@@ -1715,10 +1690,6 @@ theorem half_lt_self {a : ℝ≥0} (h : a ≠ 0) : a / 2 < a :=
   half_lt_self h.bot_lt
 #align nnreal.half_lt_self NNReal.half_lt_self
 
-theorem two_inv_lt_one : (2⁻¹ : ℝ≥0) < 1 :=
-  two_inv_lt_one
-#align nnreal.two_inv_lt_one NNReal.two_inv_lt_one
-
 /- warning: nnreal.div_lt_one_of_lt -> NNReal.div_lt_one_of_lt is a dubious translation:
 lean 3 declaration is
   forall {a : NNReal} {b : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) a b) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a b) (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))))))))
@@ -1731,22 +1702,6 @@ theorem div_lt_one_of_lt {a b : ℝ≥0} (h : a < b) : a / b < 1 :=
   exact ne_of_gt (lt_of_le_of_lt (zero_le _) h)
 #align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_lt
 
-@[field_simps]
-theorem div_add_div (a : ℝ≥0) {b : ℝ≥0} (c : ℝ≥0) {d : ℝ≥0} (hb : b ≠ 0) (hd : d ≠ 0) :
-    a / b + c / d = (a * d + b * c) / (b * d) :=
-  div_add_div _ _ hb hd
-#align nnreal.div_add_div NNReal.div_add_div
-
-@[field_simps]
-theorem add_div' (a b c : ℝ≥0) (hc : c ≠ 0) : b + a / c = (b * c + a) / c :=
-  add_div' _ _ _ hc
-#align nnreal.add_div' NNReal.add_div'
-
-@[field_simps]
-theorem div_add' (a b c : ℝ≥0) (hc : c ≠ 0) : a / c + b = (a + b * c) / c :=
-  div_add' _ _ _ hc
-#align nnreal.div_add' NNReal.div_add'
-
 /- warning: real.to_nnreal_inv -> Real.toNNReal_inv is a dubious translation:
 lean 3 declaration is
   forall {x : Real}, Eq.{1} NNReal (Real.toNNReal (Inv.inv.{0} Real Real.hasInv x)) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (Real.toNNReal x))
@@ -1794,10 +1749,6 @@ theorem inv_lt_one_iff {x : ℝ≥0} (hx : x ≠ 0) : x⁻¹ < 1 ↔ 1 < x := by
   rwa [← one_div, div_lt_iff hx, one_mul]
 #align nnreal.inv_lt_one_iff NNReal.inv_lt_one_iff
 
-theorem inv_lt_one {x : ℝ≥0} (hx : 1 < x) : x⁻¹ < 1 :=
-  inv_lt_one hx
-#align nnreal.inv_lt_one NNReal.inv_lt_one
-
 /- warning: nnreal.zpow_pos -> NNReal.zpow_pos is a dubious translation:
 lean 3 declaration is
   forall {x : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (n : Int), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (HPow.hPow.{0, 0, 0} NNReal Int NNReal (instHPow.{0, 0} NNReal Int (DivInvMonoid.Pow.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield))))))) x n))
@@ -1811,10 +1762,6 @@ theorem zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
   · simp [pow_pos hx.bot_lt _]
 #align nnreal.zpow_pos NNReal.zpow_pos
 
-theorem inv_lt_inv_iff {x y : ℝ≥0} (hx : x ≠ 0) (hy : y ≠ 0) : y⁻¹ < x⁻¹ ↔ x < y :=
-  inv_lt_inv₀ hy hx
-#align nnreal.inv_lt_inv_iff NNReal.inv_lt_inv_iff
-
 /- warning: nnreal.inv_lt_inv -> NNReal.inv_lt_inv is a dubious translation:
 lean 3 declaration is
   forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x y) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) y) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x))
@@ -1822,7 +1769,7 @@ but is expected to have type
   forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x y) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) y) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x))
 Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_inv NNReal.inv_lt_invₓ'. -/
 theorem inv_lt_inv {x y : ℝ≥0} (hx : x ≠ 0) (h : x < y) : y⁻¹ < x⁻¹ :=
-  (inv_lt_inv_iff hx (bot_le.trans_lt h).ne').2 h
+  inv_lt_inv_of_lt hx.bot_lt h
 #align nnreal.inv_lt_inv NNReal.inv_lt_inv
 
 end Inv

23aa88e3

bump to nightly-2023-02-25-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

aca219f8

Diff

@@ -1456,33 +1456,15 @@ theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
   Finset.sum_div
 #align nnreal.sum_div NNReal.sum_div
 
-/- warning: nnreal.inv_pos -> NNReal.inv_pos is a dubious translation:
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-  forall {r : NNReal}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) r)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)
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-Case conversion may be inaccurate. Consider using '#align nnreal.inv_pos NNReal.inv_posₓ'. -/
 @[simp]
 theorem inv_pos {r : ℝ≥0} : 0 < r⁻¹ ↔ 0 < r :=
   inv_pos
 #align nnreal.inv_pos NNReal.inv_pos
 
-/- warning: nnreal.div_pos -> NNReal.div_pos is a dubious translation:
-lean 3 declaration is
-  forall {r : NNReal} {p : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) p) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{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) r p))
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-  forall {r : NNReal} {p : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) r) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) p) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) r p))
-Case conversion may be inaccurate. Consider using '#align nnreal.div_pos NNReal.div_posₓ'. -/
 theorem div_pos {r p : ℝ≥0} (hr : 0 < r) (hp : 0 < p) : 0 < r / p :=
   div_pos hr hp
 #align nnreal.div_pos NNReal.div_pos
 
-/- warning: nnreal.div_self_le -> NNReal.div_self_le is a dubious translation:
-lean 3 declaration is
-  forall (r : NNReal), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) r r) (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)))))))
-but is expected to have type
-  forall (r : NNReal), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) r r) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))
-Case conversion may be inaccurate. Consider using '#align nnreal.div_self_le NNReal.div_self_leₓ'. -/
 theorem div_self_le (r : ℝ≥0) : r / r ≤ 1 :=
   div_self_le_one r
 #align nnreal.div_self_le NNReal.div_self_le
@@ -1701,32 +1683,14 @@ theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y)
     rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this
 #align nnreal.le_of_forall_lt_one_mul_le NNReal.le_of_forall_lt_one_mul_le
 
-/- warning: nnreal.div_add_div_same -> NNReal.div_add_div_same is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.div_add_div_same NNReal.div_add_div_sameₓ'. -/
 theorem div_add_div_same (a b c : ℝ≥0) : a / c + b / c = (a + b) / c :=
   div_add_div_same _ _ _
 #align nnreal.div_add_div_same NNReal.div_add_div_same
 
-/- warning: nnreal.half_pos -> NNReal.half_pos is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.half_pos NNReal.half_posₓ'. -/
 theorem half_pos {a : ℝ≥0} (h : 0 < a) : 0 < a / 2 :=
   half_pos h
 #align nnreal.half_pos NNReal.half_pos
 
-/- warning: nnreal.add_halves -> NNReal.add_halves is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.add_halves NNReal.add_halvesₓ'. -/
 theorem add_halves (a : ℝ≥0) : a / 2 + a / 2 = a :=
   add_halves _
 #align nnreal.add_halves NNReal.add_halves
@@ -1751,12 +1715,6 @@ theorem half_lt_self {a : ℝ≥0} (h : a ≠ 0) : a / 2 < a :=
   half_lt_self h.bot_lt
 #align nnreal.half_lt_self NNReal.half_lt_self
 
-/- warning: nnreal.two_inv_lt_one -> NNReal.two_inv_lt_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.two_inv_lt_one NNReal.two_inv_lt_oneₓ'. -/
 theorem two_inv_lt_one : (2⁻¹ : ℝ≥0) < 1 :=
   two_inv_lt_one
 #align nnreal.two_inv_lt_one NNReal.two_inv_lt_one
@@ -1773,35 +1731,17 @@ theorem div_lt_one_of_lt {a b : ℝ≥0} (h : a < b) : a / b < 1 :=
   exact ne_of_gt (lt_of_le_of_lt (zero_le _) h)
 #align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_lt
 
-/- warning: nnreal.div_add_div -> NNReal.div_add_div is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall (a : NNReal) {b : NNReal} (c : NNReal) {d : NNReal}, (Ne.{1} NNReal b (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Ne.{1} NNReal d (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (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)) a b) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) c d)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (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)) a d) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b d)))
-Case conversion may be inaccurate. Consider using '#align nnreal.div_add_div NNReal.div_add_divₓ'. -/
 @[field_simps]
 theorem div_add_div (a : ℝ≥0) {b : ℝ≥0} (c : ℝ≥0) {d : ℝ≥0} (hb : b ≠ 0) (hd : d ≠ 0) :
     a / b + c / d = (a * d + b * c) / (b * d) :=
   div_add_div _ _ hb hd
 #align nnreal.div_add_div NNReal.div_add_div
 
-/- warning: nnreal.add_div' -> NNReal.add_div' is a dubious translation:
-lean 3 declaration is
-  forall (a : NNReal) (b : NNReal) (c : NNReal), (Ne.{1} NNReal c (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (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))))) b (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) a c)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))) b c) a) c))
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-  forall (a : NNReal) (b : NNReal) (c : NNReal), (Ne.{1} NNReal c (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (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))))) b (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) a c)) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (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)) b c) a) c))
-Case conversion may be inaccurate. Consider using '#align nnreal.add_div' NNReal.add_div'ₓ'. -/
 @[field_simps]
 theorem add_div' (a b c : ℝ≥0) (hc : c ≠ 0) : b + a / c = (b * c + a) / c :=
   add_div' _ _ _ hc
 #align nnreal.add_div' NNReal.add_div'
 
-/- warning: nnreal.div_add' -> NNReal.div_add' is a dubious translation:
-lean 3 declaration is
-  forall (a : NNReal) (b : NNReal) (c : NNReal), (Ne.{1} NNReal c (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (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) a c) b) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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 (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))))) b c)) c))
-but is expected to have type
-  forall (a : NNReal) (b : NNReal) (c : NNReal), (Ne.{1} NNReal c (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (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)) a c) b) (HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (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 (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) b c)) c))
-Case conversion may be inaccurate. Consider using '#align nnreal.div_add' NNReal.div_add'ₓ'. -/
 @[field_simps]
 theorem div_add' (a b c : ℝ≥0) (hc : c ≠ 0) : a / c + b = (a + b * c) / c :=
   div_add' _ _ _ hc
@@ -1854,12 +1794,6 @@ theorem inv_lt_one_iff {x : ℝ≥0} (hx : x ≠ 0) : x⁻¹ < 1 ↔ 1 < x := by
   rwa [← one_div, div_lt_iff hx, one_mul]
 #align nnreal.inv_lt_one_iff NNReal.inv_lt_one_iff
 
-/- warning: nnreal.inv_lt_one -> NNReal.inv_lt_one is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{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))))))) x) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x) (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))))))))
-but is expected to have type
-  forall {x : 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)) x) -> (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)))
-Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_one NNReal.inv_lt_oneₓ'. -/
 theorem inv_lt_one {x : ℝ≥0} (hx : 1 < x) : x⁻¹ < 1 :=
   inv_lt_one hx
 #align nnreal.inv_lt_one NNReal.inv_lt_one
@@ -1877,12 +1811,6 @@ theorem zpow_pos {x : ℝ≥0} (hx : x ≠ 0) (n : ℤ) : 0 < x ^ n :=
   · simp [pow_pos hx.bot_lt _]
 #align nnreal.zpow_pos NNReal.zpow_pos
 
-/- warning: nnreal.inv_lt_inv_iff -> NNReal.inv_lt_inv_iff is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Ne.{1} NNReal y (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) y) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) x)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) x y))
-but is expected to have type
-  forall {x : NNReal} {y : NNReal}, (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Ne.{1} NNReal y (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) y) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) x)) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x y))
-Case conversion may be inaccurate. Consider using '#align nnreal.inv_lt_inv_iff NNReal.inv_lt_inv_iffₓ'. -/
 theorem inv_lt_inv_iff {x y : ℝ≥0} (hx : x ≠ 0) (hy : y ≠ 0) : y⁻¹ < x⁻¹ ↔ x < y :=
   inv_lt_inv₀ hy hx
 #align nnreal.inv_lt_inv_iff NNReal.inv_lt_inv_iff

23aa88e3

bump to nightly-2023-02-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

5c91f1b0

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit 83871f6cff322a1eafaa382ef70e9515fe240abd
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.Positivity
 /-!
 # Nonnegative real numbers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `nnreal` (notation: `ℝ≥0`) to be the type of non-negative real numbers,
 a.k.a. the interval `[0, ∞)`. We also define the following operations and structures on `ℝ≥0`:

83871f6c

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

This file has an open sync PR:
#10565 awaiting-review mathlib3-pair t-analysis t-order

mathlib3

mathlib4

chore: split Algebra.Algebra.Basic (#12486)

Splits Algebra.Algebra.Defs off Algebra.Algebra.Basic. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Algebra.Basic is now a grab-bag of unrelated results, and should probably be split further or rehomed.

This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Algebra.Basic.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

d64b17d9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Defs
 import Mathlib.Algebra.Order.BigOperators.Ring.Finset
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field

feat: add an OfScientific instance for NNRat and NNReal (#12485)

The existing RatCast.toOfScientific instance has to be removed since it forms a non-defeq diamond (there is nothing enforcing that nnratCast and ratCast are defeq).

The norm_num extension also needs some fixes, though the old design didn't make much sense anyway, as it synthesize the instances separately, thus losing important defeqs.

4e22ca74

Diff

@@ -364,6 +364,11 @@ protected theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] :
     (no_index (OfNat.ofNat n : ℝ≥0) : ℝ) = OfNat.ofNat n :=
   rfl
 
+@[simp, norm_cast]
+protected theorem coe_ofScientific (m : ℕ) (s : Bool) (e : ℕ) :
+    ↑(OfScientific.ofScientific m s e : ℝ≥0) = (OfScientific.ofScientific m s e : ℝ) :=
+  rfl
+
 noncomputable example : LinearOrder ℝ≥0 := by infer_instance
 
 @[simp, norm_cast] lemma coe_le_coe : (r₁ : ℝ) ≤ r₂ ↔ r₁ ≤ r₂ := Iff.rfl

chore: reformat deprecation warnings on one line, if possible (#12335)

Occasionally, remove a "deprecated by" or "deprecated since", to fit the line length.

This is desirable (to me) because

it's more compact: I don't see a good reason for these declarations taking up more space than needed; as I understand it, deprecated lemmas are not supposed to be used in mathlib anyway
putting the date on the same line as the attribute makes it easier to discover un-dated deprecations; they also ease writing a tool to replace these by a machine-readable version using leanprover/lean4#3968

45346d9f

Diff

@@ -165,8 +165,7 @@ protected theorem coe_injective : Injective ((↑) : ℝ≥0 → ℝ) := Subtype
   NNReal.coe_injective.eq_iff
 #align nnreal.coe_eq NNReal.coe_inj
 
--- 2024-02-03
-@[deprecated] protected alias coe_eq := coe_inj
+@[deprecated] protected alias coe_eq := coe_inj -- 2024-02-03
 
 @[simp, norm_cast] lemma coe_zero : ((0 : ℝ≥0) : ℝ) = 0 := rfl
 #align nnreal.coe_zero NNReal.coe_zero

feat: add theorem about order preservation of Real.toNNReal (#12369)

Add following theorem: if r and p are real and r.toNNReal < p.toNNReal, then r < p without any assumptions needed.

e1f6f66b

Diff

@@ -721,6 +721,9 @@ theorem toNNReal_lt_toNNReal_iff {r p : ℝ} (h : 0 < p) :
   toNNReal_lt_toNNReal_iff'.trans (and_iff_left h)
 #align real.to_nnreal_lt_to_nnreal_iff Real.toNNReal_lt_toNNReal_iff
 
+theorem lt_of_toNNReal_lt {r p : ℝ} (h : r.toNNReal < p.toNNReal) : r < p :=
+  (Real.toNNReal_lt_toNNReal_iff <| Real.toNNReal_pos.1 (ne_bot_of_gt h).bot_lt).1 h
+
 theorem toNNReal_lt_toNNReal_iff_of_nonneg {r p : ℝ} (hr : 0 ≤ r) :
     Real.toNNReal r < Real.toNNReal p ↔ r < p :=
   toNNReal_lt_toNNReal_iff'.trans ⟨And.left, fun h => ⟨h, lt_of_le_of_lt hr h⟩⟩

chore: unify date formatting in lemma deprecations (#12334)

consistently use the YYYY-MM-DD format
when easily possible, put the date on the same line as the deprecated attribute
when easily possible, format the entire declaration on the same line

Why these changes?

consistency makes it easier for tools to parse this information
compactness: I don't see a good reason for these declarations taking up more space than needed; as I understand it, deprecated lemmas are not supposed to be used in mathlib anyway
putting the date on the same line as the attribute makes it easier to discover un-dated deprecations; they also ease writing a tool to replace these by a machine-readable version using leanprover/lean4#3968

7e72dffd

Diff

@@ -401,8 +401,7 @@ theorem mk_natCast (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ
   NNReal.eq (NNReal.coe_natCast n).symm
 #align nnreal.mk_coe_nat NNReal.mk_natCast
 
--- 2024-04-05
-@[deprecated] alias mk_coe_nat := mk_natCast
+@[deprecated] alias mk_coe_nat := mk_natCast -- 2024-04-05
 
 -- Porting note: place this in the `Real` namespace
 @[simp]

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -355,9 +355,9 @@ theorem coe_nsmul (r : ℝ≥0) (n : ℕ) : ↑(n • r) = n • (r : ℝ) := rf
 #align nnreal.nsmul_coe NNReal.coe_nsmul
 
 @[simp, norm_cast]
-protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
+protected theorem coe_natCast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
   map_natCast toRealHom n
-#align nnreal.coe_nat_cast NNReal.coe_nat_cast
+#align nnreal.coe_nat_cast NNReal.coe_natCast
 
 -- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast]
@@ -398,7 +398,7 @@ theorem _root_.Real.toNNReal_coe {r : ℝ≥0} : Real.toNNReal r = r :=
 
 @[simp]
 theorem mk_natCast (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
-  NNReal.eq (NNReal.coe_nat_cast n).symm
+  NNReal.eq (NNReal.coe_natCast n).symm
 #align nnreal.mk_coe_nat NNReal.mk_natCast
 
 -- 2024-04-05
@@ -668,13 +668,13 @@ lemma toNNReal_eq_iff_eq_coe {r : ℝ} {p : ℝ≥0} (hp : p ≠ 0) : r.toNNReal
 lemma toNNReal_eq_one {r : ℝ} : r.toNNReal = 1 ↔ r = 1 := toNNReal_eq_iff_eq_coe one_ne_zero
 
 @[simp]
-lemma toNNReal_eq_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal = n ↔ r = n :=
+lemma toNNReal_eq_natCast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal = n ↔ r = n :=
   mod_cast toNNReal_eq_iff_eq_coe <| Nat.cast_ne_zero.2 hn
 
 @[simp]
 lemma toNNReal_eq_ofNat {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
     r.toNNReal = no_index (OfNat.ofNat n) ↔ r = OfNat.ofNat n :=
-  toNNReal_eq_nat_cast (NeZero.ne n)
+  toNNReal_eq_natCast (NeZero.ne n)
 
 @[simp]
 theorem toNNReal_le_toNNReal_iff {r p : ℝ} (hp : 0 ≤ p) :
@@ -690,22 +690,22 @@ lemma one_lt_toNNReal {r : ℝ} : 1 < r.toNNReal ↔ 1 < r := by
   simpa only [not_le] using toNNReal_le_one.not
 
 @[simp]
-lemma toNNReal_le_nat_cast {r : ℝ} {n : ℕ} : r.toNNReal ≤ n ↔ r ≤ n := by
+lemma toNNReal_le_natCast {r : ℝ} {n : ℕ} : r.toNNReal ≤ n ↔ r ≤ n := by
   simpa using toNNReal_le_toNNReal_iff n.cast_nonneg
 
 @[simp]
-lemma nat_cast_lt_toNNReal {r : ℝ} {n : ℕ} : n < r.toNNReal ↔ n < r := by
-  simpa only [not_le] using toNNReal_le_nat_cast.not
+lemma natCast_lt_toNNReal {r : ℝ} {n : ℕ} : n < r.toNNReal ↔ n < r := by
+  simpa only [not_le] using toNNReal_le_natCast.not
 
 @[simp]
 lemma toNNReal_le_ofNat {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
     r.toNNReal ≤ no_index (OfNat.ofNat n) ↔ r ≤ n :=
-  toNNReal_le_nat_cast
+  toNNReal_le_natCast
 
 @[simp]
 lemma ofNat_lt_toNNReal {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
     no_index (OfNat.ofNat n) < r.toNNReal ↔ n < r :=
-  nat_cast_lt_toNNReal
+  natCast_lt_toNNReal
 
 @[simp]
 theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
@@ -741,26 +741,26 @@ lemma one_le_toNNReal {r : ℝ} : 1 ≤ r.toNNReal ↔ 1 ≤ r := by
 lemma toNNReal_lt_one {r : ℝ} : r.toNNReal < 1 ↔ r < 1 := by simp only [← not_le, one_le_toNNReal]
 
 @[simp]
-lemma nat_cast_le_toNNReal' {n : ℕ} {r : ℝ} : ↑n ≤ r.toNNReal ↔ n ≤ r ∨ n = 0 := by
+lemma natCastle_toNNReal' {n : ℕ} {r : ℝ} : ↑n ≤ r.toNNReal ↔ n ≤ r ∨ n = 0 := by
   simpa [n.cast_nonneg.le_iff_eq] using toNNReal_le_toNNReal_iff' (r := n)
 
 @[simp]
-lemma toNNReal_lt_nat_cast' {n : ℕ} {r : ℝ} : r.toNNReal < n ↔ r < n ∧ n ≠ 0 := by
+lemma toNNReal_lt_natCast' {n : ℕ} {r : ℝ} : r.toNNReal < n ↔ r < n ∧ n ≠ 0 := by
   simpa [pos_iff_ne_zero] using toNNReal_lt_toNNReal_iff' (r := r) (p := n)
 
-lemma nat_cast_le_toNNReal {n : ℕ} {r : ℝ} (hn : n ≠ 0) : ↑n ≤ r.toNNReal ↔ n ≤ r := by simp [hn]
+lemma natCast_le_toNNReal {n : ℕ} {r : ℝ} (hn : n ≠ 0) : ↑n ≤ r.toNNReal ↔ n ≤ r := by simp [hn]
 
-lemma toNNReal_lt_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal < n ↔ r < n := by simp [hn]
+lemma toNNReal_lt_natCast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal < n ↔ r < n := by simp [hn]
 
 @[simp]
 lemma toNNReal_lt_ofNat {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
     r.toNNReal < no_index (OfNat.ofNat n) ↔ r < OfNat.ofNat n :=
-  toNNReal_lt_nat_cast (NeZero.ne n)
+  toNNReal_lt_natCast (NeZero.ne n)
 
 @[simp]
 lemma ofNat_le_toNNReal {n : ℕ} {r : ℝ} [n.AtLeastTwo] :
     no_index (OfNat.ofNat n) ≤ r.toNNReal ↔ OfNat.ofNat n ≤ r :=
-  nat_cast_le_toNNReal (NeZero.ne n)
+  natCast_le_toNNReal (NeZero.ne n)
 
 @[simp]
 theorem toNNReal_add {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
@@ -1187,7 +1187,7 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
 
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by
   ext
-  rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs, Int.cast_abs]
+  rw [NNReal.coe_natCast, Int.cast_natAbs, Real.coe_nnabs, Int.cast_abs]
 #align real.cast_nat_abs_eq_nnabs_cast Real.cast_natAbs_eq_nnabs_cast
 
 end Real

chore(Algebra/BigOperators): delete RingHom.map_* lemmas (#11663)

1ef4afc1

Diff

@@ -308,27 +308,27 @@ theorem coe_zpow (r : ℝ≥0) (n : ℤ) : ((r ^ n : ℝ≥0) : ℝ) = (r : ℝ)
 
 @[norm_cast]
 theorem coe_list_sum (l : List ℝ≥0) : ((l.sum : ℝ≥0) : ℝ) = (l.map (↑)).sum :=
-  toRealHom.map_list_sum l
+  map_list_sum toRealHom l
 #align nnreal.coe_list_sum NNReal.coe_list_sum
 
 @[norm_cast]
 theorem coe_list_prod (l : List ℝ≥0) : ((l.prod : ℝ≥0) : ℝ) = (l.map (↑)).prod :=
-  toRealHom.map_list_prod l
+  map_list_prod toRealHom l
 #align nnreal.coe_list_prod NNReal.coe_list_prod
 
 @[norm_cast]
 theorem coe_multiset_sum (s : Multiset ℝ≥0) : ((s.sum : ℝ≥0) : ℝ) = (s.map (↑)).sum :=
-  toRealHom.map_multiset_sum s
+  map_multiset_sum toRealHom s
 #align nnreal.coe_multiset_sum NNReal.coe_multiset_sum
 
 @[norm_cast]
 theorem coe_multiset_prod (s : Multiset ℝ≥0) : ((s.prod : ℝ≥0) : ℝ) = (s.map (↑)).prod :=
-  toRealHom.map_multiset_prod s
+  map_multiset_prod toRealHom s
 #align nnreal.coe_multiset_prod NNReal.coe_multiset_prod
 
 @[norm_cast]
 theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a) = ∑ a in s, (f a : ℝ) :=
-  toRealHom.map_sum _ _
+  map_sum toRealHom _ _
 #align nnreal.coe_sum NNReal.coe_sum
 
 theorem _root_.Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ}
@@ -340,7 +340,7 @@ theorem _root_.Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ}
 
 @[norm_cast]
 theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a) = ∏ a in s, (f a : ℝ) :=
-  toRealHom.map_prod _ _
+  map_prod toRealHom _ _
 #align nnreal.coe_prod NNReal.coe_prod
 
 theorem _root_.Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ}

chore: Rename coe_nat/coe_int/coe_rat to natCast/intCast/ratCast (#11499)

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

b2af0d13

Diff

@@ -397,9 +397,12 @@ theorem _root_.Real.toNNReal_coe {r : ℝ≥0} : Real.toNNReal r = r :=
 #align real.to_nnreal_coe Real.toNNReal_coe
 
 @[simp]
-theorem mk_coe_nat (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
+theorem mk_natCast (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ≥0) n :=
   NNReal.eq (NNReal.coe_nat_cast n).symm
-#align nnreal.mk_coe_nat NNReal.mk_coe_nat
+#align nnreal.mk_coe_nat NNReal.mk_natCast
+
+-- 2024-04-05
+@[deprecated] alias mk_coe_nat := mk_natCast
 
 -- Porting note: place this in the `Real` namespace
 @[simp]

chore: remove mathport name: <expression> lines (#11928)

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

11431c65

Diff

@@ -64,7 +64,6 @@ def NNReal := { r : ℝ // 0 ≤ r } deriving
 
 namespace NNReal
 
--- mathport name: nnreal
 scoped notation "ℝ≥0" => NNReal
 
 noncomputable instance : FloorSemiring ℝ≥0 := Nonneg.floorSemiring

chore: Sort big operator order lemmas (#11750)

Take the content of

some of Algebra.BigOperators.List.Basic
some of Algebra.BigOperators.List.Lemmas
some of Algebra.BigOperators.Multiset.Basic
some of Algebra.BigOperators.Multiset.Lemmas
Algebra.BigOperators.Multiset.Order
Algebra.BigOperators.Order

and sort it into six files:

Algebra.Order.BigOperators.Group.List. I credit Yakov for https://github.com/leanprover-community/mathlib/pull/8543.
Algebra.Order.BigOperators.Group.Multiset. Copyright inherited from Algebra.BigOperators.Multiset.Order.
Algebra.Order.BigOperators.Group.Finset. Copyright inherited from Algebra.BigOperators.Order.
Algebra.Order.BigOperators.Ring.List. I credit Stuart for https://github.com/leanprover-community/mathlib/pull/10184.
Algebra.Order.BigOperators.Ring.Multiset. I credit Ruben for https://github.com/leanprover-community/mathlib/pull/8787.
Algebra.Order.BigOperators.Ring.Finset. I credit Floris for https://github.com/leanprover-community/mathlib/pull/1294.

Here are the design decisions at play:

Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import Data.Nat.Order.Basic in a few List files.
It's Algebra.Order.BigOperators instead of Algebra.BigOperators.Order because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators.
There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under Algebra.Order.BigOperators.Group should be additivisable (except a few Nat- or Int-specific lemmas). In contrast, things under Algebra.Order.BigOperators.Ring are more prone to having heavy imports.
Lemmas are separated according to List vs Multiset vs Finset. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the AbsoluteValue lemmas from Algebra.Order.BigOperators.Ring.Finset to a file Algebra.Order.BigOperators.Ring.AbsoluteValue and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset, Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset, etc...
Finsupp big operator and finprod/finsum order lemmas also belong in Algebra.Order.BigOperators. I haven't done so in this PR because the diff is big enough like that.

3cc22ef5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
 import Mathlib.Algebra.Algebra.Basic
-import Mathlib.Algebra.BigOperators.Order
+import Mathlib.Algebra.Order.BigOperators.Ring.Finset
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -968,7 +968,7 @@ nonrec theorem div_le_div_left {a b c : ℝ≥0} (a0 : 0 < a) (b0 : 0 < b) (c0 :
 theorem le_of_forall_lt_one_mul_le {x y : ℝ≥0} (h : ∀ a < 1, a * x ≤ y) : x ≤ y :=
   le_of_forall_ge_of_dense fun a ha => by
     have hx : x ≠ 0 := pos_iff_ne_zero.1 (lt_of_le_of_lt (zero_le _) ha)
-    have hx' : x⁻¹ ≠ 0 := by rwa [Ne.def, inv_eq_zero]
+    have hx' : x⁻¹ ≠ 0 := by rwa [Ne, inv_eq_zero]
     have : a * x⁻¹ < 1 := by rwa [← lt_inv_iff_mul_lt hx', inv_inv]
     have : a * x⁻¹ * x ≤ y := h _ this
     rwa [mul_assoc, inv_mul_cancel hx, mul_one] at this

feat: Real.toNNReal_abs (#11606)

Partially forward-port https://github.com/leanprover-community/mathlib/pull/16976

Also fix an unused argument that somehow made it to master, likely from #10661.

a0e02a93

Diff

@@ -12,7 +12,7 @@ import Mathlib.Data.Real.Pointwise
 import Mathlib.Order.ConditionallyCompleteLattice.Group
 import Mathlib.Tactic.GCongr.Core
 
-#align_import data.real.nnreal from "leanprover-community/mathlib"@"de29c328903507bb7aff506af9135f4bdaf1849c"
+#align_import data.real.nnreal from "leanprover-community/mathlib"@"b1abe23ae96fef89ad30d9f4362c307f72a55010"
 
 /-!
 # Nonnegative real numbers
@@ -1180,6 +1180,9 @@ theorem coe_toNNReal_le (x : ℝ) : (toNNReal x : ℝ) ≤ |x| :=
   max_le (le_abs_self _) (abs_nonneg _)
 #align real.coe_to_nnreal_le Real.coe_toNNReal_le
 
+@[simp] lemma toNNReal_abs (x : ℝ) : |x|.toNNReal = nnabs x := NNReal.coe_injective <| by simp
+#align real.to_nnreal_abs Real.toNNReal_abs
+
 theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n := by
   ext
   rw [NNReal.coe_nat_cast, Int.cast_natAbs, Real.coe_nnabs, Int.cast_abs]

chore: classify todo porting notes (#11216)

Classifies by adding issue number #11215 to porting notes claiming "TODO".

86f95a40

Diff

@@ -223,7 +223,7 @@ example : CommSemiring ℝ≥0 := by infer_instance
 
 /-- Coercion `ℝ≥0 → ℝ` as a `RingHom`.
 
-Porting note: todo: what if we define `Coe ℝ≥0 ℝ` using this function? -/
+Porting note (#11215): TODO: what if we define `Coe ℝ≥0 ℝ` using this function? -/
 def toRealHom : ℝ≥0 →+* ℝ where
   toFun := (↑)
   map_one' := NNReal.coe_one
@@ -264,7 +264,7 @@ instance {M : Type*} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction 
 instance {M : Type*} [AddCommMonoid M] [Module ℝ M] : Module ℝ≥0 M :=
   Module.compHom M toRealHom
 
--- Porting note: TODO: after this line, `↑` uses `Algebra.cast` instead of `toReal`
+-- Porting note (#11215): TODO: after this line, `↑` uses `Algebra.cast` instead of `toReal`
 /-- An `Algebra` over `ℝ` restricts to an `Algebra` over `ℝ≥0`. -/
 instance {A : Type*} [Semiring A] [Algebra ℝ A] : Algebra ℝ≥0 A where
   smul := (· • ·)
@@ -351,7 +351,7 @@ theorem _root_.Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ
   exact Finset.prod_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonneg
 
--- Porting note: todo: `simp`? `norm_cast`?
+-- Porting note (#11215): TODO: `simp`? `norm_cast`?
 theorem coe_nsmul (r : ℝ≥0) (n : ℕ) : ↑(n • r) = n • (r : ℝ) := rfl
 #align nnreal.nsmul_coe NNReal.coe_nsmul
 
@@ -462,7 +462,7 @@ instance instSMulPosStrictMono {α} [Zero α] [Preorder α] [MulAction ℝ α] [
 
 /-- If `a` is a nonnegative real number, then the closed interval `[0, a]` in `ℝ` is order
 isomorphic to the interval `Set.Iic a`. -/
--- Porting note: todo: restore once `simps` supports `ℝ≥0` @[simps!? apply_coe_coe]
+-- Porting note (#11215): TODO: restore once `simps` supports `ℝ≥0` @[simps!? apply_coe_coe]
 def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a where
   toEquiv := Equiv.Set.sep (Set.Ici 0) fun x : ℝ => x ≤ a
   map_rel_iff' := Iff.rfl
@@ -551,7 +551,7 @@ theorem le_iInf_add_iInf {ι ι' : Sort*} [Nonempty ι] [Nonempty ι'] {f : ι 
 
 example : Archimedean ℝ≥0 := by infer_instance
 
--- Porting note: TODO: remove?
+-- Porting note (#11215): TODO: remove?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) := inferInstance
 #align nnreal.covariant_add NNReal.covariant_add
 
@@ -561,7 +561,7 @@ instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· <
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) := inferInstance
 #align nnreal.covariant_mul NNReal.covariant_mul
 
--- Porting note: TODO: delete?
+-- Porting note (#11215): TODO: delete?
 nonrec theorem le_of_forall_pos_le_add {a b : ℝ≥0} (h : ∀ ε, 0 < ε → a ≤ b + ε) : a ≤ b :=
   le_of_forall_pos_le_add h
 #align nnreal.le_of_forall_pos_le_add NNReal.le_of_forall_pos_le_add
@@ -1132,7 +1132,7 @@ theorem image_coe_nnreal_real (h : t.OrdConnected) : ((↑) '' t : Set ℝ).OrdC
       forall_mem_image.2 fun _y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
 #align set.ord_connected.image_coe_nnreal_real Set.OrdConnected.image_coe_nnreal_real
 
--- Porting note: todo: does it generalize to a `GaloisInsertion`?
+-- Porting note (#11215): TODO: does it generalize to a `GaloisInsertion`?
 theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConnected := by
   refine' ⟨forall_mem_image.2 fun x hx => forall_mem_image.2 fun y hy z hz => _⟩
   rcases le_total y 0 with hy₀ | hy₀

chore: Remove ball and bex from lemma names (#10816)

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

c697e040

Diff

@@ -1128,13 +1128,13 @@ theorem preimage_coe_nnreal_real (h : s.OrdConnected) : ((↑) ⁻¹' s : Set 
 #align set.ord_connected.preimage_coe_nnreal_real Set.OrdConnected.preimage_coe_nnreal_real
 
 theorem image_coe_nnreal_real (h : t.OrdConnected) : ((↑) '' t : Set ℝ).OrdConnected :=
-  ⟨ball_image_iff.2 fun x hx =>
-      ball_image_iff.2 fun _y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
+  ⟨forall_mem_image.2 fun x hx =>
+      forall_mem_image.2 fun _y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
 #align set.ord_connected.image_coe_nnreal_real Set.OrdConnected.image_coe_nnreal_real
 
 -- Porting note: todo: does it generalize to a `GaloisInsertion`?
 theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConnected := by
-  refine' ⟨ball_image_iff.2 fun x hx => ball_image_iff.2 fun y hy z hz => _⟩
+  refine' ⟨forall_mem_image.2 fun x hx => forall_mem_image.2 fun y hy z hz => _⟩
   rcases le_total y 0 with hy₀ | hy₀
   · rw [mem_Icc, Real.toNNReal_of_nonpos hy₀, nonpos_iff_eq_zero] at hz
     exact ⟨y, hy, (toNNReal_of_nonpos hy₀).trans hz.2.symm⟩

chore: Rename monotonicity of / lemmas (#10634)

The new names and argument orders match the corresponding * lemmas, which I already took care of in a previous PR.

From LeanAPAP

c8e50e0c

Diff

@@ -955,10 +955,9 @@ theorem mul_lt_of_lt_div {a b r : ℝ≥0} (h : a < b / r) : a * r < b :=
   (lt_div_iff fun hr => False.elim <| by simp [hr] at h).1 h
 #align nnreal.mul_lt_of_lt_div NNReal.mul_lt_of_lt_div
 
--- Porting note: drop an unneeded assumption, assume `≠ 0`
 theorem div_le_div_left_of_le {a b c : ℝ≥0} (c0 : c ≠ 0) (cb : c ≤ b) :
     a / b ≤ a / c :=
-  div_le_div_of_le_left (zero_le _) c0.bot_lt cb
+  div_le_div_of_nonneg_left (zero_le _) c0.bot_lt cb
 #align nnreal.div_le_div_left_of_le NNReal.div_le_div_left_of_leₓ
 
 nonrec theorem div_le_div_left {a b c : ℝ≥0} (a0 : 0 < a) (b0 : 0 < b) (c0 : 0 < c) :

chore: classify removed @[pp_nodot] porting notes (#11181)

Classifies by adding issue number #11180 to porting notes claiming:

removed @[pp_nodot]

76aa1eb1

Diff

@@ -1155,7 +1155,7 @@ end Set
 namespace Real
 
 /-- The absolute value on `ℝ` as a map to `ℝ≥0`. -/
--- Porting note: removed @[pp_nodot]
+-- Porting note (#11180): removed @[pp_nodot]
 def nnabs : ℝ →*₀ ℝ≥0 where
   toFun x := ⟨|x|, abs_nonneg x⟩
   map_zero' := by ext; simp

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -264,7 +264,7 @@ instance {M : Type*} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction 
 instance {M : Type*} [AddCommMonoid M] [Module ℝ M] : Module ℝ≥0 M :=
   Module.compHom M toRealHom
 
--- porting note: TODO: after this line, `↑` uses `Algebra.cast` instead of `toReal`
+-- Porting note: TODO: after this line, `↑` uses `Algebra.cast` instead of `toReal`
 /-- An `Algebra` over `ℝ` restricts to an `Algebra` over `ℝ≥0`. -/
 instance {A : Type*} [Semiring A] [Algebra ℝ A] : Algebra ℝ≥0 A where
   smul := (· • ·)
@@ -351,7 +351,7 @@ theorem _root_.Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ
   exact Finset.prod_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonneg
 
--- porting note: todo: `simp`? `norm_cast`?
+-- Porting note: todo: `simp`? `norm_cast`?
 theorem coe_nsmul (r : ℝ≥0) (n : ℕ) : ↑(n • r) = n • (r : ℝ) := rfl
 #align nnreal.nsmul_coe NNReal.coe_nsmul
 
@@ -462,7 +462,7 @@ instance instSMulPosStrictMono {α} [Zero α] [Preorder α] [MulAction ℝ α] [
 
 /-- If `a` is a nonnegative real number, then the closed interval `[0, a]` in `ℝ` is order
 isomorphic to the interval `Set.Iic a`. -/
--- porting note: todo: restore once `simps` supports `ℝ≥0` @[simps!? apply_coe_coe]
+-- Porting note: todo: restore once `simps` supports `ℝ≥0` @[simps!? apply_coe_coe]
 def orderIsoIccZeroCoe (a : ℝ≥0) : Set.Icc (0 : ℝ) a ≃o Set.Iic a where
   toEquiv := Equiv.Set.sep (Set.Ici 0) fun x : ℝ => x ≤ a
   map_rel_iff' := Iff.rfl
@@ -516,7 +516,7 @@ theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup (((↑) : ℝ≥
     exact bddAbove_coe.1 H
 #align nnreal.coe_Sup NNReal.coe_sSup
 
-@[simp, norm_cast] -- porting note: add `simp`
+@[simp, norm_cast] -- Porting note: add `simp`
 theorem coe_iSup {ι : Sort*} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, ↑(s i) := by
   rw [iSup, iSup, coe_sSup, ← Set.range_comp]; rfl
 #align nnreal.coe_supr NNReal.coe_iSup
@@ -551,7 +551,7 @@ theorem le_iInf_add_iInf {ι ι' : Sort*} [Nonempty ι] [Nonempty ι'] {f : ι 
 
 example : Archimedean ℝ≥0 := by infer_instance
 
--- porting note: TODO: remove?
+-- Porting note: TODO: remove?
 instance covariant_add : CovariantClass ℝ≥0 ℝ≥0 (· + ·) (· ≤ ·) := inferInstance
 #align nnreal.covariant_add NNReal.covariant_add
 
@@ -561,7 +561,7 @@ instance contravariant_add : ContravariantClass ℝ≥0 ℝ≥0 (· + ·) (· <
 instance covariant_mul : CovariantClass ℝ≥0 ℝ≥0 (· * ·) (· ≤ ·) := inferInstance
 #align nnreal.covariant_mul NNReal.covariant_mul
 
--- porting note: TODO: delete?
+-- Porting note: TODO: delete?
 nonrec theorem le_of_forall_pos_le_add {a b : ℝ≥0} (h : ∀ ε, 0 < ε → a ≤ b + ε) : a ≤ b :=
   le_of_forall_pos_le_add h
 #align nnreal.le_of_forall_pos_le_add NNReal.le_of_forall_pos_le_add
@@ -955,7 +955,7 @@ theorem mul_lt_of_lt_div {a b r : ℝ≥0} (h : a < b / r) : a * r < b :=
   (lt_div_iff fun hr => False.elim <| by simp [hr] at h).1 h
 #align nnreal.mul_lt_of_lt_div NNReal.mul_lt_of_lt_div
 
--- porting note: drop an unneeded assumption, assume `≠ 0`
+-- Porting note: drop an unneeded assumption, assume `≠ 0`
 theorem div_le_div_left_of_le {a b c : ℝ≥0} (c0 : c ≠ 0) (cb : c ≤ b) :
     a / b ≤ a / c :=
   div_le_div_of_le_left (zero_le _) c0.bot_lt cb
@@ -1079,19 +1079,19 @@ theorem iSup_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i,
   simp only [div_eq_mul_inv, iSup_mul]
 #align nnreal.supr_div NNReal.iSup_div
 
--- porting note: generalized to allow empty `ι`
+-- Porting note: generalized to allow empty `ι`
 theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a := by
   rw [mul_iSup]
   exact ciSup_le' H
 #align nnreal.mul_supr_le NNReal.mul_iSup_le
 
--- porting note: generalized to allow empty `ι`
+-- Porting note: generalized to allow empty `ι`
 theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a := by
   rw [iSup_mul]
   exact ciSup_le' H
 #align nnreal.supr_mul_le NNReal.iSup_mul_le
 
--- porting note: generalized to allow empty `ι`
+-- Porting note: generalized to allow empty `ι`
 theorem iSup_mul_iSup_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
     iSup g * iSup h ≤ a :=
   iSup_mul_le fun _ => mul_iSup_le <| H _
@@ -1133,7 +1133,7 @@ theorem image_coe_nnreal_real (h : t.OrdConnected) : ((↑) '' t : Set ℝ).OrdC
       ball_image_iff.2 fun _y hy z hz => ⟨⟨z, x.2.trans hz.1⟩, h.out hx hy hz, rfl⟩⟩
 #align set.ord_connected.image_coe_nnreal_real Set.OrdConnected.image_coe_nnreal_real
 
--- porting note: todo: does it generalize to a `GaloisInsertion`?
+-- Porting note: todo: does it generalize to a `GaloisInsertion`?
 theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConnected := by
   refine' ⟨ball_image_iff.2 fun x hx => ball_image_iff.2 fun y hy z hz => _⟩
   rcases le_total y 0 with hy₀ | hy₀
@@ -1155,7 +1155,7 @@ end Set
 namespace Real
 
 /-- The absolute value on `ℝ` as a map to `ℝ≥0`. -/
--- porting note: removed @[pp_nodot]
+-- Porting note: removed @[pp_nodot]
 def nnabs : ℝ →*₀ ℝ≥0 where
   toFun x := ⟨|x|, abs_nonneg x⟩
   map_zero' := by ext; simp

chore: add instance from Nat.AtLeastTwo n to NeZero n (#10964)

This PR cleans up some lemmas where we're taking named instance parameters [h : Nat.AtLeastTwo n] and manually proving inequalities like 0 < n from h by adding an instance of NeZero n from Nat.AtLeastTwo n as well as a couple of other helper lemmas.

This removes Nat.AtLeastTwo.ne_zero, as NeZero.ne_zero replaces it.

da1fa193

Diff

@@ -670,9 +670,9 @@ lemma toNNReal_eq_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal = n 
   mod_cast toNNReal_eq_iff_eq_coe <| Nat.cast_ne_zero.2 hn
 
 @[simp]
-lemma toNNReal_eq_ofNat {r : ℝ} {n : ℕ} [h : n.AtLeastTwo] :
+lemma toNNReal_eq_ofNat {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
     r.toNNReal = no_index (OfNat.ofNat n) ↔ r = OfNat.ofNat n :=
-  toNNReal_eq_nat_cast h.ne_zero
+  toNNReal_eq_nat_cast (NeZero.ne n)
 
 @[simp]
 theorem toNNReal_le_toNNReal_iff {r p : ℝ} (hp : 0 ≤ p) :
@@ -751,14 +751,14 @@ lemma nat_cast_le_toNNReal {n : ℕ} {r : ℝ} (hn : n ≠ 0) : ↑n ≤ r.toNNR
 lemma toNNReal_lt_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal < n ↔ r < n := by simp [hn]
 
 @[simp]
-lemma toNNReal_lt_ofNat {r : ℝ} {n : ℕ} [h : n.AtLeastTwo] :
+lemma toNNReal_lt_ofNat {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
     r.toNNReal < no_index (OfNat.ofNat n) ↔ r < OfNat.ofNat n :=
-  toNNReal_lt_nat_cast h.ne_zero
+  toNNReal_lt_nat_cast (NeZero.ne n)
 
 @[simp]
-lemma ofNat_le_toNNReal {n : ℕ} {r : ℝ} [h : n.AtLeastTwo] :
+lemma ofNat_le_toNNReal {n : ℕ} {r : ℝ} [n.AtLeastTwo] :
     no_index (OfNat.ofNat n) ≤ r.toNNReal ↔ OfNat.ofNat n ≤ r :=
-  nat_cast_le_toNNReal h.ne_zero
+  nat_cast_le_toNNReal (NeZero.ne n)
 
 @[simp]
 theorem toNNReal_add {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :

feat: ℝ≥0 is a star-ordered ring (#10547)

and other basic lemmas, including a version of Cauchy-Schwarz stated using Real.sqrt

From LeanAPAP

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

1e0f1e2a

Diff

@@ -617,6 +617,12 @@ theorem zero_le_coe {q : ℝ≥0} : 0 ≤ (q : ℝ) :=
   q.2
 #align nnreal.zero_le_coe NNReal.zero_le_coe
 
+instance instOrderedSMul {M : Type*} [OrderedAddCommMonoid M] [Module ℝ M] [OrderedSMul ℝ M] :
+    OrderedSMul ℝ≥0 M where
+  smul_lt_smul_of_pos hab hc := (smul_lt_smul_of_pos_left hab (NNReal.coe_pos.2 hc) : _)
+  lt_of_smul_lt_smul_of_pos {a b c} hab _ :=
+    lt_of_smul_lt_smul_of_nonneg_left (by exact hab) (NNReal.coe_nonneg c)
+
 end NNReal
 
 open NNReal

refactor(Tactic/Positivity): use stricter Qq matching (#10196)

The previous code often discarded the safety features of Qq by casting quoted terms to Expr and back. This is far from an exhaustive replacement.

This makes use of a bug fix in Lean 4.6.0rc1 that allows us to write things like

match u, α, e with
| 0, ~q(ℤ), ~q([@Int](https://github.com/Int).floor $α' $i $j $a) =>

Previously these matches did not generalize u correctly.

To make Qq happy, we introduce a few more assertInstancesCommute that were not previously here. Without them, there is a higher risk that positivity produces an ill-typed proof in weird situations. Like every assertInstancesCommute, this comes at a small performance cost that could be eliminated by using the unsafe assumeInstancesCommute instead.

Another very small performance hit here is from the (possibly unnecessary) defeq check of the types before checking defeq of the values. On the other hand, this might actually increase performance when the match fails due to a type mismatch.

There is probably some boilerplate that can be extracted from the repetition here; but I am declaring that out of scope for this PR: the goal is to establish a canonical spelling for this sort of matching, so that future extensions copy-pasted from these extensions inherit the spelling automatically.

5bb66741

Diff

@@ -1190,14 +1190,14 @@ private alias ⟨_, nnreal_coe_pos⟩ := coe_pos
 
 /-- Extension for the `positivity` tactic: cast from `ℝ≥0` to `ℝ`. -/
 @[positivity NNReal.toReal _]
-def evalNNRealtoReal : PositivityExt where eval {_ _} _zα _pα e := do
-  let (.app _ (a : Q(NNReal))) ← whnfR e | throwError "not NNReal.toReal"
-  let zα' ← synthInstanceQ (q(Zero NNReal) : Q(Type))
-  let pα' ← synthInstanceQ (q(PartialOrder NNReal) : Q(Type))
-  let ra ← core zα' pα' a
-  assertInstancesCommute
-  match ra with
-  | .positive pa => pure (.positive (q(nnreal_coe_pos $pa) : Expr))
-  | _ => pure (.nonnegative (q(NNReal.coe_nonneg $a) : Expr))
+def evalNNRealtoReal : PositivityExt where eval {u α} _zα _pα e := do
+  match u, α, e with
+  | 0, ~q(ℝ), ~q(NNReal.toReal $a) =>
+    let ra ← core q(inferInstance) q(inferInstance) a
+    assertInstancesCommute
+    match ra with
+    | .positive pa => pure (.positive q(nnreal_coe_pos $pa))
+    | _ => pure (.nonnegative q(NNReal.coe_nonneg $a))
+  | _, _, _ => throwError "not NNReal.toReal"
 
 end Mathlib.Meta.Positivity

chore(NNRat): Rearrange imports (#10392)

The goal is to separate the field material on Rat/NNRat from everything before to make way for NNRat.cast. We achieve this by

splitting Data.Rat.NNRat into
- Data.NNRat.Defs for the foundationl stuff that will be needed in the definition of Field
- Data.NNRat.Lemmas for the field and big operators material
moving the field material from Data.Rat.Order to Data.Rat.Basic
proving a few lemmas by rfl rather than coeHom.some_now_unavailable_lemma
renaming Data.Rat.NNRat.BigOperators to Data.NNRat.BigOperators

2357b645

Diff

@@ -68,7 +68,7 @@ namespace NNReal
 scoped notation "ℝ≥0" => NNReal
 
 noncomputable instance : FloorSemiring ℝ≥0 := Nonneg.floorSemiring
-instance : DenselyOrdered ℝ≥0 := Nonneg.densely_ordered
+instance instDenselyOrdered : DenselyOrdered ℝ≥0 := Nonneg.instDenselyOrdered
 instance : OrderBot ℝ≥0 := inferInstance
 instance : Archimedean ℝ≥0 := Nonneg.archimedean
 noncomputable instance : Sub ℝ≥0 := Nonneg.sub

feat: Complete NNReal coercion lemmas (#10214)

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

bc539a7b

Diff

@@ -162,19 +162,17 @@ example : Nontrivial ℝ≥0 := by infer_instance
 protected theorem coe_injective : Injective ((↑) : ℝ≥0 → ℝ) := Subtype.coe_injective
 #align nnreal.coe_injective NNReal.coe_injective
 
-@[simp, norm_cast]
-protected theorem coe_eq {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) = r₂ ↔ r₁ = r₂ :=
+@[simp, norm_cast] lemma coe_inj {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) = r₂ ↔ r₁ = r₂ :=
   NNReal.coe_injective.eq_iff
-#align nnreal.coe_eq NNReal.coe_eq
+#align nnreal.coe_eq NNReal.coe_inj
 
-@[simp, norm_cast]
-protected theorem coe_zero : ((0 : ℝ≥0) : ℝ) = 0 :=
-  rfl
+-- 2024-02-03
+@[deprecated] protected alias coe_eq := coe_inj
+
+@[simp, norm_cast] lemma coe_zero : ((0 : ℝ≥0) : ℝ) = 0 := rfl
 #align nnreal.coe_zero NNReal.coe_zero
 
-@[simp, norm_cast]
-protected theorem coe_one : ((1 : ℝ≥0) : ℝ) = 1 :=
-  rfl
+@[simp, norm_cast] lemma coe_one : ((1 : ℝ≥0) : ℝ) = 1 := rfl
 #align nnreal.coe_one NNReal.coe_one
 
 @[simp, norm_cast]
@@ -208,20 +206,19 @@ protected theorem coe_sub {r₁ r₂ : ℝ≥0} (h : r₂ ≤ r₁) : ((r₁ - r
   max_eq_left <| le_sub_comm.2 <| by simp [show (r₂ : ℝ) ≤ r₁ from h]
 #align nnreal.coe_sub NNReal.coe_sub
 
-@[simp, norm_cast]
-protected theorem coe_eq_zero (r : ℝ≥0) : ↑r = (0 : ℝ) ↔ r = 0 := by
-  rw [← NNReal.coe_zero, NNReal.coe_eq]
-#align nnreal.coe_eq_zero NNReal.coe_eq_zero
+variable {r r₁ r₂ : ℝ≥0} {x y : ℝ}
 
-@[simp, norm_cast]
-protected theorem coe_eq_one (r : ℝ≥0) : ↑r = (1 : ℝ) ↔ r = 1 := by
-  rw [← NNReal.coe_one, NNReal.coe_eq]
-#align nnreal.coe_eq_one NNReal.coe_eq_one
+@[simp, norm_cast] lemma coe_eq_zero : (r : ℝ) = 0 ↔ r = 0 := by rw [← coe_zero, coe_inj]
+#align coe_eq_zero NNReal.coe_eq_zero
 
--- porting note: why `norm_cast` fails?
-theorem coe_ne_zero {r : ℝ≥0} : (r : ℝ) ≠ 0 ↔ r ≠ 0 := r.coe_eq_zero.not
+@[simp, norm_cast] lemma coe_eq_one : (r : ℝ) = 1 ↔ r = 1 := by rw [← coe_one, coe_inj]
+#align coe_inj_one NNReal.coe_eq_one
+
+@[norm_cast] lemma coe_ne_zero : (r : ℝ) ≠ 0 ↔ r ≠ 0 := coe_eq_zero.not
 #align nnreal.coe_ne_zero NNReal.coe_ne_zero
 
+@[norm_cast] lemma coe_ne_one : (r : ℝ) ≠ 1 ↔ r ≠ 1 := coe_eq_one.not
+
 example : CommSemiring ℝ≥0 := by infer_instance
 
 /-- Coercion `ℝ≥0 → ℝ` as a `RingHom`.
@@ -275,11 +272,7 @@ instance {A : Type*} [Semiring A] [Algebra ℝ A] : Algebra ℝ≥0 A where
   smul_def' r x := by simp [← Algebra.smul_def (r : ℝ) x, smul_def]
   toRingHom := (algebraMap ℝ A).comp (toRealHom : ℝ≥0 →+* ℝ)
 
-instance : StarRing ℝ≥0 where
-  star := id
-  star_involutive _ := rfl
-  star_mul := mul_comm
-  star_add _ _ := rfl
+instance : StarRing ℝ≥0 := starRingOfComm
 
 instance : TrivialStar ℝ≥0 where
   star_trivial _ := rfl
@@ -342,7 +335,7 @@ theorem coe_sum {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∑ a in s, f a)
 theorem _root_.Real.toNNReal_sum_of_nonneg {α} {s : Finset α} {f : α → ℝ}
     (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∑ a in s, f a) = ∑ a in s, Real.toNNReal (f a) := by
-  rw [← NNReal.coe_eq, NNReal.coe_sum, Real.coe_toNNReal _ (Finset.sum_nonneg hf)]
+  rw [← coe_inj, NNReal.coe_sum, Real.coe_toNNReal _ (Finset.sum_nonneg hf)]
   exact Finset.sum_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_sum_of_nonneg Real.toNNReal_sum_of_nonneg
 
@@ -354,7 +347,7 @@ theorem coe_prod {α} {s : Finset α} {f : α → ℝ≥0} : ↑(∏ a in s, f a
 theorem _root_.Real.toNNReal_prod_of_nonneg {α} {s : Finset α} {f : α → ℝ}
     (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     Real.toNNReal (∏ a in s, f a) = ∏ a in s, Real.toNNReal (f a) := by
-  rw [← NNReal.coe_eq, NNReal.coe_prod, Real.coe_toNNReal _ (Finset.prod_nonneg hf)]
+  rw [← coe_inj, NNReal.coe_prod, Real.coe_toNNReal _ (Finset.prod_nonneg hf)]
   exact Finset.prod_congr rfl fun x hxs => by rw [Real.coe_toNNReal _ (hf x hxs)]
 #align real.to_nnreal_prod_of_nonneg Real.toNNReal_prod_of_nonneg
 
@@ -375,26 +368,25 @@ protected theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] :
 
 noncomputable example : LinearOrder ℝ≥0 := by infer_instance
 
-@[simp, norm_cast]
-protected theorem coe_le_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) ≤ r₂ ↔ r₁ ≤ r₂ :=
-  Iff.rfl
+@[simp, norm_cast] lemma coe_le_coe : (r₁ : ℝ) ≤ r₂ ↔ r₁ ≤ r₂ := Iff.rfl
 #align nnreal.coe_le_coe NNReal.coe_le_coe
 
-@[simp, norm_cast]
-protected theorem coe_lt_coe {r₁ r₂ : ℝ≥0} : (r₁ : ℝ) < r₂ ↔ r₁ < r₂ :=
-  Iff.rfl
+@[simp, norm_cast] lemma coe_lt_coe : (r₁ : ℝ) < r₂ ↔ r₁ < r₂ := Iff.rfl
 #align nnreal.coe_lt_coe NNReal.coe_lt_coe
 
-@[simp, norm_cast]
-protected theorem coe_pos {r : ℝ≥0} : (0 : ℝ) < r ↔ 0 < r :=
-  Iff.rfl
+@[simp, norm_cast] lemma coe_pos : (0 : ℝ) < r ↔ 0 < r := Iff.rfl
 #align nnreal.coe_pos NNReal.coe_pos
 
-protected theorem coe_mono : Monotone ((↑) : ℝ≥0 → ℝ) := fun _ _ => NNReal.coe_le_coe.2
+@[simp, norm_cast] lemma one_le_coe : 1 ≤ (r : ℝ) ↔ 1 ≤ r := by rw [← coe_le_coe, coe_one]
+@[simp, norm_cast] lemma one_lt_coe : 1 < (r : ℝ) ↔ 1 < r := by rw [← coe_lt_coe, coe_one]
+@[simp, norm_cast] lemma coe_le_one : (r : ℝ) ≤ 1 ↔ r ≤ 1 := by rw [← coe_le_coe, coe_one]
+@[simp, norm_cast] lemma coe_lt_one : (r : ℝ) < 1 ↔ r < 1 := by rw [← coe_lt_coe, coe_one]
+
+@[mono] lemma coe_mono : Monotone ((↑) : ℝ≥0 → ℝ) := fun _ _ => NNReal.coe_le_coe.2
 #align nnreal.coe_mono NNReal.coe_mono
 
-@[gcongr]
-theorem _root_.NNReal.toReal_le_toReal {x y : NNReal} (h : x ≤ y) : (x : ℝ) ≤ y := NNReal.coe_mono h
+/-- Alias for the use of `gcongr` -/
+@[gcongr] alias ⟨_, GCongr.toReal_le_toReal⟩ := coe_le_coe
 
 protected theorem _root_.Real.toNNReal_mono : Monotone Real.toNNReal := fun _ _ h =>
   max_le_max h (le_refl 0)
@@ -460,6 +452,14 @@ example : DenselyOrdered ℝ≥0 := by infer_instance
 
 example : NoMaxOrder ℝ≥0 := by infer_instance
 
+instance instPosSMulStrictMono {α} [Preorder α] [MulAction ℝ α] [PosSMulStrictMono ℝ α] :
+    PosSMulStrictMono ℝ≥0 α where
+  elim _r hr _a₁ _a₂ ha := (smul_lt_smul_of_pos_left ha (coe_pos.2 hr):)
+
+instance instSMulPosStrictMono {α} [Zero α] [Preorder α] [MulAction ℝ α] [SMulPosStrictMono ℝ α] :
+    SMulPosStrictMono ℝ≥0 α where
+  elim _a ha _r₁ _r₂ hr := (smul_lt_smul_of_pos_right (coe_lt_coe.2 hr) ha:)
+
 /-- If `a` is a nonnegative real number, then the closed interval `[0, a]` in `ℝ` is order
 isomorphic to the interval `Set.Iic a`. -/
 -- porting note: todo: restore once `simps` supports `ℝ≥0` @[simps!? apply_coe_coe]
@@ -524,7 +524,7 @@ theorem coe_iSup {ι : Sort*} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = 
 @[norm_cast]
 theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf (((↑) : ℝ≥0 → ℝ) '' s) := by
   rcases Set.eq_empty_or_nonempty s with rfl|hs
-  · simp only [Set.image_empty, Real.sInf_empty, NNReal.coe_eq_zero]
+  · simp only [Set.image_empty, Real.sInf_empty, coe_eq_zero]
     exact @subset_sInf_emptyset ℝ (Set.Ici (0 : ℝ)) _ _ (_)
   have A : sInf (Subtype.val '' s) ∈ Set.Ici 0 := by
     apply Real.sInf_nonneg
@@ -535,7 +535,7 @@ theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf (((↑) : ℝ≥
 
 @[simp]
 theorem sInf_empty : sInf (∅ : Set ℝ≥0) = 0 := by
-  rw [← NNReal.coe_eq_zero, coe_sInf, Set.image_empty, Real.sInf_empty]
+  rw [← coe_eq_zero, coe_sInf, Set.image_empty, Real.sInf_empty]
 #align nnreal.Inf_empty NNReal.sInf_empty
 
 @[norm_cast]
@@ -701,7 +701,7 @@ lemma ofNat_lt_toNNReal {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
 
 @[simp]
 theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
-    toNNReal r = toNNReal p ↔ r = p := by simp [← NNReal.coe_eq, coe_toNNReal, hr, hp]
+    toNNReal r = toNNReal p ↔ r = p := by simp [← coe_inj, coe_toNNReal, hr, hp]
 #align real.to_nnreal_eq_to_nnreal_iff Real.toNNReal_eq_toNNReal_iff
 
 @[simp]
@@ -798,7 +798,7 @@ theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔
 #noalign real.to_nnreal_bit1
 
 theorem toNNReal_pow {x : ℝ} (hx : 0 ≤ x) (n : ℕ) : (x ^ n).toNNReal = x.toNNReal ^ n := by
-  rw [← NNReal.coe_eq, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),
+  rw [← coe_inj, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),
     Real.coe_toNNReal x hx]
 #align real.to_nnreal_pow Real.toNNReal_pow
 
@@ -1030,7 +1030,7 @@ theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y
 
 nonrec theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 := by
   rw [← bddAbove_coe] at hs
-  rw [← NNReal.coe_eq, coe_sSup, NNReal.coe_zero]
+  rw [← coe_inj, coe_sSup, NNReal.coe_zero]
   exact sSup_of_not_bddAbove hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
 
@@ -1046,12 +1046,12 @@ theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : ⨅ i, f i = 0 := by
 
 @[simp]
 theorem iInf_const_zero {α : Sort*} : ⨅ _ : α, (0 : ℝ≥0) = 0 := by
-  rw [← NNReal.coe_eq, coe_iInf]
+  rw [← coe_inj, coe_iInf]
   exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero
 
 theorem iInf_mul (f : ι → ℝ≥0) (a : ℝ≥0) : iInf f * a = ⨅ i, f i * a := by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, coe_iInf, coe_iInf]
+  rw [← coe_inj, NNReal.coe_mul, coe_iInf, coe_iInf]
   exact Real.iInf_mul_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.infi_mul NNReal.iInf_mul
 
@@ -1060,7 +1060,7 @@ theorem mul_iInf (f : ι → ℝ≥0) (a : ℝ≥0) : a * iInf f = ⨅ i, a * f
 #align nnreal.mul_infi NNReal.mul_iInf
 
 theorem mul_iSup (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i := by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
+  rw [← coe_inj, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
   exact Real.mul_iSup_of_nonneg (NNReal.coe_nonneg _) _
 #align nnreal.mul_supr NNReal.mul_iSup
 
@@ -1186,8 +1186,7 @@ namespace Mathlib.Meta.Positivity
 
 open Lean Meta Qq Function
 
-private theorem nnreal_coe_pos {r : ℝ≥0} : 0 < r → 0 < (r : ℝ) :=
-  NNReal.coe_pos.2
+private alias ⟨_, nnreal_coe_pos⟩ := coe_pos
 
 /-- Extension for the `positivity` tactic: cast from `ℝ≥0` to `ℝ`. -/
 @[positivity NNReal.toReal _]

chore: Split off WithTop lemmas (#10239)

from Algebra.BigOperators.Order . Add the corresponding WithBot lemmas.

fa3313a1

Diff

@@ -5,7 +5,6 @@ Authors: Johan Commelin
 -/
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.BigOperators.Order
-import Mathlib.Algebra.BigOperators.Ring
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor

chore: Rename Real.ciSup_empty (#10217)

and a few more to clarify that they are about IsEmpty, not about ∅. Make a few more lemmas simp.`

69f70a5a

Diff

@@ -1042,7 +1042,7 @@ theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : ⨆ i, f i = 0 :=
 theorem iSup_empty [IsEmpty ι] (f : ι → ℝ≥0) : ⨆ i, f i = 0 := ciSup_of_empty f
 
 theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : ⨅ i, f i = 0 := by
-  rw [iInf_of_empty', sInf_empty]
+  rw [_root_.iInf_of_isEmpty, sInf_empty]
 #align nnreal.infi_empty NNReal.iInf_empty
 
 @[simp]

refactor: Delete Algebra.GroupPower.Lemmas (#9411)

Algebra.GroupPower.Lemmas used to be a big bag of lemmas that made it there on the criterion that they needed "more imports". This was completely untrue, as all lemmas could be moved to earlier files in PRs:

There are several reasons for this:

Necessary lemmas have been moved to earlier files since lemmas were dumped in Algebra.GroupPower.Lemmas
In the Lean 3 → Lean 4 transition, Std acquired basic Int and Nat lemmas which let us shortcircuit the part of the algebraic order hierarchy on which the corresponding general lemmas rest
Some proofs were overpowered
Some earlier files were tangled and I have untangled them

This PR finishes the job by moving the last few lemmas out of Algebra.GroupPower.Lemmas, which is therefore deleted.

6eb43dc3

Diff

@@ -6,7 +6,6 @@ Authors: Johan Commelin
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.BigOperators.Ring
-import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor

chore: remove spurious imports of positivity (#9924)

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

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

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

26c5ad69

Diff

@@ -12,7 +12,6 @@ import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor
 import Mathlib.Data.Real.Pointwise
 import Mathlib.Order.ConditionallyCompleteLattice.Group
-import Mathlib.Tactic.Positivity
 import Mathlib.Tactic.GCongr.Core
 
 #align_import data.real.nnreal from "leanprover-community/mathlib"@"de29c328903507bb7aff506af9135f4bdaf1849c"

chore: Move order lemmas about zpow (#9805)

These lemmas can be proved earlier.

Part of #9411

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

91ac6909

Diff

@@ -6,6 +6,7 @@ Authors: Johan Commelin
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.BigOperators.Ring
+import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor

chore: Relocate big operator lemmas (#9383)

A bunch of lemmas in Algebra.BigOperators.Ring were not about rings. This PR moves them along with some lemmas from Data.Fintype.BigOperators to their correct place.

I create a new file with the content from #6605 to avoid importing Fin material in finset files as a result.

From LeanAPAP

b8dc3667

Diff

@@ -877,10 +877,7 @@ end Sub
 
 section Inv
 
-theorem sum_div {ι} (s : Finset ι) (f : ι → ℝ≥0) (b : ℝ≥0) :
-    (∑ i in s, f i) / b = ∑ i in s, f i / b :=
-  Finset.sum_div
-#align nnreal.sum_div NNReal.sum_div
+#align nnreal.sum_div Finset.sum_div
 
 @[simp]
 theorem inv_le {r p : ℝ≥0} (h : r ≠ 0) : r⁻¹ ≤ p ↔ 1 ≤ r * p := by

chore: remove uses of cases' (#9171)

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.

3fca282c

Diff

@@ -988,7 +988,7 @@ theorem div_lt_one_of_lt {a b : ℝ≥0} (h : a < b) : a / b < 1 := by
 #align nnreal.div_lt_one_of_lt NNReal.div_lt_one_of_lt
 
 theorem _root_.Real.toNNReal_inv {x : ℝ} : Real.toNNReal x⁻¹ = (Real.toNNReal x)⁻¹ := by
-  cases' le_total 0 x with hx hx
+  rcases le_total 0 x with hx | hx
   · nth_rw 1 [← Real.coe_toNNReal x hx]
     rw [← NNReal.coe_inv, Real.toNNReal_coe]
   · rw [toNNReal_eq_zero.mpr hx, inv_zero, toNNReal_eq_zero.mpr (inv_nonpos.mpr hx)]
@@ -1135,7 +1135,7 @@ theorem image_coe_nnreal_real (h : t.OrdConnected) : ((↑) '' t : Set ℝ).OrdC
 -- porting note: todo: does it generalize to a `GaloisInsertion`?
 theorem image_real_toNNReal (h : s.OrdConnected) : (Real.toNNReal '' s).OrdConnected := by
   refine' ⟨ball_image_iff.2 fun x hx => ball_image_iff.2 fun y hy z hz => _⟩
-  cases' le_total y 0 with hy₀ hy₀
+  rcases le_total y 0 with hy₀ | hy₀
   · rw [mem_Icc, Real.toNNReal_of_nonpos hy₀, nonpos_iff_eq_zero] at hz
     exact ⟨y, hy, (toNNReal_of_nonpos hy₀).trans hz.2.symm⟩
   · lift y to ℝ≥0 using hy₀

chore: Sink Algebra.Support down the import tree (#8919)

Function.support is a very basic definition. Nevertheless, it is a pretty heavy import because it imports most objects a support lemma can be written about.

This PR reverses the dependencies between those objects and Function.support, so that the latter can become a much more lightweight import.

Only two import could not easily be reversed, namely the ones to Data.Set.Finite and Order.ConditionallyCompleteLattice.Basic, so I created two new files instead.

I credit:

Yury for https://github.com/leanprover-community/mathlib/pull/6791
Oliver for https://github.com/leanprover-community/mathlib/pull/7439

82ddb54f

Diff

@@ -6,7 +6,6 @@ Authors: Johan Commelin
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.BigOperators.Order
 import Mathlib.Algebra.BigOperators.Ring
-import Mathlib.Algebra.IndicatorFunction
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor

feat: add star instances for ℝ≥0 (#8988)

a9f7e646

Diff

@@ -278,6 +278,18 @@ instance {A : Type*} [Semiring A] [Algebra ℝ A] : Algebra ℝ≥0 A where
   smul_def' r x := by simp [← Algebra.smul_def (r : ℝ) x, smul_def]
   toRingHom := (algebraMap ℝ A).comp (toRealHom : ℝ≥0 →+* ℝ)
 
+instance : StarRing ℝ≥0 where
+  star := id
+  star_involutive _ := rfl
+  star_mul := mul_comm
+  star_add _ _ := rfl
+
+instance : TrivialStar ℝ≥0 where
+  star_trivial _ := rfl
+
+instance : StarModule ℝ≥0 ℝ where
+  star_smul := by simp only [star_trivial, eq_self_iff_true, forall_const]
+
 -- verify that the above produces instances we might care about
 example : Algebra ℝ≥0 ℝ := by infer_instance

chore: replace exact_mod_cast tactic with mod_cast elaborator where possible (#8404)

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>

693fd795

Diff

@@ -651,8 +651,8 @@ lemma toNNReal_eq_iff_eq_coe {r : ℝ} {p : ℝ≥0} (hp : p ≠ 0) : r.toNNReal
 lemma toNNReal_eq_one {r : ℝ} : r.toNNReal = 1 ↔ r = 1 := toNNReal_eq_iff_eq_coe one_ne_zero
 
 @[simp]
-lemma toNNReal_eq_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal = n ↔ r = n := by
-  exact_mod_cast toNNReal_eq_iff_eq_coe <| Nat.cast_ne_zero.2 hn
+lemma toNNReal_eq_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal = n ↔ r = n :=
+  mod_cast toNNReal_eq_iff_eq_coe <| Nat.cast_ne_zero.2 hn
 
 @[simp]
 lemma toNNReal_eq_ofNat {r : ℝ} {n : ℕ} [h : n.AtLeastTwo] :

chore: redistribute some of the results in LinearAlgebra.Basic (#7801)

This reduces the file from ~2600 lines to ~1600 lines.

Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

eb292821

Diff

@@ -4,6 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
 import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.BigOperators.Order
+import Mathlib.Algebra.BigOperators.Ring
+import Mathlib.Algebra.IndicatorFunction
 import Mathlib.Algebra.Order.Field.Canonical.Basic
 import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Nonneg.Floor

chore: add missing "no_index around OfNat.ofNat" library notes (#8316)

Co-authored-by: timotree3 <timorcb@gmail.com>

68b9af61

Diff

@@ -355,6 +355,7 @@ protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
   map_natCast toRealHom n
 #align nnreal.coe_nat_cast NNReal.coe_nat_cast
 
+-- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast]
 protected theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] :
     (no_index (OfNat.ofNat n : ℝ≥0) : ℝ) = OfNat.ofNat n :=
@@ -403,6 +404,7 @@ theorem toNNReal_coe_nat (n : ℕ) : Real.toNNReal n = n :=
   NNReal.eq <| by simp [Real.coe_toNNReal]
 #align nnreal.to_nnreal_coe_nat NNReal.toNNReal_coe_nat
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem _root_.Real.toNNReal_ofNat (n : ℕ) [n.AtLeastTwo] :
     Real.toNNReal (no_index (OfNat.ofNat n)) = OfNat.ofNat n :=

feat(Data/Real/NNReal): add lemmas about Real.toNNReal (#8136)

Add lemmas about comparison between Real.toNNReal and Nat.cast/OfNat.ofNat. Also add a few supporting lemmas.

d8418cc7

Diff

@@ -638,11 +638,53 @@ theorem toNNReal_of_nonpos {r : ℝ} : r ≤ 0 → Real.toNNReal r = 0 :=
   toNNReal_eq_zero.2
 #align real.to_nnreal_of_nonpos Real.toNNReal_of_nonpos
 
+lemma toNNReal_eq_iff_eq_coe {r : ℝ} {p : ℝ≥0} (hp : p ≠ 0) : r.toNNReal = p ↔ r = p :=
+  ⟨fun h ↦ h ▸ (coe_toNNReal _ <| not_lt.1 fun hlt ↦ hp <| h ▸ toNNReal_of_nonpos hlt.le).symm,
+    fun h ↦ h.symm ▸ toNNReal_coe⟩
+
+@[simp]
+lemma toNNReal_eq_one {r : ℝ} : r.toNNReal = 1 ↔ r = 1 := toNNReal_eq_iff_eq_coe one_ne_zero
+
+@[simp]
+lemma toNNReal_eq_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal = n ↔ r = n := by
+  exact_mod_cast toNNReal_eq_iff_eq_coe <| Nat.cast_ne_zero.2 hn
+
+@[simp]
+lemma toNNReal_eq_ofNat {r : ℝ} {n : ℕ} [h : n.AtLeastTwo] :
+    r.toNNReal = no_index (OfNat.ofNat n) ↔ r = OfNat.ofNat n :=
+  toNNReal_eq_nat_cast h.ne_zero
+
 @[simp]
 theorem toNNReal_le_toNNReal_iff {r p : ℝ} (hp : 0 ≤ p) :
     toNNReal r ≤ toNNReal p ↔ r ≤ p := by simp [← NNReal.coe_le_coe, hp]
 #align real.to_nnreal_le_to_nnreal_iff Real.toNNReal_le_toNNReal_iff
 
+@[simp]
+lemma toNNReal_le_one {r : ℝ} : r.toNNReal ≤ 1 ↔ r ≤ 1 := by
+  simpa using toNNReal_le_toNNReal_iff zero_le_one
+
+@[simp]
+lemma one_lt_toNNReal {r : ℝ} : 1 < r.toNNReal ↔ 1 < r := by
+  simpa only [not_le] using toNNReal_le_one.not
+
+@[simp]
+lemma toNNReal_le_nat_cast {r : ℝ} {n : ℕ} : r.toNNReal ≤ n ↔ r ≤ n := by
+  simpa using toNNReal_le_toNNReal_iff n.cast_nonneg
+
+@[simp]
+lemma nat_cast_lt_toNNReal {r : ℝ} {n : ℕ} : n < r.toNNReal ↔ n < r := by
+  simpa only [not_le] using toNNReal_le_nat_cast.not
+
+@[simp]
+lemma toNNReal_le_ofNat {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
+    r.toNNReal ≤ no_index (OfNat.ofNat n) ↔ r ≤ n :=
+  toNNReal_le_nat_cast
+
+@[simp]
+lemma ofNat_lt_toNNReal {r : ℝ} {n : ℕ} [n.AtLeastTwo] :
+    no_index (OfNat.ofNat n) < r.toNNReal ↔ n < r :=
+  nat_cast_lt_toNNReal
+
 @[simp]
 theorem toNNReal_eq_toNNReal_iff {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     toNNReal r = toNNReal p ↔ r = p := by simp [← NNReal.coe_eq, coe_toNNReal, hr, hp]
@@ -663,6 +705,41 @@ theorem toNNReal_lt_toNNReal_iff_of_nonneg {r p : ℝ} (hr : 0 ≤ r) :
   toNNReal_lt_toNNReal_iff'.trans ⟨And.left, fun h => ⟨h, lt_of_le_of_lt hr h⟩⟩
 #align real.to_nnreal_lt_to_nnreal_iff_of_nonneg Real.toNNReal_lt_toNNReal_iff_of_nonneg
 
+lemma toNNReal_le_toNNReal_iff' {r p : ℝ} : r.toNNReal ≤ p.toNNReal ↔ r ≤ p ∨ r ≤ 0 := by
+  simp_rw [← not_lt, toNNReal_lt_toNNReal_iff', not_and_or]
+
+lemma toNNReal_le_toNNReal_iff_of_pos {r p : ℝ} (hr : 0 < r) : r.toNNReal ≤ p.toNNReal ↔ r ≤ p := by
+  simp [toNNReal_le_toNNReal_iff', hr.not_le]
+
+@[simp]
+lemma one_le_toNNReal {r : ℝ} : 1 ≤ r.toNNReal ↔ 1 ≤ r := by
+  simpa using toNNReal_le_toNNReal_iff_of_pos one_pos
+
+@[simp]
+lemma toNNReal_lt_one {r : ℝ} : r.toNNReal < 1 ↔ r < 1 := by simp only [← not_le, one_le_toNNReal]
+
+@[simp]
+lemma nat_cast_le_toNNReal' {n : ℕ} {r : ℝ} : ↑n ≤ r.toNNReal ↔ n ≤ r ∨ n = 0 := by
+  simpa [n.cast_nonneg.le_iff_eq] using toNNReal_le_toNNReal_iff' (r := n)
+
+@[simp]
+lemma toNNReal_lt_nat_cast' {n : ℕ} {r : ℝ} : r.toNNReal < n ↔ r < n ∧ n ≠ 0 := by
+  simpa [pos_iff_ne_zero] using toNNReal_lt_toNNReal_iff' (r := r) (p := n)
+
+lemma nat_cast_le_toNNReal {n : ℕ} {r : ℝ} (hn : n ≠ 0) : ↑n ≤ r.toNNReal ↔ n ≤ r := by simp [hn]
+
+lemma toNNReal_lt_nat_cast {r : ℝ} {n : ℕ} (hn : n ≠ 0) : r.toNNReal < n ↔ r < n := by simp [hn]
+
+@[simp]
+lemma toNNReal_lt_ofNat {r : ℝ} {n : ℕ} [h : n.AtLeastTwo] :
+    r.toNNReal < no_index (OfNat.ofNat n) ↔ r < OfNat.ofNat n :=
+  toNNReal_lt_nat_cast h.ne_zero
+
+@[simp]
+lemma ofNat_le_toNNReal {n : ℕ} {r : ℝ} [h : n.AtLeastTwo] :
+    no_index (OfNat.ofNat n) ≤ r.toNNReal ↔ OfNat.ofNat n ≤ r :=
+  nat_cast_le_toNNReal h.ne_zero
+
 @[simp]
 theorem toNNReal_add {r p : ℝ} (hr : 0 ≤ r) (hp : 0 ≤ p) :
     Real.toNNReal (r + p) = Real.toNNReal r + Real.toNNReal p :=

chore: rename CanonicallyOrderedAddMonoid to ..AddCommMonoid (#7503)

Renames:

CanonicallyOrderedMonoid -> CanonicallyOrderedCommMonoid

CanonicallyOrderedAddMonoid -> CanonicallyOrderedAddCommMonoid

CanonicallyLinearOrderedMonoid -> CanonicallyLinearOrderedCommMonoid

CanonicallyLinearOrderedAddMonoid -> CanonicallyLinearOrderedAddCommMonoid

f3bc24c3

Diff

@@ -32,7 +32,7 @@ a.k.a. the interval `[0, ∞)`. We also define the following operations and stru
   - `OrderedCommSemiring ℝ≥0`;
   - `CanonicallyOrderedCommSemiring ℝ≥0`;
   - `LinearOrderedCommGroupWithZero ℝ≥0`;
-  - `CanonicallyLinearOrderedAddMonoid ℝ≥0`;
+  - `CanonicallyLinearOrderedAddCommMonoid ℝ≥0`;
   - `Archimedean ℝ≥0`;
   - `ConditionallyCompleteLinearOrderBot ℝ≥0`.
 
@@ -420,7 +420,7 @@ example : OrderBot ℝ≥0 := by infer_instance
 
 example : PartialOrder ℝ≥0 := by infer_instance
 
-noncomputable example : CanonicallyLinearOrderedAddMonoid ℝ≥0 := by infer_instance
+noncomputable example : CanonicallyLinearOrderedAddCommMonoid ℝ≥0 := by infer_instance
 
 noncomputable example : LinearOrderedAddCommMonoid ℝ≥0 := by infer_instance

feat: change junk value for supremum of unbounded sets (#6870)

We switch from sSup univ to sSup ∅ for the supremum of unbounded sets in a conditionally complete linear order. These quantities already coincide for all concrete instances in mathlib. With the new convention one gets additionally the theorem

theorem cbiSup_eq_of_not_forall {p : ι → Prop} {f : Subtype p → α} (hp : ¬ (∀ i, p i)) :
    ⨆ (i) (h : p i), f ⟨i, h⟩ = iSup f ⊔ sSup ∅

which will be convenient for general measurability statements.

99d76919

Diff

@@ -484,13 +484,22 @@ theorem bddBelow_coe (s : Set ℝ≥0) : BddBelow (((↑) : ℝ≥0 → ℝ) ''
 #align nnreal.bdd_below_coe NNReal.bddBelow_coe
 
 noncomputable instance : ConditionallyCompleteLinearOrderBot ℝ≥0 :=
-  Nonneg.conditionallyCompleteLinearOrderBot Real.sSup_empty.le
+  Nonneg.conditionallyCompleteLinearOrderBot 0
 
 @[norm_cast]
-theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup (((↑) : ℝ≥0 → ℝ) '' s) :=
-  Eq.symm <|
-    @subset_sSup_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
-      Real.sSup_nonneg _ fun _y ⟨x, _, hy⟩ => hy ▸ x.2
+theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup (((↑) : ℝ≥0 → ℝ) '' s) := by
+  rcases Set.eq_empty_or_nonempty s with rfl|hs
+  · simp
+  by_cases H : BddAbove s
+  · have A : sSup (Subtype.val '' s) ∈ Set.Ici 0 := by
+      apply Real.sSup_nonneg
+      rintro - ⟨y, -, rfl⟩
+      exact y.2
+    exact (@subset_sSup_of_within ℝ (Set.Ici (0 : ℝ)) _ _ (_) s hs H A).symm
+  · simp only [csSup_of_not_bddAbove H, csSup_empty, bot_eq_zero', NNReal.coe_zero]
+    apply (Real.sSup_of_not_bddAbove ?_).symm
+    contrapose! H
+    exact bddAbove_coe.1 H
 #align nnreal.coe_Sup NNReal.coe_sSup
 
 @[simp, norm_cast] -- porting note: add `simp`
@@ -499,10 +508,15 @@ theorem coe_iSup {ι : Sort*} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = 
 #align nnreal.coe_supr NNReal.coe_iSup
 
 @[norm_cast]
-theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf (((↑) : ℝ≥0 → ℝ) '' s) :=
-  Eq.symm <|
-    @subset_sInf_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
-      Real.sInf_nonneg _ fun _y ⟨x, _, hy⟩ => hy ▸ x.2
+theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf (((↑) : ℝ≥0 → ℝ) '' s) := by
+  rcases Set.eq_empty_or_nonempty s with rfl|hs
+  · simp only [Set.image_empty, Real.sInf_empty, NNReal.coe_eq_zero]
+    exact @subset_sInf_emptyset ℝ (Set.Ici (0 : ℝ)) _ _ (_)
+  have A : sInf (Subtype.val '' s) ∈ Set.Ici 0 := by
+    apply Real.sInf_nonneg
+    rintro - ⟨y, -, rfl⟩
+    exact y.2
+  exact (@subset_sInf_of_within ℝ (Set.Ici (0 : ℝ)) _ _ (_) s hs (OrderBot.bddBelow s) A).symm
 #align nnreal.coe_Inf NNReal.coe_sInf
 
 @[simp]

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -241,35 +241,35 @@ def toRealHom : ℝ≥0 →+* ℝ where
 section Actions
 
 /-- A `MulAction` over `ℝ` restricts to a `MulAction` over `ℝ≥0`. -/
-instance {M : Type _} [MulAction ℝ M] : MulAction ℝ≥0 M :=
+instance {M : Type*} [MulAction ℝ M] : MulAction ℝ≥0 M :=
   MulAction.compHom M toRealHom.toMonoidHom
 
-theorem smul_def {M : Type _} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x = (c : ℝ) • x :=
+theorem smul_def {M : Type*} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x = (c : ℝ) • x :=
   rfl
 #align nnreal.smul_def NNReal.smul_def
 
-instance {M N : Type _} [MulAction ℝ M] [MulAction ℝ N] [SMul M N] [IsScalarTower ℝ M N] :
+instance {M N : Type*} [MulAction ℝ M] [MulAction ℝ N] [SMul M N] [IsScalarTower ℝ M N] :
     IsScalarTower ℝ≥0 M N where smul_assoc r := (smul_assoc (r : ℝ) : _)
 
-instance smulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
+instance smulCommClass_left {M N : Type*} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
     SMulCommClass ℝ≥0 M N where smul_comm r := (smul_comm (r : ℝ) : _)
 #align nnreal.smul_comm_class_left NNReal.smulCommClass_left
 
-instance smulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
+instance smulCommClass_right {M N : Type*} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
     SMulCommClass M ℝ≥0 N where smul_comm m r := (smul_comm m (r : ℝ) : _)
 #align nnreal.smul_comm_class_right NNReal.smulCommClass_right
 
 /-- A `DistribMulAction` over `ℝ` restricts to a `DistribMulAction` over `ℝ≥0`. -/
-instance {M : Type _} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction ℝ≥0 M :=
+instance {M : Type*} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction ℝ≥0 M :=
   DistribMulAction.compHom M toRealHom.toMonoidHom
 
 /-- A `Module` over `ℝ` restricts to a `Module` over `ℝ≥0`. -/
-instance {M : Type _} [AddCommMonoid M] [Module ℝ M] : Module ℝ≥0 M :=
+instance {M : Type*} [AddCommMonoid M] [Module ℝ M] : Module ℝ≥0 M :=
   Module.compHom M toRealHom
 
 -- porting note: TODO: after this line, `↑` uses `Algebra.cast` instead of `toReal`
 /-- An `Algebra` over `ℝ` restricts to an `Algebra` over `ℝ≥0`. -/
-instance {A : Type _} [Semiring A] [Algebra ℝ A] : Algebra ℝ≥0 A where
+instance {A : Type*} [Semiring A] [Algebra ℝ A] : Algebra ℝ≥0 A where
   smul := (· • ·)
   commutes' r x := by simp [Algebra.commutes]
   smul_def' r x := by simp [← Algebra.smul_def (r : ℝ) x, smul_def]
@@ -494,7 +494,7 @@ theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup (((↑) : ℝ≥
 #align nnreal.coe_Sup NNReal.coe_sSup
 
 @[simp, norm_cast] -- porting note: add `simp`
-theorem coe_iSup {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, ↑(s i) := by
+theorem coe_iSup {ι : Sort*} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, ↑(s i) := by
   rw [iSup, iSup, coe_sSup, ← Set.range_comp]; rfl
 #align nnreal.coe_supr NNReal.coe_iSup
 
@@ -511,11 +511,11 @@ theorem sInf_empty : sInf (∅ : Set ℝ≥0) = 0 := by
 #align nnreal.Inf_empty NNReal.sInf_empty
 
 @[norm_cast]
-theorem coe_iInf {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, ↑(s i) := by
+theorem coe_iInf {ι : Sort*} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, ↑(s i) := by
   rw [iInf, iInf, coe_sInf, ← Set.range_comp]; rfl
 #align nnreal.coe_infi NNReal.coe_iInf
 
-theorem le_iInf_add_iInf {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
+theorem le_iInf_add_iInf {ι ι' : Sort*} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
     {a : ℝ≥0} (h : ∀ i j, a ≤ f i + g j) : a ≤ (⨅ i, f i) + ⨅ j, g j := by
   rw [← NNReal.coe_le_coe, NNReal.coe_add, coe_iInf, coe_iInf]
   exact le_ciInf_add_ciInf h
@@ -920,7 +920,7 @@ section Csupr
 
 open Set
 
-variable {ι : Sort _} {f : ι → ℝ≥0}
+variable {ι : Sort*} {f : ι → ℝ≥0}
 
 theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y.toNNReal :=
   (le_toNNReal_iff_coe_le <| x.2.trans h).2 h
@@ -943,7 +943,7 @@ theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : ⨅ i, f i = 0 := by
 #align nnreal.infi_empty NNReal.iInf_empty
 
 @[simp]
-theorem iInf_const_zero {α : Sort _} : ⨅ _ : α, (0 : ℝ≥0) = 0 := by
+theorem iInf_const_zero {α : Sort*} : ⨅ _ : α, (0 : ℝ≥0) = 0 := by
   rw [← NNReal.coe_eq, coe_iInf]
   exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit de29c328903507bb7aff506af9135f4bdaf1849c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.Order.Field.Canonical.Basic
@@ -17,6 +12,8 @@ import Mathlib.Order.ConditionallyCompleteLattice.Group
 import Mathlib.Tactic.Positivity
 import Mathlib.Tactic.GCongr.Core
 
+#align_import data.real.nnreal from "leanprover-community/mathlib"@"de29c328903507bb7aff506af9135f4bdaf1849c"
+
 /-!
 # Nonnegative real numbers

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -359,7 +359,8 @@ protected theorem coe_nat_cast (n : ℕ) : (↑(↑n : ℝ≥0) : ℝ) = n :=
 #align nnreal.coe_nat_cast NNReal.coe_nat_cast
 
 @[simp, norm_cast]
-protected theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] : ((OfNat.ofNat n : ℝ≥0) : ℝ) = OfNat.ofNat n :=
+protected theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] :
+    (no_index (OfNat.ofNat n : ℝ≥0) : ℝ) = OfNat.ofNat n :=
   rfl
 
 noncomputable example : LinearOrder ℝ≥0 := by infer_instance
@@ -407,7 +408,7 @@ theorem toNNReal_coe_nat (n : ℕ) : Real.toNNReal n = n :=
 
 @[simp]
 theorem _root_.Real.toNNReal_ofNat (n : ℕ) [n.AtLeastTwo] :
-  Real.toNNReal (OfNat.ofNat n) = OfNat.ofNat n :=
+    Real.toNNReal (no_index (OfNat.ofNat n)) = OfNat.ofNat n :=
   toNNReal_coe_nat n
 
 /-- `Real.toNNReal` and `NNReal.toReal : ℝ≥0 → ℝ` form a Galois insertion. -/

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -934,18 +934,18 @@ nonrec theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupS
   exact sSup_of_not_bddAbove hs
 #align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
 
-theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
+theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : ⨆ i, f i = 0 :=
   sSup_of_not_bddAbove hf
 #align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAbove
 
-theorem iSup_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨆ i, f i) = 0 := ciSup_of_empty f
+theorem iSup_empty [IsEmpty ι] (f : ι → ℝ≥0) : ⨆ i, f i = 0 := ciSup_of_empty f
 
-theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by
+theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : ⨅ i, f i = 0 := by
   rw [iInf_of_empty', sInf_empty]
 #align nnreal.infi_empty NNReal.iInf_empty
 
 @[simp]
-theorem iInf_const_zero {α : Sort _} : (⨅ _ : α, (0 : ℝ≥0)) = 0 := by
+theorem iInf_const_zero {α : Sort _} : ⨅ _ : α, (0 : ℝ≥0) = 0 := by
   rw [← NNReal.coe_eq, coe_iInf]
   exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -383,7 +383,7 @@ protected theorem coe_mono : Monotone ((↑) : ℝ≥0 → ℝ) := fun _ _ => NN
 #align nnreal.coe_mono NNReal.coe_mono
 
 @[gcongr]
-theorem _root_.NNReal.toReal_le_toReal {x y : NNReal} (h : x ≤ y) : (x:ℝ) ≤ y := NNReal.coe_mono h
+theorem _root_.NNReal.toReal_le_toReal {x y : NNReal} (h : x ≤ y) : (x : ℝ) ≤ y := NNReal.coe_mono h
 
 protected theorem _root_.Real.toNNReal_mono : Monotone Real.toNNReal := fun _ _ h =>
   max_le_max h (le_refl 0)

feat: port MeasureTheory.Measure.Lebesgue.EqHaar (#4666)

Co-authored-by: Johan Commelin <johan@commelin.net>

1b2a311a

Diff

@@ -399,11 +399,17 @@ theorem mk_coe_nat (n : ℕ) : @Eq ℝ≥0 (⟨(n : ℝ), n.cast_nonneg⟩ : ℝ
   NNReal.eq (NNReal.coe_nat_cast n).symm
 #align nnreal.mk_coe_nat NNReal.mk_coe_nat
 
+-- Porting note: place this in the `Real` namespace
 @[simp]
 theorem toNNReal_coe_nat (n : ℕ) : Real.toNNReal n = n :=
   NNReal.eq <| by simp [Real.coe_toNNReal]
 #align nnreal.to_nnreal_coe_nat NNReal.toNNReal_coe_nat
 
+@[simp]
+theorem _root_.Real.toNNReal_ofNat (n : ℕ) [n.AtLeastTwo] :
+  Real.toNNReal (OfNat.ofNat n) = OfNat.ofNat n :=
+  toNNReal_coe_nat n
+
 /-- `Real.toNNReal` and `NNReal.toReal : ℝ≥0 → ℝ` form a Galois insertion. -/
 noncomputable def gi : GaloisInsertion Real.toNNReal (↑) :=
   GaloisInsertion.monotoneIntro NNReal.coe_mono Real.toNNReal_mono Real.le_coe_toNNReal fun _ =>

feat: tactic gcongr for "relational congruence" (#3965)

This PR implements a new tactic, gcongr, which applies "relational congruence" rules, reducing a relational goal between a LHS and RHS matching the same pattern to relational subgoals between the differing inputs to the pattern. For example,

example {a b x c d : ℝ} (h1 : a + 1 ≤ b + 1) (h2 : c + 2 ≤ d + 2) :
    x ^ 4 * a + c ≤ x ^ 4 * b + d := by
  gcongr
  · linarith
  · linarith

This example has the goal of proving the relation ≤ between a LHS and RHS both of the pattern

x ^ 4 * ?_ + ?_

(with inputs a, c on the left and b, d on the right); after the use of gcongr, we have the simpler goals a ≤ b and c ≤ d.

For a sense of the style of argument facilitated by the tactic, this commit (which will be PR'd separately) gives >100 examples of use cases in the existing library.

The tactic's syntax allows for a pattern to be provided explicitly; this is useful if a non-maximal match is desired:

example {a b c d x : ℝ} (h : a + c + 1 ≤ b + d + 1) :
    x ^ 4 * (a + c) + 5 ≤ x ^ 4 * (b + d) + 5 := by
  gcongr x ^ 4 * ?_ + 5
  linarith

This feature is the analogue for general relations of the mathlib3 congrm tactic.

The "relational congruence" rules used are the library lemmas which have been tagged with the attribute @[gcongr]. For example, the first example constructs the proof term

add_le_add (mul_le_mul_of_nonneg_left _ (pow_bit0_nonneg x 2)) _

using the relational congruence lemmas add_le_add and mul_le_mul_of_nonneg_left. In this initial implementation, the @[gcongr] tagging has been set up for arithmetic head functions (+, * etc) and the relations ≤, < and congruence-mod-n.

The tactic attempts to discharge side goals to these "relational congruence" lemmas (such as the side goal 0 ≤ x ^ 4 in the above application of mul_le_mul_of_nonneg_left) using the tactic gcongr_discharger, which wraps positivity but can also be extended. Side goals not discharged in this way are left for the user.

Zulip discussion

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

Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>

fb7ec3ed

Diff

@@ -15,6 +15,7 @@ import Mathlib.Algebra.Order.Nonneg.Floor
 import Mathlib.Data.Real.Pointwise
 import Mathlib.Order.ConditionallyCompleteLattice.Group
 import Mathlib.Tactic.Positivity
+import Mathlib.Tactic.GCongr.Core
 
 /-!
 # Nonnegative real numbers
@@ -381,6 +382,9 @@ protected theorem coe_pos {r : ℝ≥0} : (0 : ℝ) < r ↔ 0 < r :=
 protected theorem coe_mono : Monotone ((↑) : ℝ≥0 → ℝ) := fun _ _ => NNReal.coe_le_coe.2
 #align nnreal.coe_mono NNReal.coe_mono
 
+@[gcongr]
+theorem _root_.NNReal.toReal_le_toReal {x y : NNReal} (h : x ≤ y) : (x:ℝ) ≤ y := NNReal.coe_mono h
+
 protected theorem _root_.Real.toNNReal_mono : Monotone Real.toNNReal := fun _ _ h =>
   max_le_max h (le_refl 0)
 #align real.to_nnreal_mono Real.toNNReal_mono

style: allow _ for an argument in notation3 & replace _foo with _ in notation3 (#4652)

e2b5ca37

Diff

@@ -935,7 +935,7 @@ theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by
 #align nnreal.infi_empty NNReal.iInf_empty
 
 @[simp]
-theorem iInf_const_zero {α : Sort _} : (⨅ _i : α, (0 : ℝ≥0)) = 0 := by
+theorem iInf_const_zero {α : Sort _} : (⨅ _ : α, (0 : ℝ≥0)) = 0 := by
   rw [← NNReal.coe_eq, coe_iInf]
   exact Real.ciInf_const_zero
 #align nnreal.infi_const_zero NNReal.iInf_const_zero

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -45,7 +45,7 @@ a.k.a. the interval `[0, ∞)`. We also define the following operations and stru
   `↑(Real.toNNReal x) = 0` otherwise.
 
 We also define an instance `CanLift ℝ ℝ≥0`. This instance can be used by the `lift` tactic to
-replace `x : ℝ` and `hx : 0 ≤ x` in the proof context with `x : ℝ≥0` while replacing all occurences
+replace `x : ℝ` and `hx : 0 ≤ x` in the proof context with `x : ℝ≥0` while replacing all occurrences
 of `x` with `↑x`. This tactic also works for a function `f : α → ℝ` with a hypothesis
 `hf : ∀ x, 0 ≤ f x`.

feat: assorted positivity extensions (#3907)

Positivity extensions for NonnegHomClass (this includes AbsoluteValue and Seminorm), IsAbsoluteValue, norm, the NNReal-to-Real coercion, factorials, square roots, distance (in a metric space), and diameter.

I tried to do these "properly" using Qq but I hit various errors I couldn't fix -- see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Qq.20doesn't.20know.20that.20two.20things.20have.20the.20same.20type for some examples.

cc @dwrensha

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

e7e38679

Diff

@@ -1072,27 +1072,23 @@ theorem cast_natAbs_eq_nnabs_cast (n : ℤ) : (n.natAbs : ℝ≥0) = nnabs n :=
 
 end Real
 
-/-
-namespace Tactic
+namespace Mathlib.Meta.Positivity
 
-open Positivity
+open Lean Meta Qq Function
 
 private theorem nnreal_coe_pos {r : ℝ≥0} : 0 < r → 0 < (r : ℝ) :=
   NNReal.coe_pos.2
-#align tactic.nnreal_coe_pos tactic.nnreal_coe_pos
 
 /-- Extension for the `positivity` tactic: cast from `ℝ≥0` to `ℝ`. -/
-@[positivity]
-unsafe def positivity_coe_nnreal_real : expr → tactic strictness
-  | q(@coe _ _ $(inst) $(a)) => do
-    unify inst q(@coeToLift _ _ <| @coeBase _ _ NNReal.Real.hasCoe)
-    let strictness_a ← core a
-    match strictness_a with
-      | positive p => positive <$> mk_app `` nnreal_coe_pos [p]
-      | _ => nonnegative <$> mk_app `` NNReal.coe_nonneg [a]
-  | e =>
-    pp e >>= fail ∘ format.bracket "The expression " " is not of the form `(r : ℝ)` for `r : ℝ≥0`"
-#align tactic.positivity_coe_nnreal_real tactic.positivity_coe_nnreal_real
-
-end Tactic
--/
+@[positivity NNReal.toReal _]
+def evalNNRealtoReal : PositivityExt where eval {_ _} _zα _pα e := do
+  let (.app _ (a : Q(NNReal))) ← whnfR e | throwError "not NNReal.toReal"
+  let zα' ← synthInstanceQ (q(Zero NNReal) : Q(Type))
+  let pα' ← synthInstanceQ (q(PartialOrder NNReal) : Q(Type))
+  let ra ← core zα' pα' a
+  assertInstancesCommute
+  match ra with
+  | .positive pa => pure (.positive (q(nnreal_coe_pos $pa) : Expr))
+  | _ => pure (.nonnegative (q(NNReal.coe_nonneg $a) : Expr))
+
+end Mathlib.Meta.Positivity

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -476,42 +476,42 @@ theorem bddBelow_coe (s : Set ℝ≥0) : BddBelow (((↑) : ℝ≥0 → ℝ) ''
 #align nnreal.bdd_below_coe NNReal.bddBelow_coe
 
 noncomputable instance : ConditionallyCompleteLinearOrderBot ℝ≥0 :=
-  Nonneg.conditionallyCompleteLinearOrderBot Real.supₛ_empty.le
+  Nonneg.conditionallyCompleteLinearOrderBot Real.sSup_empty.le
 
 @[norm_cast]
-theorem coe_supₛ (s : Set ℝ≥0) : (↑(supₛ s) : ℝ) = supₛ (((↑) : ℝ≥0 → ℝ) '' s) :=
+theorem coe_sSup (s : Set ℝ≥0) : (↑(sSup s) : ℝ) = sSup (((↑) : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
-    @subset_supₛ_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
-      Real.supₛ_nonneg _ fun _y ⟨x, _, hy⟩ => hy ▸ x.2
-#align nnreal.coe_Sup NNReal.coe_supₛ
+    @subset_sSup_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
+      Real.sSup_nonneg _ fun _y ⟨x, _, hy⟩ => hy ▸ x.2
+#align nnreal.coe_Sup NNReal.coe_sSup
 
 @[simp, norm_cast] -- porting note: add `simp`
-theorem coe_supᵢ {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, ↑(s i) := by
-  rw [supᵢ, supᵢ, coe_supₛ, ← Set.range_comp]; rfl
-#align nnreal.coe_supr NNReal.coe_supᵢ
+theorem coe_iSup {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨆ i, s i) : ℝ) = ⨆ i, ↑(s i) := by
+  rw [iSup, iSup, coe_sSup, ← Set.range_comp]; rfl
+#align nnreal.coe_supr NNReal.coe_iSup
 
 @[norm_cast]
-theorem coe_infₛ (s : Set ℝ≥0) : (↑(infₛ s) : ℝ) = infₛ (((↑) : ℝ≥0 → ℝ) '' s) :=
+theorem coe_sInf (s : Set ℝ≥0) : (↑(sInf s) : ℝ) = sInf (((↑) : ℝ≥0 → ℝ) '' s) :=
   Eq.symm <|
-    @subset_infₛ_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
-      Real.infₛ_nonneg _ fun _y ⟨x, _, hy⟩ => hy ▸ x.2
-#align nnreal.coe_Inf NNReal.coe_infₛ
+    @subset_sInf_of_within ℝ (Set.Ici 0) _ ⟨(0 : ℝ≥0)⟩ s <|
+      Real.sInf_nonneg _ fun _y ⟨x, _, hy⟩ => hy ▸ x.2
+#align nnreal.coe_Inf NNReal.coe_sInf
 
 @[simp]
-theorem infₛ_empty : infₛ (∅ : Set ℝ≥0) = 0 := by
-  rw [← NNReal.coe_eq_zero, coe_infₛ, Set.image_empty, Real.infₛ_empty]
-#align nnreal.Inf_empty NNReal.infₛ_empty
+theorem sInf_empty : sInf (∅ : Set ℝ≥0) = 0 := by
+  rw [← NNReal.coe_eq_zero, coe_sInf, Set.image_empty, Real.sInf_empty]
+#align nnreal.Inf_empty NNReal.sInf_empty
 
 @[norm_cast]
-theorem coe_infᵢ {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, ↑(s i) := by
-  rw [infᵢ, infᵢ, coe_infₛ, ← Set.range_comp]; rfl
-#align nnreal.coe_infi NNReal.coe_infᵢ
+theorem coe_iInf {ι : Sort _} (s : ι → ℝ≥0) : (↑(⨅ i, s i) : ℝ) = ⨅ i, ↑(s i) := by
+  rw [iInf, iInf, coe_sInf, ← Set.range_comp]; rfl
+#align nnreal.coe_infi NNReal.coe_iInf
 
-theorem le_infᵢ_add_infᵢ {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
+theorem le_iInf_add_iInf {ι ι' : Sort _} [Nonempty ι] [Nonempty ι'] {f : ι → ℝ≥0} {g : ι' → ℝ≥0}
     {a : ℝ≥0} (h : ∀ i j, a ≤ f i + g j) : a ≤ (⨅ i, f i) + ⨅ j, g j := by
-  rw [← NNReal.coe_le_coe, NNReal.coe_add, coe_infᵢ, coe_infᵢ]
-  exact le_cinfᵢ_add_cinfᵢ h
-#align nnreal.le_infi_add_infi NNReal.le_infᵢ_add_infᵢ
+  rw [← NNReal.coe_le_coe, NNReal.coe_add, coe_iInf, coe_iInf]
+  exact le_ciInf_add_ciInf h
+#align nnreal.le_infi_add_infi NNReal.le_iInf_add_iInf
 
 example : Archimedean ℝ≥0 := by infer_instance
 
@@ -918,85 +918,85 @@ theorem le_toNNReal_of_coe_le {x : ℝ≥0} {y : ℝ} (h : ↑x ≤ y) : x ≤ y
   (le_toNNReal_iff_coe_le <| x.2.trans h).2 h
 #align nnreal.le_to_nnreal_of_coe_le NNReal.le_toNNReal_of_coe_le
 
-nonrec theorem supₛ_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.supₛ s = 0 := by
+nonrec theorem sSup_of_not_bddAbove {s : Set ℝ≥0} (hs : ¬BddAbove s) : SupSet.sSup s = 0 := by
   rw [← bddAbove_coe] at hs
-  rw [← NNReal.coe_eq, coe_supₛ, NNReal.coe_zero]
-  exact supₛ_of_not_bddAbove hs
-#align nnreal.Sup_of_not_bdd_above NNReal.supₛ_of_not_bddAbove
+  rw [← NNReal.coe_eq, coe_sSup, NNReal.coe_zero]
+  exact sSup_of_not_bddAbove hs
+#align nnreal.Sup_of_not_bdd_above NNReal.sSup_of_not_bddAbove
 
-theorem supᵢ_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
-  supₛ_of_not_bddAbove hf
-#align nnreal.supr_of_not_bdd_above NNReal.supᵢ_of_not_bddAbove
+theorem iSup_of_not_bddAbove (hf : ¬BddAbove (range f)) : (⨆ i, f i) = 0 :=
+  sSup_of_not_bddAbove hf
+#align nnreal.supr_of_not_bdd_above NNReal.iSup_of_not_bddAbove
 
-theorem supᵢ_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨆ i, f i) = 0 := csupᵢ_of_empty f
+theorem iSup_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨆ i, f i) = 0 := ciSup_of_empty f
 
-theorem infᵢ_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by
-  rw [infᵢ_of_empty', infₛ_empty]
-#align nnreal.infi_empty NNReal.infᵢ_empty
+theorem iInf_empty [IsEmpty ι] (f : ι → ℝ≥0) : (⨅ i, f i) = 0 := by
+  rw [iInf_of_empty', sInf_empty]
+#align nnreal.infi_empty NNReal.iInf_empty
 
 @[simp]
-theorem infᵢ_const_zero {α : Sort _} : (⨅ _i : α, (0 : ℝ≥0)) = 0 := by
-  rw [← NNReal.coe_eq, coe_infᵢ]
-  exact Real.cinfᵢ_const_zero
-#align nnreal.infi_const_zero NNReal.infᵢ_const_zero
-
-theorem infᵢ_mul (f : ι → ℝ≥0) (a : ℝ≥0) : infᵢ f * a = ⨅ i, f i * a := by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, coe_infᵢ, coe_infᵢ]
-  exact Real.infᵢ_mul_of_nonneg (NNReal.coe_nonneg _) _
-#align nnreal.infi_mul NNReal.infᵢ_mul
-
-theorem mul_infᵢ (f : ι → ℝ≥0) (a : ℝ≥0) : a * infᵢ f = ⨅ i, a * f i := by
-  simpa only [mul_comm] using infᵢ_mul f a
-#align nnreal.mul_infi NNReal.mul_infᵢ
-
-theorem mul_supᵢ (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i := by
-  rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_supᵢ, NNReal.coe_supᵢ]
-  exact Real.mul_supᵢ_of_nonneg (NNReal.coe_nonneg _) _
-#align nnreal.mul_supr NNReal.mul_supᵢ
-
-theorem supᵢ_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a := by
-  rw [mul_comm, mul_supᵢ]
+theorem iInf_const_zero {α : Sort _} : (⨅ _i : α, (0 : ℝ≥0)) = 0 := by
+  rw [← NNReal.coe_eq, coe_iInf]
+  exact Real.ciInf_const_zero
+#align nnreal.infi_const_zero NNReal.iInf_const_zero
+
+theorem iInf_mul (f : ι → ℝ≥0) (a : ℝ≥0) : iInf f * a = ⨅ i, f i * a := by
+  rw [← NNReal.coe_eq, NNReal.coe_mul, coe_iInf, coe_iInf]
+  exact Real.iInf_mul_of_nonneg (NNReal.coe_nonneg _) _
+#align nnreal.infi_mul NNReal.iInf_mul
+
+theorem mul_iInf (f : ι → ℝ≥0) (a : ℝ≥0) : a * iInf f = ⨅ i, a * f i := by
+  simpa only [mul_comm] using iInf_mul f a
+#align nnreal.mul_infi NNReal.mul_iInf
+
+theorem mul_iSup (f : ι → ℝ≥0) (a : ℝ≥0) : (a * ⨆ i, f i) = ⨆ i, a * f i := by
+  rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]
+  exact Real.mul_iSup_of_nonneg (NNReal.coe_nonneg _) _
+#align nnreal.mul_supr NNReal.mul_iSup
+
+theorem iSup_mul (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) * a = ⨆ i, f i * a := by
+  rw [mul_comm, mul_iSup]
   simp_rw [mul_comm]
-#align nnreal.supr_mul NNReal.supᵢ_mul
+#align nnreal.supr_mul NNReal.iSup_mul
 
-theorem supᵢ_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i, f i / a := by
-  simp only [div_eq_mul_inv, supᵢ_mul]
-#align nnreal.supr_div NNReal.supᵢ_div
+theorem iSup_div (f : ι → ℝ≥0) (a : ℝ≥0) : (⨆ i, f i) / a = ⨆ i, f i / a := by
+  simp only [div_eq_mul_inv, iSup_mul]
+#align nnreal.supr_div NNReal.iSup_div
 
 -- porting note: generalized to allow empty `ι`
-theorem mul_supᵢ_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * supᵢ h ≤ a := by
-  rw [mul_supᵢ]
-  exact csupᵢ_le' H
-#align nnreal.mul_supr_le NNReal.mul_supᵢ_le
+theorem mul_iSup_le {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, g * h j ≤ a) : g * iSup h ≤ a := by
+  rw [mul_iSup]
+  exact ciSup_le' H
+#align nnreal.mul_supr_le NNReal.mul_iSup_le
 
 -- porting note: generalized to allow empty `ι`
-theorem supᵢ_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : supᵢ g * h ≤ a := by
-  rw [supᵢ_mul]
-  exact csupᵢ_le' H
-#align nnreal.supr_mul_le NNReal.supᵢ_mul_le
+theorem iSup_mul_le {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, g i * h ≤ a) : iSup g * h ≤ a := by
+  rw [iSup_mul]
+  exact ciSup_le' H
+#align nnreal.supr_mul_le NNReal.iSup_mul_le
 
 -- porting note: generalized to allow empty `ι`
-theorem supᵢ_mul_supᵢ_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
-    supᵢ g * supᵢ h ≤ a :=
-  supᵢ_mul_le fun _ => mul_supᵢ_le <| H _
-#align nnreal.supr_mul_supr_le NNReal.supᵢ_mul_supᵢ_le
+theorem iSup_mul_iSup_le {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, g i * h j ≤ a) :
+    iSup g * iSup h ≤ a :=
+  iSup_mul_le fun _ => mul_iSup_le <| H _
+#align nnreal.supr_mul_supr_le NNReal.iSup_mul_iSup_le
 
 variable [Nonempty ι]
 
-theorem le_mul_infᵢ {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * infᵢ h := by
-  rw [mul_infᵢ]
-  exact le_cinfᵢ H
-#align nnreal.le_mul_infi NNReal.le_mul_infᵢ
+theorem le_mul_iInf {a : ℝ≥0} {g : ℝ≥0} {h : ι → ℝ≥0} (H : ∀ j, a ≤ g * h j) : a ≤ g * iInf h := by
+  rw [mul_iInf]
+  exact le_ciInf H
+#align nnreal.le_mul_infi NNReal.le_mul_iInf
 
-theorem le_infᵢ_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ infᵢ g * h := by
-  rw [infᵢ_mul]
-  exact le_cinfᵢ H
-#align nnreal.le_infi_mul NNReal.le_infᵢ_mul
+theorem le_iInf_mul {a : ℝ≥0} {g : ι → ℝ≥0} {h : ℝ≥0} (H : ∀ i, a ≤ g i * h) : a ≤ iInf g * h := by
+  rw [iInf_mul]
+  exact le_ciInf H
+#align nnreal.le_infi_mul NNReal.le_iInf_mul
 
-theorem le_infᵢ_mul_infᵢ {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a ≤ g i * h j) :
-    a ≤ infᵢ g * infᵢ h :=
-  le_infᵢ_mul fun i => le_mul_infᵢ <| H i
-#align nnreal.le_infi_mul_infi NNReal.le_infᵢ_mul_infᵢ
+theorem le_iInf_mul_iInf {a : ℝ≥0} {g h : ι → ℝ≥0} (H : ∀ i j, a ≤ g i * h j) :
+    a ≤ iInf g * iInf h :=
+  le_iInf_mul fun i => le_mul_iInf <| H i
+#align nnreal.le_infi_mul_infi NNReal.le_iInf_mul_iInf
 
 end Csupr

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -692,7 +692,6 @@ theorem toNNReal_pow {x : ℝ} (hx : 0 ≤ x) (n : ℕ) : (x ^ n).toNNReal = x.t
 theorem toNNReal_mul {p q : ℝ} (hp : 0 ≤ p) :
     Real.toNNReal (p * q) = Real.toNNReal p * Real.toNNReal q :=
   NNReal.eq <| by simp [mul_max_of_nonneg, hp]
-
 #align real.to_nnreal_mul Real.toNNReal_mul
 
 end ToNNReal

chore: forward port mathlib#18810, 18798, 18738 (#3443)

algebra.order.sub.defs, data.real.nnreal: leanprover-community/mathlib#18810, which is itself a backport. Also fixes a docstring typo.
linear_algebra.matrix.dot_product: leanprover-community/mathlib#18798
data.matrix.basic: leanprover-community/mathlib#18738

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

e978148f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit b3f4f007a962e3787aa0f3b5c7942a1317f7d88e
+! leanprover-community/mathlib commit de29c328903507bb7aff506af9135f4bdaf1849c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -742,7 +742,7 @@ section Sub
 
 In this section we provide a few lemmas about subtraction that do not fit well into any other
 typeclass. For lemmas about subtraction and addition see lemmas about `OrderedSub` in the file
-`Mathlib.Algebra.Order.Sub.Bsic`. See also `mul_tsub` and `tsub_mul`.
+`Mathlib.Algebra.Order.Sub.Basic`. See also `mul_tsub` and `tsub_mul`.
 -/
 
 theorem sub_def {r p : ℝ≥0} : r - p = Real.toNNReal (r - p) :=
@@ -753,7 +753,7 @@ theorem coe_sub_def {r p : ℝ≥0} : ↑(r - p) = max (r - p : ℝ) 0 :=
   rfl
 #align nnreal.coe_sub_def NNReal.coe_sub_def
 
-noncomputable example : OrderedSub ℝ≥0 := by infer_instance
+example : OrderedSub ℝ≥0 := by infer_instance
 
 theorem sub_div (a b c : ℝ≥0) : (a - b) / c = a / c - b / c :=
   tsub_div _ _ _

Match https://github.com/leanprover-community/mathlib/pull/18590 and https://github.com/leanprover-community/mathlib/pull/18596

chore: Split off and golf ulift field instances (#2911)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

5163d8ce

Diff

@@ -4,15 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.real.nnreal
-! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
+! leanprover-community/mathlib commit b3f4f007a962e3787aa0f3b5c7942a1317f7d88e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Order.ConditionallyCompleteLattice.Group
 import Mathlib.Algebra.Algebra.Basic
-import Mathlib.Algebra.Order.Nonneg.Field
 import Mathlib.Algebra.Order.Field.Canonical.Basic
+import Mathlib.Algebra.Order.Nonneg.Field
+import Mathlib.Algebra.Order.Nonneg.Floor
 import Mathlib.Data.Real.Pointwise
+import Mathlib.Order.ConditionallyCompleteLattice.Group
 import Mathlib.Tactic.Positivity
 
 /-!

chore: mathlib4-ify names (#2557)

is_scalar_tower is now IsScalarTower etc.

As discussed on Zulip, this also renames sMulCommClass to smulCommClass. The later was already the majority spelling.

fc37ee9e

Diff

@@ -252,13 +252,13 @@ theorem smul_def {M : Type _} [MulAction ℝ M] (c : ℝ≥0) (x : M) : c • x
 instance {M N : Type _} [MulAction ℝ M] [MulAction ℝ N] [SMul M N] [IsScalarTower ℝ M N] :
     IsScalarTower ℝ≥0 M N where smul_assoc r := (smul_assoc (r : ℝ) : _)
 
-instance sMulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
+instance smulCommClass_left {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass ℝ M N] :
     SMulCommClass ℝ≥0 M N where smul_comm r := (smul_comm (r : ℝ) : _)
-#align nnreal.smul_comm_class_left NNReal.sMulCommClass_left
+#align nnreal.smul_comm_class_left NNReal.smulCommClass_left
 
-instance sMulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
+instance smulCommClass_right {M N : Type _} [MulAction ℝ N] [SMul M N] [SMulCommClass M ℝ N] :
     SMulCommClass M ℝ≥0 N where smul_comm m r := (smul_comm m (r : ℝ) : _)
-#align nnreal.smul_comm_class_right NNReal.sMulCommClass_right
+#align nnreal.smul_comm_class_right NNReal.smulCommClass_right
 
 /-- A `DistribMulAction` over `ℝ` restricts to a `DistribMulAction` over `ℝ≥0`. -/
 instance {M : Type _} [AddMonoid M] [DistribMulAction ℝ M] : DistribMulAction ℝ≥0 M :=