analysis.calculus.lhopital ⟷ Mathlib.Analysis.Calculus.LHopital

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

@@ -129,20 +129,20 @@ theorem lhopital_zero_left_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x)
     comp x (hff' (-x) hx) (hasDerivAt_neg x)
   have hdng : ∀ x ∈ -Ioo a b, HasDerivAt (g ∘ Neg.neg) (g' (-x) * -1) x := fun x hx =>
     comp x (hgg' (-x) hx) (hasDerivAt_neg x)
-  rw [preimage_neg_Ioo] at hdnf 
-  rw [preimage_neg_Ioo] at hdng 
+  rw [preimage_neg_Ioo] at hdnf
+  rw [preimage_neg_Ioo] at hdng
   have :=
     lhopital_zero_right_on_Ioo (neg_lt_neg hab) hdnf hdng
       (by
         intro x hx h
-        apply hg' _ (by rw [← preimage_neg_Ioo] at hx ; exact hx)
-        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h )
+        apply hg' _ (by rw [← preimage_neg_Ioo] at hx; exact hx)
+        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h)
       (hfb.comp tendsto_neg_nhdsWithin_Ioi_neg) (hgb.comp tendsto_neg_nhdsWithin_Ioi_neg)
       (by
         simp only [neg_div_neg_eq, mul_one, mul_neg]
         exact (tendsto_congr fun x => rfl).mp (hdiv.comp tendsto_neg_nhdsWithin_Ioi_neg))
   have := this.comp tendsto_neg_nhdsWithin_Iio
-  unfold Function.comp at this 
+  unfold Function.comp at this
   simpa only [neg_neg]
 #align has_deriv_at.lhopital_zero_left_on_Ioo HasDerivAt.lhopital_zero_left_on_Ioo
 -/
@@ -193,7 +193,7 @@ theorem lhopital_zero_atTop_on_Ioi (hff' : ∀ x ∈ Ioi a, HasDerivAt f (f' x)
         erw [mul_div_mul_right]
         refine' neg_ne_zero.mpr (inv_ne_zero <| pow_ne_zero _ <| ne_of_gt hx))
   have := this.comp tendsto_inv_atTop_zero'
-  unfold Function.comp at this 
+  unfold Function.comp at this
   simpa only [inv_inv]
 #align has_deriv_at.lhopital_zero_at_top_on_Ioi HasDerivAt.lhopital_zero_atTop_on_Ioi
 -/
@@ -209,20 +209,20 @@ theorem lhopital_zero_atBot_on_Iio (hff' : ∀ x ∈ Iio a, HasDerivAt f (f' x)
     comp x (hff' (-x) hx) (hasDerivAt_neg x)
   have hdng : ∀ x ∈ -Iio a, HasDerivAt (g ∘ Neg.neg) (g' (-x) * -1) x := fun x hx =>
     comp x (hgg' (-x) hx) (hasDerivAt_neg x)
-  rw [preimage_neg_Iio] at hdnf 
-  rw [preimage_neg_Iio] at hdng 
+  rw [preimage_neg_Iio] at hdnf
+  rw [preimage_neg_Iio] at hdng
   have :=
     lhopital_zero_at_top_on_Ioi hdnf hdng
       (by
         intro x hx h
-        apply hg' _ (by rw [← preimage_neg_Iio] at hx ; exact hx)
-        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h )
+        apply hg' _ (by rw [← preimage_neg_Iio] at hx; exact hx)
+        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h)
       (hfbot.comp tendsto_neg_at_top_at_bot) (hgbot.comp tendsto_neg_at_top_at_bot)
       (by
         simp only [mul_one, mul_neg, neg_div_neg_eq]
         exact (tendsto_congr fun x => rfl).mp (hdiv.comp tendsto_neg_at_top_at_bot))
   have := this.comp tendsto_neg_at_bot_at_top
-  unfold Function.comp at this 
+  unfold Function.comp at this
   simpa only [neg_neg]
 #align has_deriv_at.lhopital_zero_at_bot_on_Iio HasDerivAt.lhopital_zero_atBot_on_Iio
 -/
@@ -337,7 +337,7 @@ theorem lhopital_zero_nhds_right (hff' : ∀ᶠ x in 𝓝[>] a, HasDerivAt f (f'
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ 𝓝[>] a := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset] at hs 
+  rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset] at hs
   rcases hs with ⟨u, hau, hu⟩
   refine' lhopital_zero_right_on_Ioo hau _ _ _ hfa hga hdiv <;> intro x hx <;> apply_assumption <;>
     first
@@ -360,7 +360,7 @@ theorem lhopital_zero_nhds_left (hff' : ∀ᶠ x in 𝓝[<] a, HasDerivAt f (f'
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ 𝓝[<] a := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_nhdsWithin_Iio_iff_exists_Ioo_subset] at hs 
+  rw [mem_nhdsWithin_Iio_iff_exists_Ioo_subset] at hs
   rcases hs with ⟨l, hal, hl⟩
   refine' lhopital_zero_left_on_Ioo hal _ _ _ hfa hga hdiv <;> intro x hx <;> apply_assumption <;>
     first
@@ -412,7 +412,7 @@ theorem lhopital_zero_atTop (hff' : ∀ᶠ x in atTop, HasDerivAt f (f' x) x)
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ at_top := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_at_top_sets] at hs 
+  rw [mem_at_top_sets] at hs
   rcases hs with ⟨l, hl⟩
   have hl' : Ioi l ⊆ s := fun x hx => hl x (le_of_lt hx)
   refine' lhopital_zero_at_top_on_Ioi _ _ (fun x hx => hg' x <| (hl' hx).2) hftop hgtop hdiv <;>
@@ -437,7 +437,7 @@ theorem lhopital_zero_atBot (hff' : ∀ᶠ x in atBot, HasDerivAt f (f' x) x)
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ at_bot := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_at_bot_sets] at hs 
+  rw [mem_at_bot_sets] at hs
   rcases hs with ⟨l, hl⟩
   have hl' : Iio l ⊆ s := fun x hx => hl x (le_of_lt hx)
   refine' lhopital_zero_at_bot_on_Iio _ _ (fun x hx => hg' x <| (hl' hx).2) hfbot hgbot hdiv <;>

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 -/
-import Mathbin.Analysis.Calculus.MeanValue
-import Mathbin.Analysis.Calculus.Deriv.Inv
+import Analysis.Calculus.MeanValue
+import Analysis.Calculus.Deriv.Inv
 
 #align_import analysis.calculus.lhopital from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.calculus.lhopital
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.MeanValue
 import Mathbin.Analysis.Calculus.Deriv.Inv
 
+#align_import analysis.calculus.lhopital from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # L'Hôpital's rule for 0/0 indeterminate forms
 

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

@@ -54,8 +54,7 @@ to be satisfied on an explicitly-provided interval.
 
 namespace HasDerivAt
 
-include hab
-
+#print HasDerivAt.lhopital_zero_right_on_Ioo /-
 theorem lhopital_zero_right_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x) x)
     (hgg' : ∀ x ∈ Ioo a b, HasDerivAt g (g' x) x) (hg' : ∀ x ∈ Ioo a b, g' x ≠ 0)
     (hfa : Tendsto f (𝓝[>] a) (𝓝 0)) (hga : Tendsto g (𝓝[>] a) (𝓝 0))
@@ -106,7 +105,9 @@ theorem lhopital_zero_right_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x
     try simp
     linarith [this]
 #align has_deriv_at.lhopital_zero_right_on_Ioo HasDerivAt.lhopital_zero_right_on_Ioo
+-/
 
+#print HasDerivAt.lhopital_zero_right_on_Ico /-
 theorem lhopital_zero_right_on_Ico (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x) x)
     (hgg' : ∀ x ∈ Ioo a b, HasDerivAt g (g' x) x) (hcf : ContinuousOn f (Ico a b))
     (hcg : ContinuousOn g (Ico a b)) (hg' : ∀ x ∈ Ioo a b, g' x ≠ 0) (hfa : f a = 0) (hga : g a = 0)
@@ -118,7 +119,9 @@ theorem lhopital_zero_right_on_Ico (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x
   · rw [← hga, ← nhdsWithin_Ioo_eq_nhdsWithin_Ioi hab]
     exact ((hcg a <| left_mem_Ico.mpr hab).mono Ioo_subset_Ico_self).Tendsto
 #align has_deriv_at.lhopital_zero_right_on_Ico HasDerivAt.lhopital_zero_right_on_Ico
+-/
 
+#print HasDerivAt.lhopital_zero_left_on_Ioo /-
 theorem lhopital_zero_left_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x) x)
     (hgg' : ∀ x ∈ Ioo a b, HasDerivAt g (g' x) x) (hg' : ∀ x ∈ Ioo a b, g' x ≠ 0)
     (hfb : Tendsto f (𝓝[<] b) (𝓝 0)) (hgb : Tendsto g (𝓝[<] b) (𝓝 0))
@@ -145,7 +148,9 @@ theorem lhopital_zero_left_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x)
   unfold Function.comp at this 
   simpa only [neg_neg]
 #align has_deriv_at.lhopital_zero_left_on_Ioo HasDerivAt.lhopital_zero_left_on_Ioo
+-/
 
+#print HasDerivAt.lhopital_zero_left_on_Ioc /-
 theorem lhopital_zero_left_on_Ioc (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x) x)
     (hgg' : ∀ x ∈ Ioo a b, HasDerivAt g (g' x) x) (hcf : ContinuousOn f (Ioc a b))
     (hcg : ContinuousOn g (Ioc a b)) (hg' : ∀ x ∈ Ioo a b, g' x ≠ 0) (hfb : f b = 0) (hgb : g b = 0)
@@ -157,9 +162,9 @@ theorem lhopital_zero_left_on_Ioc (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x)
   · rw [← hgb, ← nhdsWithin_Ioo_eq_nhdsWithin_Iio hab]
     exact ((hcg b <| right_mem_Ioc.mpr hab).mono Ioo_subset_Ioc_self).Tendsto
 #align has_deriv_at.lhopital_zero_left_on_Ioc HasDerivAt.lhopital_zero_left_on_Ioc
+-/
 
-omit hab
-
+#print HasDerivAt.lhopital_zero_atTop_on_Ioi /-
 theorem lhopital_zero_atTop_on_Ioi (hff' : ∀ x ∈ Ioi a, HasDerivAt f (f' x) x)
     (hgg' : ∀ x ∈ Ioi a, HasDerivAt g (g' x) x) (hg' : ∀ x ∈ Ioi a, g' x ≠ 0)
     (hftop : Tendsto f atTop (𝓝 0)) (hgtop : Tendsto g atTop (𝓝 0))
@@ -194,7 +199,9 @@ theorem lhopital_zero_atTop_on_Ioi (hff' : ∀ x ∈ Ioi a, HasDerivAt f (f' x)
   unfold Function.comp at this 
   simpa only [inv_inv]
 #align has_deriv_at.lhopital_zero_at_top_on_Ioi HasDerivAt.lhopital_zero_atTop_on_Ioi
+-/
 
+#print HasDerivAt.lhopital_zero_atBot_on_Iio /-
 theorem lhopital_zero_atBot_on_Iio (hff' : ∀ x ∈ Iio a, HasDerivAt f (f' x) x)
     (hgg' : ∀ x ∈ Iio a, HasDerivAt g (g' x) x) (hg' : ∀ x ∈ Iio a, g' x ≠ 0)
     (hfbot : Tendsto f atBot (𝓝 0)) (hgbot : Tendsto g atBot (𝓝 0))
@@ -221,13 +228,13 @@ theorem lhopital_zero_atBot_on_Iio (hff' : ∀ x ∈ Iio a, HasDerivAt f (f' x)
   unfold Function.comp at this 
   simpa only [neg_neg]
 #align has_deriv_at.lhopital_zero_at_bot_on_Iio HasDerivAt.lhopital_zero_atBot_on_Iio
+-/
 
 end HasDerivAt
 
 namespace deriv
 
-include hab
-
+#print deriv.lhopital_zero_right_on_Ioo /-
 theorem lhopital_zero_right_on_Ioo (hdf : DifferentiableOn ℝ f (Ioo a b))
     (hg' : ∀ x ∈ Ioo a b, deriv g x ≠ 0) (hfa : Tendsto f (𝓝[>] a) (𝓝 0))
     (hga : Tendsto g (𝓝[>] a) (𝓝 0))
@@ -242,7 +249,9 @@ theorem lhopital_zero_right_on_Ioo (hdf : DifferentiableOn ℝ f (Ioo a b))
     HasDerivAt.lhopital_zero_right_on_Ioo hab (fun x hx => (hdf x hx).HasDerivAt)
       (fun x hx => (hdg x hx).HasDerivAt) hg' hfa hga hdiv
 #align deriv.lhopital_zero_right_on_Ioo deriv.lhopital_zero_right_on_Ioo
+-/
 
+#print deriv.lhopital_zero_right_on_Ico /-
 theorem lhopital_zero_right_on_Ico (hdf : DifferentiableOn ℝ f (Ioo a b))
     (hcf : ContinuousOn f (Ico a b)) (hcg : ContinuousOn g (Ico a b))
     (hg' : ∀ x ∈ Ioo a b, (deriv g) x ≠ 0) (hfa : f a = 0) (hga : g a = 0)
@@ -255,7 +264,9 @@ theorem lhopital_zero_right_on_Ico (hdf : DifferentiableOn ℝ f (Ioo a b))
   · rw [← hga, ← nhdsWithin_Ioo_eq_nhdsWithin_Ioi hab]
     exact ((hcg a <| left_mem_Ico.mpr hab).mono Ioo_subset_Ico_self).Tendsto
 #align deriv.lhopital_zero_right_on_Ico deriv.lhopital_zero_right_on_Ico
+-/
 
+#print deriv.lhopital_zero_left_on_Ioo /-
 theorem lhopital_zero_left_on_Ioo (hdf : DifferentiableOn ℝ f (Ioo a b))
     (hg' : ∀ x ∈ Ioo a b, (deriv g) x ≠ 0) (hfb : Tendsto f (𝓝[<] b) (𝓝 0))
     (hgb : Tendsto g (𝓝[<] b) (𝓝 0))
@@ -270,9 +281,9 @@ theorem lhopital_zero_left_on_Ioo (hdf : DifferentiableOn ℝ f (Ioo a b))
     HasDerivAt.lhopital_zero_left_on_Ioo hab (fun x hx => (hdf x hx).HasDerivAt)
       (fun x hx => (hdg x hx).HasDerivAt) hg' hfb hgb hdiv
 #align deriv.lhopital_zero_left_on_Ioo deriv.lhopital_zero_left_on_Ioo
+-/
 
-omit hab
-
+#print deriv.lhopital_zero_atTop_on_Ioi /-
 theorem lhopital_zero_atTop_on_Ioi (hdf : DifferentiableOn ℝ f (Ioi a))
     (hg' : ∀ x ∈ Ioi a, (deriv g) x ≠ 0) (hftop : Tendsto f atTop (𝓝 0))
     (hgtop : Tendsto g atTop (𝓝 0)) (hdiv : Tendsto (fun x => (deriv f) x / (deriv g) x) atTop l) :
@@ -286,7 +297,9 @@ theorem lhopital_zero_atTop_on_Ioi (hdf : DifferentiableOn ℝ f (Ioi a))
     HasDerivAt.lhopital_zero_atTop_on_Ioi (fun x hx => (hdf x hx).HasDerivAt)
       (fun x hx => (hdg x hx).HasDerivAt) hg' hftop hgtop hdiv
 #align deriv.lhopital_zero_at_top_on_Ioi deriv.lhopital_zero_atTop_on_Ioi
+-/
 
+#print deriv.lhopital_zero_atBot_on_Iio /-
 theorem lhopital_zero_atBot_on_Iio (hdf : DifferentiableOn ℝ f (Iio a))
     (hg' : ∀ x ∈ Iio a, (deriv g) x ≠ 0) (hfbot : Tendsto f atBot (𝓝 0))
     (hgbot : Tendsto g atBot (𝓝 0)) (hdiv : Tendsto (fun x => (deriv f) x / (deriv g) x) atBot l) :
@@ -300,6 +313,7 @@ theorem lhopital_zero_atBot_on_Iio (hdf : DifferentiableOn ℝ f (Iio a))
     HasDerivAt.lhopital_zero_atBot_on_Iio (fun x hx => (hdf x hx).HasDerivAt)
       (fun x hx => (hdg x hx).HasDerivAt) hg' hfbot hgbot hdiv
 #align deriv.lhopital_zero_at_bot_on_Iio deriv.lhopital_zero_atBot_on_Iio
+-/
 
 end deriv
 
@@ -313,6 +327,7 @@ conditions holding eventually.
 
 namespace HasDerivAt
 
+#print HasDerivAt.lhopital_zero_nhds_right /-
 /-- L'Hôpital's rule for approaching a real from the right, `has_deriv_at` version -/
 theorem lhopital_zero_nhds_right (hff' : ∀ᶠ x in 𝓝[>] a, HasDerivAt f (f' x) x)
     (hgg' : ∀ᶠ x in 𝓝[>] a, HasDerivAt g (g' x) x) (hg' : ∀ᶠ x in 𝓝[>] a, g' x ≠ 0)
@@ -333,7 +348,9 @@ theorem lhopital_zero_nhds_right (hff' : ∀ᶠ x in 𝓝[>] a, HasDerivAt f (f'
     | exact (hu hx).1.2
     | exact (hu hx).2
 #align has_deriv_at.lhopital_zero_nhds_right HasDerivAt.lhopital_zero_nhds_right
+-/
 
+#print HasDerivAt.lhopital_zero_nhds_left /-
 /-- L'Hôpital's rule for approaching a real from the left, `has_deriv_at` version -/
 theorem lhopital_zero_nhds_left (hff' : ∀ᶠ x in 𝓝[<] a, HasDerivAt f (f' x) x)
     (hgg' : ∀ᶠ x in 𝓝[<] a, HasDerivAt g (g' x) x) (hg' : ∀ᶠ x in 𝓝[<] a, g' x ≠ 0)
@@ -354,7 +371,9 @@ theorem lhopital_zero_nhds_left (hff' : ∀ᶠ x in 𝓝[<] a, HasDerivAt f (f'
     | exact (hl hx).1.2
     | exact (hl hx).2
 #align has_deriv_at.lhopital_zero_nhds_left HasDerivAt.lhopital_zero_nhds_left
+-/
 
+#print HasDerivAt.lhopital_zero_nhds' /-
 /-- L'Hôpital's rule for approaching a real, `has_deriv_at` version. This
   does not require anything about the situation at `a` -/
 theorem lhopital_zero_nhds' (hff' : ∀ᶠ x in 𝓝[≠] a, HasDerivAt f (f' x) x)
@@ -367,7 +386,9 @@ theorem lhopital_zero_nhds' (hff' : ∀ᶠ x in 𝓝[≠] a, HasDerivAt f (f' x)
     ⟨lhopital_zero_nhds_left hff'.1 hgg'.1 hg'.1 hfa.1 hga.1 hdiv.1,
       lhopital_zero_nhds_right hff'.2 hgg'.2 hg'.2 hfa.2 hga.2 hdiv.2⟩
 #align has_deriv_at.lhopital_zero_nhds' HasDerivAt.lhopital_zero_nhds'
+-/
 
+#print HasDerivAt.lhopital_zero_nhds /-
 /-- **L'Hôpital's rule** for approaching a real, `has_deriv_at` version -/
 theorem lhopital_zero_nhds (hff' : ∀ᶠ x in 𝓝 a, HasDerivAt f (f' x) x)
     (hgg' : ∀ᶠ x in 𝓝 a, HasDerivAt g (g' x) x) (hg' : ∀ᶠ x in 𝓝 a, g' x ≠ 0)
@@ -379,7 +400,9 @@ theorem lhopital_zero_nhds (hff' : ∀ᶠ x in 𝓝 a, HasDerivAt f (f' x) x)
       | apply tendsto_nhdsWithin_of_tendsto_nhds <;>
     assumption
 #align has_deriv_at.lhopital_zero_nhds HasDerivAt.lhopital_zero_nhds
+-/
 
+#print HasDerivAt.lhopital_zero_atTop /-
 /-- L'Hôpital's rule for approaching +∞, `has_deriv_at` version -/
 theorem lhopital_zero_atTop (hff' : ∀ᶠ x in atTop, HasDerivAt f (f' x) x)
     (hgg' : ∀ᶠ x in atTop, HasDerivAt g (g' x) x) (hg' : ∀ᶠ x in atTop, g' x ≠ 0)
@@ -402,7 +425,9 @@ theorem lhopital_zero_atTop (hff' : ∀ᶠ x in atTop, HasDerivAt f (f' x) x)
     | exact (hl' hx).1.1
     | exact (hl' hx).1.2
 #align has_deriv_at.lhopital_zero_at_top HasDerivAt.lhopital_zero_atTop
+-/
 
+#print HasDerivAt.lhopital_zero_atBot /-
 /-- L'Hôpital's rule for approaching -∞, `has_deriv_at` version -/
 theorem lhopital_zero_atBot (hff' : ∀ᶠ x in atBot, HasDerivAt f (f' x) x)
     (hgg' : ∀ᶠ x in atBot, HasDerivAt g (g' x) x) (hg' : ∀ᶠ x in atBot, g' x ≠ 0)
@@ -425,11 +450,13 @@ theorem lhopital_zero_atBot (hff' : ∀ᶠ x in atBot, HasDerivAt f (f' x) x)
     | exact (hl' hx).1.1
     | exact (hl' hx).1.2
 #align has_deriv_at.lhopital_zero_at_bot HasDerivAt.lhopital_zero_atBot
+-/
 
 end HasDerivAt
 
 namespace deriv
 
+#print deriv.lhopital_zero_nhds_right /-
 /-- **L'Hôpital's rule** for approaching a real from the right, `deriv` version -/
 theorem lhopital_zero_nhds_right (hdf : ∀ᶠ x in 𝓝[>] a, DifferentiableAt ℝ f x)
     (hg' : ∀ᶠ x in 𝓝[>] a, deriv g x ≠ 0) (hfa : Tendsto f (𝓝[>] a) (𝓝 0))
@@ -447,7 +474,9 @@ theorem lhopital_zero_nhds_right (hdf : ∀ᶠ x in 𝓝[>] a, DifferentiableAt
     hdg.mp (eventually_of_forall fun _ => DifferentiableAt.hasDerivAt)
   exact HasDerivAt.lhopital_zero_nhds_right hdf' hdg' hg' hfa hga hdiv
 #align deriv.lhopital_zero_nhds_right deriv.lhopital_zero_nhds_right
+-/
 
+#print deriv.lhopital_zero_nhds_left /-
 /-- **L'Hôpital's rule** for approaching a real from the left, `deriv` version -/
 theorem lhopital_zero_nhds_left (hdf : ∀ᶠ x in 𝓝[<] a, DifferentiableAt ℝ f x)
     (hg' : ∀ᶠ x in 𝓝[<] a, deriv g x ≠ 0) (hfa : Tendsto f (𝓝[<] a) (𝓝 0))
@@ -465,7 +494,9 @@ theorem lhopital_zero_nhds_left (hdf : ∀ᶠ x in 𝓝[<] a, DifferentiableAt 
     hdg.mp (eventually_of_forall fun _ => DifferentiableAt.hasDerivAt)
   exact HasDerivAt.lhopital_zero_nhds_left hdf' hdg' hg' hfa hga hdiv
 #align deriv.lhopital_zero_nhds_left deriv.lhopital_zero_nhds_left
+-/
 
+#print deriv.lhopital_zero_nhds' /-
 /-- **L'Hôpital's rule** for approaching a real, `deriv` version. This
   does not require anything about the situation at `a` -/
 theorem lhopital_zero_nhds' (hdf : ∀ᶠ x in 𝓝[≠] a, DifferentiableAt ℝ f x)
@@ -479,7 +510,9 @@ theorem lhopital_zero_nhds' (hdf : ∀ᶠ x in 𝓝[≠] a, DifferentiableAt ℝ
     ⟨lhopital_zero_nhds_left hdf.1 hg'.1 hfa.1 hga.1 hdiv.1,
       lhopital_zero_nhds_right hdf.2 hg'.2 hfa.2 hga.2 hdiv.2⟩
 #align deriv.lhopital_zero_nhds' deriv.lhopital_zero_nhds'
+-/
 
+#print deriv.lhopital_zero_nhds /-
 /-- **L'Hôpital's rule** for approaching a real, `deriv` version -/
 theorem lhopital_zero_nhds (hdf : ∀ᶠ x in 𝓝 a, DifferentiableAt ℝ f x)
     (hg' : ∀ᶠ x in 𝓝 a, deriv g x ≠ 0) (hfa : Tendsto f (𝓝 a) (𝓝 0)) (hga : Tendsto g (𝓝 a) (𝓝 0))
@@ -491,7 +524,9 @@ theorem lhopital_zero_nhds (hdf : ∀ᶠ x in 𝓝 a, DifferentiableAt ℝ f x)
       | apply tendsto_nhdsWithin_of_tendsto_nhds <;>
     assumption
 #align deriv.lhopital_zero_nhds deriv.lhopital_zero_nhds
+-/
 
+#print deriv.lhopital_zero_atTop /-
 /-- **L'Hôpital's rule** for approaching +∞, `deriv` version -/
 theorem lhopital_zero_atTop (hdf : ∀ᶠ x : ℝ in atTop, DifferentiableAt ℝ f x)
     (hg' : ∀ᶠ x : ℝ in atTop, deriv g x ≠ 0) (hftop : Tendsto f atTop (𝓝 0))
@@ -508,7 +543,9 @@ theorem lhopital_zero_atTop (hdf : ∀ᶠ x : ℝ in atTop, DifferentiableAt ℝ
     hdg.mp (eventually_of_forall fun _ => DifferentiableAt.hasDerivAt)
   exact HasDerivAt.lhopital_zero_atTop hdf' hdg' hg' hftop hgtop hdiv
 #align deriv.lhopital_zero_at_top deriv.lhopital_zero_atTop
+-/
 
+#print deriv.lhopital_zero_atBot /-
 /-- **L'Hôpital's rule** for approaching -∞, `deriv` version -/
 theorem lhopital_zero_atBot (hdf : ∀ᶠ x : ℝ in atBot, DifferentiableAt ℝ f x)
     (hg' : ∀ᶠ x : ℝ in atBot, deriv g x ≠ 0) (hfbot : Tendsto f atBot (𝓝 0))
@@ -525,6 +562,7 @@ theorem lhopital_zero_atBot (hdf : ∀ᶠ x : ℝ in atBot, DifferentiableAt ℝ
     hdg.mp (eventually_of_forall fun _ => DifferentiableAt.hasDerivAt)
   exact HasDerivAt.lhopital_zero_atBot hdf' hdg' hg' hfbot hgbot hdiv
 #align deriv.lhopital_zero_at_bot deriv.lhopital_zero_atBot
+-/
 
 end deriv
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 
 ! This file was ported from Lean 3 source module analysis.calculus.lhopital
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Calculus.Deriv.Inv
 /-!
 # L'Hôpital's rule for 0/0 indeterminate forms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we prove several forms of "L'Hopital's rule" for computing 0/0
 indeterminate forms. The proof of `has_deriv_at.lhopital_zero_right_on_Ioo`
 is based on the one given in the corresponding

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

@@ -126,20 +126,20 @@ theorem lhopital_zero_left_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x)
     comp x (hff' (-x) hx) (hasDerivAt_neg x)
   have hdng : ∀ x ∈ -Ioo a b, HasDerivAt (g ∘ Neg.neg) (g' (-x) * -1) x := fun x hx =>
     comp x (hgg' (-x) hx) (hasDerivAt_neg x)
-  rw [preimage_neg_Ioo] at hdnf
-  rw [preimage_neg_Ioo] at hdng
+  rw [preimage_neg_Ioo] at hdnf 
+  rw [preimage_neg_Ioo] at hdng 
   have :=
     lhopital_zero_right_on_Ioo (neg_lt_neg hab) hdnf hdng
       (by
         intro x hx h
-        apply hg' _ (by rw [← preimage_neg_Ioo] at hx; exact hx)
-        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h)
+        apply hg' _ (by rw [← preimage_neg_Ioo] at hx ; exact hx)
+        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h )
       (hfb.comp tendsto_neg_nhdsWithin_Ioi_neg) (hgb.comp tendsto_neg_nhdsWithin_Ioi_neg)
       (by
         simp only [neg_div_neg_eq, mul_one, mul_neg]
         exact (tendsto_congr fun x => rfl).mp (hdiv.comp tendsto_neg_nhdsWithin_Ioi_neg))
   have := this.comp tendsto_neg_nhdsWithin_Iio
-  unfold Function.comp at this
+  unfold Function.comp at this 
   simpa only [neg_neg]
 #align has_deriv_at.lhopital_zero_left_on_Ioo HasDerivAt.lhopital_zero_left_on_Ioo
 
@@ -188,7 +188,7 @@ theorem lhopital_zero_atTop_on_Ioi (hff' : ∀ x ∈ Ioi a, HasDerivAt f (f' x)
         erw [mul_div_mul_right]
         refine' neg_ne_zero.mpr (inv_ne_zero <| pow_ne_zero _ <| ne_of_gt hx))
   have := this.comp tendsto_inv_atTop_zero'
-  unfold Function.comp at this
+  unfold Function.comp at this 
   simpa only [inv_inv]
 #align has_deriv_at.lhopital_zero_at_top_on_Ioi HasDerivAt.lhopital_zero_atTop_on_Ioi
 
@@ -202,20 +202,20 @@ theorem lhopital_zero_atBot_on_Iio (hff' : ∀ x ∈ Iio a, HasDerivAt f (f' x)
     comp x (hff' (-x) hx) (hasDerivAt_neg x)
   have hdng : ∀ x ∈ -Iio a, HasDerivAt (g ∘ Neg.neg) (g' (-x) * -1) x := fun x hx =>
     comp x (hgg' (-x) hx) (hasDerivAt_neg x)
-  rw [preimage_neg_Iio] at hdnf
-  rw [preimage_neg_Iio] at hdng
+  rw [preimage_neg_Iio] at hdnf 
+  rw [preimage_neg_Iio] at hdng 
   have :=
     lhopital_zero_at_top_on_Ioi hdnf hdng
       (by
         intro x hx h
-        apply hg' _ (by rw [← preimage_neg_Iio] at hx; exact hx)
-        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h)
+        apply hg' _ (by rw [← preimage_neg_Iio] at hx ; exact hx)
+        rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h )
       (hfbot.comp tendsto_neg_at_top_at_bot) (hgbot.comp tendsto_neg_at_top_at_bot)
       (by
         simp only [mul_one, mul_neg, neg_div_neg_eq]
         exact (tendsto_congr fun x => rfl).mp (hdiv.comp tendsto_neg_at_top_at_bot))
   have := this.comp tendsto_neg_at_bot_at_top
-  unfold Function.comp at this
+  unfold Function.comp at this 
   simpa only [neg_neg]
 #align has_deriv_at.lhopital_zero_at_bot_on_Iio HasDerivAt.lhopital_zero_atBot_on_Iio
 
@@ -322,10 +322,13 @@ theorem lhopital_zero_nhds_right (hff' : ∀ᶠ x in 𝓝[>] a, HasDerivAt f (f'
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ 𝓝[>] a := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset] at hs
+  rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset] at hs 
   rcases hs with ⟨u, hau, hu⟩
   refine' lhopital_zero_right_on_Ioo hau _ _ _ hfa hga hdiv <;> intro x hx <;> apply_assumption <;>
-    first |exact (hu hx).1.1|exact (hu hx).1.2|exact (hu hx).2
+    first
+    | exact (hu hx).1.1
+    | exact (hu hx).1.2
+    | exact (hu hx).2
 #align has_deriv_at.lhopital_zero_nhds_right HasDerivAt.lhopital_zero_nhds_right
 
 /-- L'Hôpital's rule for approaching a real from the left, `has_deriv_at` version -/
@@ -340,10 +343,13 @@ theorem lhopital_zero_nhds_left (hff' : ∀ᶠ x in 𝓝[<] a, HasDerivAt f (f'
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ 𝓝[<] a := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_nhdsWithin_Iio_iff_exists_Ioo_subset] at hs
+  rw [mem_nhdsWithin_Iio_iff_exists_Ioo_subset] at hs 
   rcases hs with ⟨l, hal, hl⟩
   refine' lhopital_zero_left_on_Ioo hal _ _ _ hfa hga hdiv <;> intro x hx <;> apply_assumption <;>
-    first |exact (hl hx).1.1|exact (hl hx).1.2|exact (hl hx).2
+    first
+    | exact (hl hx).1.1
+    | exact (hl hx).1.2
+    | exact (hl hx).2
 #align has_deriv_at.lhopital_zero_nhds_left HasDerivAt.lhopital_zero_nhds_left
 
 /-- L'Hôpital's rule for approaching a real, `has_deriv_at` version. This
@@ -366,7 +372,8 @@ theorem lhopital_zero_nhds (hff' : ∀ᶠ x in 𝓝 a, HasDerivAt f (f' x) x)
     (hdiv : Tendsto (fun x => f' x / g' x) (𝓝 a) l) : Tendsto (fun x => f x / g x) (𝓝[≠] a) l := by
   apply @lhopital_zero_nhds' _ _ _ f' _ g' <;>
       first
-        |apply eventually_nhdsWithin_of_eventually_nhds|apply tendsto_nhdsWithin_of_tendsto_nhds <;>
+      | apply eventually_nhdsWithin_of_eventually_nhds
+      | apply tendsto_nhdsWithin_of_tendsto_nhds <;>
     assumption
 #align has_deriv_at.lhopital_zero_nhds HasDerivAt.lhopital_zero_nhds
 
@@ -382,13 +389,15 @@ theorem lhopital_zero_atTop (hff' : ∀ᶠ x in atTop, HasDerivAt f (f' x) x)
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ at_top := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_at_top_sets] at hs
+  rw [mem_at_top_sets] at hs 
   rcases hs with ⟨l, hl⟩
   have hl' : Ioi l ⊆ s := fun x hx => hl x (le_of_lt hx)
   refine' lhopital_zero_at_top_on_Ioi _ _ (fun x hx => hg' x <| (hl' hx).2) hftop hgtop hdiv <;>
         intro x hx <;>
       apply_assumption <;>
-    first |exact (hl' hx).1.1|exact (hl' hx).1.2
+    first
+    | exact (hl' hx).1.1
+    | exact (hl' hx).1.2
 #align has_deriv_at.lhopital_zero_at_top HasDerivAt.lhopital_zero_atTop
 
 /-- L'Hôpital's rule for approaching -∞, `has_deriv_at` version -/
@@ -403,13 +412,15 @@ theorem lhopital_zero_atBot (hff' : ∀ᶠ x in atBot, HasDerivAt f (f' x) x)
   rcases hg' with ⟨s₃, hs₃, hg'⟩
   let s := s₁ ∩ s₂ ∩ s₃
   have hs : s ∈ at_bot := inter_mem (inter_mem hs₁ hs₂) hs₃
-  rw [mem_at_bot_sets] at hs
+  rw [mem_at_bot_sets] at hs 
   rcases hs with ⟨l, hl⟩
   have hl' : Iio l ⊆ s := fun x hx => hl x (le_of_lt hx)
   refine' lhopital_zero_at_bot_on_Iio _ _ (fun x hx => hg' x <| (hl' hx).2) hfbot hgbot hdiv <;>
         intro x hx <;>
       apply_assumption <;>
-    first |exact (hl' hx).1.1|exact (hl' hx).1.2
+    first
+    | exact (hl' hx).1.1
+    | exact (hl' hx).1.2
 #align has_deriv_at.lhopital_zero_at_bot HasDerivAt.lhopital_zero_atBot
 
 end HasDerivAt
@@ -473,7 +484,8 @@ theorem lhopital_zero_nhds (hdf : ∀ᶠ x in 𝓝 a, DifferentiableAt ℝ f x)
     Tendsto (fun x => f x / g x) (𝓝[≠] a) l := by
   apply lhopital_zero_nhds' <;>
       first
-        |apply eventually_nhdsWithin_of_eventually_nhds|apply tendsto_nhdsWithin_of_tendsto_nhds <;>
+      | apply eventually_nhdsWithin_of_eventually_nhds
+      | apply tendsto_nhdsWithin_of_tendsto_nhds <;>
     assumption
 #align deriv.lhopital_zero_nhds deriv.lhopital_zero_nhds
 

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

@@ -37,7 +37,7 @@ L'Hôpital's rule, L'Hopital's rule
 
 open Filter Set
 
-open Filter Topology Pointwise
+open scoped Filter Topology Pointwise
 
 variable {a b : ℝ} (hab : a < b) {l : Filter ℝ} {f f' g g' : ℝ → ℝ}
 

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

@@ -132,11 +132,7 @@ theorem lhopital_zero_left_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x)
     lhopital_zero_right_on_Ioo (neg_lt_neg hab) hdnf hdng
       (by
         intro x hx h
-        apply
-          hg' _
-            (by
-              rw [← preimage_neg_Ioo] at hx
-              exact hx)
+        apply hg' _ (by rw [← preimage_neg_Ioo] at hx; exact hx)
         rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h)
       (hfb.comp tendsto_neg_nhdsWithin_Ioi_neg) (hgb.comp tendsto_neg_nhdsWithin_Ioi_neg)
       (by
@@ -212,11 +208,7 @@ theorem lhopital_zero_atBot_on_Iio (hff' : ∀ x ∈ Iio a, HasDerivAt f (f' x)
     lhopital_zero_at_top_on_Ioi hdnf hdng
       (by
         intro x hx h
-        apply
-          hg' _
-            (by
-              rw [← preimage_neg_Iio] at hx
-              exact hx)
+        apply hg' _ (by rw [← preimage_neg_Iio] at hx; exact hx)
         rwa [mul_comm, ← neg_eq_neg_one_mul, neg_eq_zero] at h)
       (hfbot.comp tendsto_neg_at_top_at_bot) (hgbot.comp tendsto_neg_at_top_at_bot)
       (by

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

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 
 ! This file was ported from Lean 3 source module analysis.calculus.lhopital
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.MeanValue
+import Mathbin.Analysis.Calculus.Deriv.Inv
 
 /-!
 # L'Hôpital's rule for 0/0 indeterminate forms

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

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -60,8 +60,8 @@ theorem lhopital_zero_right_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x
     have : Tendsto g (𝓝[<] x) (𝓝 0) := by
       rw [← h, ← nhdsWithin_Ioo_eq_nhdsWithin_Iio hx.1]
       exact ((hgg' x hx).continuousAt.continuousWithinAt.mono <| sub x hx).tendsto
-    obtain ⟨y, hyx, hy⟩ : ∃ c ∈ Ioo a x, g' c = 0
-    exact exists_hasDerivAt_eq_zero' hx.1 hga this fun y hy => hgg' y <| sub x hx hy
+    obtain ⟨y, hyx, hy⟩ : ∃ c ∈ Ioo a x, g' c = 0 :=
+      exists_hasDerivAt_eq_zero' hx.1 hga this fun y hy => hgg' y <| sub x hx hy
     exact hg' y (sub x hx hyx) hy
   have : ∀ x ∈ Ioo a b, ∃ c ∈ Ioo a x, f x * g' c = g x * f' c := by
     intro x hx

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

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

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

@@ -168,7 +168,7 @@ theorem lhopital_zero_atTop_on_Ioi (hff' : ∀ x ∈ Ioi a, HasDerivAt f (f' x)
       unfold Function.comp
       simp only
       erw [mul_div_mul_right]
-      refine' neg_ne_zero.mpr (inv_ne_zero <| pow_ne_zero _ <| ne_of_gt hx))
+      exact neg_ne_zero.mpr (inv_ne_zero <| pow_ne_zero _ <| ne_of_gt hx))
   have := this.comp tendsto_inv_atTop_zero'
   unfold Function.comp at this
   simpa only [inv_inv]

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

@@ -80,7 +80,6 @@ theorem lhopital_zero_right_on_Ioo (hff' : ∀ x ∈ Ioo a b, HasDerivAt f (f' x
   have cmp : ∀ x ∈ Ioo a b, a < c x ∧ c x < x := fun x hx => (hc x hx).1
   rw [← nhdsWithin_Ioo_eq_nhdsWithin_Ioi hab]
   apply tendsto_nhdsWithin_congr this
-  simp only
   apply hdiv.comp
   refine' tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within _
     (tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.calculus.lhopital
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Calculus.MeanValue
 import Mathlib.Analysis.Calculus.Deriv.Inv
 
+#align_import analysis.calculus.lhopital from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-!
 # L'Hôpital's rule for 0/0 indeterminate forms
 

These are all doc fixes

@@ -14,7 +14,7 @@ import Mathlib.Analysis.Calculus.Deriv.Inv
 /-!
 # L'Hôpital's rule for 0/0 indeterminate forms
 
-In this file, we prove several forms of "L'Hopital's rule" for computing 0/0
+In this file, we prove several forms of "L'Hôpital's rule" for computing 0/0
 indeterminate forms. The proof of `HasDerivAt.lhopital_zero_right_on_Ioo`
 is based on the one given in the corresponding
 [Wikibooks](https://en.wikibooks.org/wiki/Calculus/L%27H%C3%B4pital%27s_Rule)

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>