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

@@ -301,7 +301,7 @@ theorem mul_sq_le_sum_sq (hst : s ⊆ t) (f : ι → 𝕜) (hs : x ^ 2 ≤ ((∑
     (hs' : (s.card : 𝕜) ≠ 0) : (s.card : 𝕜) * x ^ 2 ≤ ∑ i in t, f i ^ 2 :=
   (mul_le_mul_of_nonneg_left (hs.trans sum_div_card_sq_le_sum_sq_div_card) <|
         Nat.cast_nonneg _).trans <|
-    (mul_div_cancel' _ hs').le.trans <| sum_le_sum_of_subset_of_nonneg hst fun i _ _ => sq_nonneg _
+    (mul_div_cancel₀ _ hs').le.trans <| sum_le_sum_of_subset_of_nonneg hst fun i _ _ => sq_nonneg _
 #align szemeredi_regularity.mul_sq_le_sum_sq SzemerediRegularity.mul_sq_le_sum_sq
 -/
 
@@ -319,9 +319,9 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
   have h₂ : x ^ 2 ≤ ((∑ i in s, (f i - (∑ j in t, f j) / t.card)) / s.card) ^ 2 :=
     by
     apply h₁.trans
-    rw [sum_sub_distrib, sum_const, nsmul_eq_mul, sub_div, mul_div_cancel_left _ hscard.ne']
+    rw [sum_sub_distrib, sum_const, nsmul_eq_mul, sub_div, mul_div_cancel_left₀ _ hscard.ne']
   apply (add_le_add_right ht _).trans
-  rw [← mul_div_right_comm, le_div_iff htcard, add_mul, div_mul_cancel _ htcard.ne']
+  rw [← mul_div_right_comm, le_div_iff htcard, add_mul, div_mul_cancel₀ _ htcard.ne']
   have h₃ := mul_sq_le_sum_sq hst (fun i => f i - (∑ j in t, f j) / t.card) h₂ hscard.ne'
   apply (add_le_add_left h₃ _).trans
   simp [← mul_div_right_comm _ (t.card : 𝕜), sub_div' _ _ _ htcard.ne', ← sum_div, ← add_div,

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

@@ -210,7 +210,7 @@ theorem card_aux₂ (hP : P.IsEquipartition) (hu : u ∈ P.parts)
     by
     rw [step_bound, ← Nat.div_div_eq_div_mul]
     exact Nat.div_mul_le_self _ _
-  rw [Nat.add_sub_of_le this] at hucard 
+  rw [Nat.add_sub_of_le this] at hucard
   rw [(hP.card_parts_eq_average hu).resolve_left hucard, mul_add, mul_one, ← add_assoc, ← add_mul,
     Nat.sub_add_cancel a_add_one_le_four_pow_parts_card, ← add_assoc, mul_comm,
     Nat.add_sub_of_le this, card_univ]

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

@@ -60,7 +60,7 @@ theorem stepBound_mono : Monotone stepBound := fun a b h =>
 
 #print SzemerediRegularity.stepBound_pos_iff /-
 theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
-  zero_lt_mul_right <| by positivity
+  mul_pos_iff_of_pos_right <| by positivity
 #align szemeredi_regularity.step_bound_pos_iff SzemerediRegularity.stepBound_pos_iff
 -/
 

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

@@ -54,7 +54,7 @@ theorem le_stepBound : id ≤ stepBound := fun n => Nat.le_mul_of_pos_right <| p
 
 #print SzemerediRegularity.stepBound_mono /-
 theorem stepBound_mono : Monotone stepBound := fun a b h =>
-  Nat.mul_le_mul h <| Nat.pow_le_pow_of_le_right (by norm_num) h
+  Nat.mul_le_mul h <| Nat.pow_le_pow_right (by norm_num) h
 #align szemeredi_regularity.step_bound_mono SzemerediRegularity.stepBound_mono
 -/
 
@@ -86,7 +86,7 @@ private theorem eps_pos {ε : ℝ} {n : ℕ} (h : 100 ≤ 4 ^ n * ε ^ 5) : 0 <
   pow_bit1_pos_iff.1 <| pos_of_mul_pos_right (h.trans_lt' <| by norm_num) <| by positivity
 
 private theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m :=
-  Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_of_le_left (by norm_num) _).trans hPα) <|
+  Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_left (by norm_num) _).trans hPα) <|
     stepBound_pos (P.parts_nonempty <| univ_nonempty.ne_empty).card_pos
 
 -- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.

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

@@ -260,7 +260,7 @@ theorem hundred_lt_pow_initialBound_mul {ε : ℝ} (hε : 0 < ε) (l : ℕ) :
   by
   rw [← rpow_nat_cast 4, ← div_lt_iff (pow_pos hε 5), lt_rpow_iff_log_lt _ zero_lt_four, ←
     div_lt_iff, initial_bound, Nat.cast_max, Nat.cast_max]
-  · push_cast ; exact lt_max_of_lt_right (lt_max_of_lt_right <| Nat.lt_floor_add_one _)
+  · push_cast; exact lt_max_of_lt_right (lt_max_of_lt_right <| Nat.lt_floor_add_one _)
   · exact log_pos (by norm_num)
   · exact div_pos (by norm_num) (pow_pos hε 5)
 #align szemeredi_regularity.hundred_lt_pow_initial_bound_mul SzemerediRegularity.hundred_lt_pow_initialBound_mul

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

@@ -187,7 +187,7 @@ theorem hundred_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤
 theorem a_add_one_le_four_pow_parts_card : a + 1 ≤ 4 ^ P.parts.card :=
   by
   have h : 1 ≤ 4 ^ P.parts.card := one_le_pow_of_one_le (by norm_num) _
-  rw [step_bound, ← Nat.div_div_eq_div_mul, ← Nat.le_sub_iff_right h, tsub_le_iff_left, ←
+  rw [step_bound, ← Nat.div_div_eq_div_mul, ← Nat.le_sub_iff_add_le h, tsub_le_iff_left, ←
     Nat.add_sub_assoc h]
   exact Nat.le_pred_of_lt (Nat.lt_div_mul_add h)
 #align szemeredi_regularity.a_add_one_le_four_pow_parts_card SzemerediRegularity.a_add_one_le_four_pow_parts_card

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 -/
-import Mathbin.Algebra.Order.Chebyshev
-import Mathbin.Analysis.SpecialFunctions.Pow.Real
-import Mathbin.Order.Partition.Equipartition
+import Algebra.Order.Chebyshev
+import Analysis.SpecialFunctions.Pow.Real
+import Order.Partition.Equipartition
 
 #align_import combinatorics.simple_graph.regularity.bound from "leanprover-community/mathlib"@"08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -64,7 +64,7 @@ theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
 #align szemeredi_regularity.step_bound_pos_iff SzemerediRegularity.stepBound_pos_iff
 -/
 
-alias step_bound_pos_iff ↔ _ step_bound_pos
+alias ⟨_, step_bound_pos⟩ := step_bound_pos_iff
 #align szemeredi_regularity.step_bound_pos SzemerediRegularity.stepBound_pos
 
 end szemeredi_regularity

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
-
-! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit 08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Chebyshev
 import Mathbin.Analysis.SpecialFunctions.Pow.Real
 import Mathbin.Order.Partition.Equipartition
 
+#align_import combinatorics.simple_graph.regularity.bound from "leanprover-community/mathlib"@"08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5"
+
 /-!
 # Numerical bounds for Szemerédi Regularity Lemma
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit bf7ef0e83e5b7e6c1169e97f055e58a2e4e9d52d
+! leanprover-community/mathlib commit 08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Order.Partition.Equipartition
 /-!
 # Numerical bounds for Szemerédi Regularity Lemma
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file gathers the numerical facts required by the proof of Szemerédi's regularity lemma.
 
 This entire file is internal to the proof of Szemerédi Regularity Lemma.

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -37,7 +37,7 @@ open Finset Fintype Function Real
 
 open scoped BigOperators
 
-namespace SzemerediRegularity
+namespace szemeredi_regularity
 
 #print SzemerediRegularity.stepBound /-
 /-- Auxiliary function for Szemerédi's regularity lemma. Blowing up a partition of size `n` during
@@ -67,9 +67,9 @@ theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
 alias step_bound_pos_iff ↔ _ step_bound_pos
 #align szemeredi_regularity.step_bound_pos SzemerediRegularity.stepBound_pos
 
-end SzemerediRegularity
+end szemeredi_regularity
 
-open SzemerediRegularity
+open szemeredi_regularity
 
 variable {α : Type _} [DecidableEq α] [Fintype α] {P : Finpartition (univ : Finset α)}
   {u : Finset α} {ε : ℝ}
@@ -131,7 +131,7 @@ end Tactic
 
 attribute [local positivity] tactic.positivity_szemeredi_regularity
 
-namespace SzemerediRegularity
+namespace szemeredi_regularity
 
 #print SzemerediRegularity.m_pos /-
 theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m := by
@@ -331,11 +331,11 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
 #align szemeredi_regularity.add_div_le_sum_sq_div_card SzemerediRegularity.add_div_le_sum_sq_div_card
 -/
 
-end SzemerediRegularity
+end szemeredi_regularity
 
 namespace Tactic
 
-open Positivity SzemerediRegularity
+open Positivity szemeredi_regularity
 
 /-- Extension for the `positivity` tactic: `szemeredi_regularity.initial_bound` and
 `szemeredi_regularity.bound` are always positive. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -39,22 +39,30 @@ open scoped BigOperators
 
 namespace SzemerediRegularity
 
+#print SzemerediRegularity.stepBound /-
 /-- Auxiliary function for Szemerédi's regularity lemma. Blowing up a partition of size `n` during
 the induction results in a partition of size at most `step_bound n`. -/
 def stepBound (n : ℕ) : ℕ :=
   n * 4 ^ n
 #align szemeredi_regularity.step_bound SzemerediRegularity.stepBound
+-/
 
+#print SzemerediRegularity.le_stepBound /-
 theorem le_stepBound : id ≤ stepBound := fun n => Nat.le_mul_of_pos_right <| pow_pos (by norm_num) n
 #align szemeredi_regularity.le_step_bound SzemerediRegularity.le_stepBound
+-/
 
+#print SzemerediRegularity.stepBound_mono /-
 theorem stepBound_mono : Monotone stepBound := fun a b h =>
   Nat.mul_le_mul h <| Nat.pow_le_pow_of_le_right (by norm_num) h
 #align szemeredi_regularity.step_bound_mono SzemerediRegularity.stepBound_mono
+-/
 
+#print SzemerediRegularity.stepBound_pos_iff /-
 theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
   zero_lt_mul_right <| by positivity
 #align szemeredi_regularity.step_bound_pos_iff SzemerediRegularity.stepBound_pos_iff
+-/
 
 alias step_bound_pos_iff ↔ _ step_bound_pos
 #align szemeredi_regularity.step_bound_pos SzemerediRegularity.stepBound_pos
@@ -125,25 +133,36 @@ attribute [local positivity] tactic.positivity_szemeredi_regularity
 
 namespace SzemerediRegularity
 
+#print SzemerediRegularity.m_pos /-
 theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m := by
   positivity
 #align szemeredi_regularity.m_pos SzemerediRegularity.m_pos
+-/
 
+#print SzemerediRegularity.coe_m_add_one_pos /-
 theorem coe_m_add_one_pos : 0 < (m : ℝ) + 1 := by positivity
 #align szemeredi_regularity.coe_m_add_one_pos SzemerediRegularity.coe_m_add_one_pos
+-/
 
+#print SzemerediRegularity.one_le_m_coe /-
 theorem one_le_m_coe [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : (1 : ℝ) ≤ m :=
   Nat.one_le_cast.2 <| m_pos hPα
 #align szemeredi_regularity.one_le_m_coe SzemerediRegularity.one_le_m_coe
+-/
 
+#print SzemerediRegularity.eps_pow_five_pos /-
 theorem eps_pow_five_pos (hPε : 100 ≤ 4 ^ P.parts.card * ε ^ 5) : 0 < ε ^ 5 :=
   pos_of_mul_pos_right ((by norm_num : (0 : ℝ) < 100).trans_le hPε) <| pow_nonneg (by norm_num) _
 #align szemeredi_regularity.eps_pow_five_pos SzemerediRegularity.eps_pow_five_pos
+-/
 
+#print SzemerediRegularity.eps_pos /-
 theorem eps_pos (hPε : 100 ≤ 4 ^ P.parts.card * ε ^ 5) : 0 < ε :=
   pow_bit1_pos_iff.1 <| eps_pow_five_pos hPε
 #align szemeredi_regularity.eps_pos SzemerediRegularity.eps_pos
+-/
 
+#print SzemerediRegularity.hundred_div_ε_pow_five_le_m /-
 theorem hundred_div_ε_pow_five_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)
     (hPε : 100 ≤ 4 ^ P.parts.card * ε ^ 5) : 100 / ε ^ 5 ≤ m :=
   (div_le_of_nonneg_of_le_mul (eps_pow_five_pos hPε).le (by positivity) hPε).trans
@@ -153,14 +172,18 @@ theorem hundred_div_ε_pow_five_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P
           (step_bound_pos (P.parts_nonempty <| univ_nonempty.ne_empty).card_pos),
         step_bound, mul_left_comm, ← mul_pow])
 #align szemeredi_regularity.hundred_div_ε_pow_five_le_m SzemerediRegularity.hundred_div_ε_pow_five_le_m
+-/
 
+#print SzemerediRegularity.hundred_le_m /-
 theorem hundred_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)
     (hPε : 100 ≤ 4 ^ P.parts.card * ε ^ 5) (hε : ε ≤ 1) : 100 ≤ m := by
   exact_mod_cast
     (hundred_div_ε_pow_five_le_m hPα hPε).trans'
       (le_div_self (by norm_num) (by positivity) <| pow_le_one _ (by positivity) hε)
 #align szemeredi_regularity.hundred_le_m SzemerediRegularity.hundred_le_m
+-/
 
+#print SzemerediRegularity.a_add_one_le_four_pow_parts_card /-
 theorem a_add_one_le_four_pow_parts_card : a + 1 ≤ 4 ^ P.parts.card :=
   by
   have h : 1 ≤ 4 ^ P.parts.card := one_le_pow_of_one_le (by norm_num) _
@@ -168,13 +191,17 @@ theorem a_add_one_le_four_pow_parts_card : a + 1 ≤ 4 ^ P.parts.card :=
     Nat.add_sub_assoc h]
   exact Nat.le_pred_of_lt (Nat.lt_div_mul_add h)
 #align szemeredi_regularity.a_add_one_le_four_pow_parts_card SzemerediRegularity.a_add_one_le_four_pow_parts_card
+-/
 
+#print SzemerediRegularity.card_aux₁ /-
 theorem card_aux₁ (hucard : u.card = m * 4 ^ P.parts.card + a) :
     (4 ^ P.parts.card - a) * m + a * (m + 1) = u.card := by
   rw [hucard, mul_add, mul_one, ← add_assoc, ← add_mul,
     Nat.sub_add_cancel ((Nat.le_succ _).trans a_add_one_le_four_pow_parts_card), mul_comm]
 #align szemeredi_regularity.card_aux₁ SzemerediRegularity.card_aux₁
+-/
 
+#print SzemerediRegularity.card_aux₂ /-
 theorem card_aux₂ (hP : P.IsEquipartition) (hu : u ∈ P.parts)
     (hucard : ¬u.card = m * 4 ^ P.parts.card + a) :
     (4 ^ P.parts.card - (a + 1)) * m + (a + 1) * (m + 1) = u.card :=
@@ -188,34 +215,46 @@ theorem card_aux₂ (hP : P.IsEquipartition) (hu : u ∈ P.parts)
     Nat.sub_add_cancel a_add_one_le_four_pow_parts_card, ← add_assoc, mul_comm,
     Nat.add_sub_of_le this, card_univ]
 #align szemeredi_regularity.card_aux₂ SzemerediRegularity.card_aux₂
+-/
 
+#print SzemerediRegularity.pow_mul_m_le_card_part /-
 theorem pow_mul_m_le_card_part (hP : P.IsEquipartition) (hu : u ∈ P.parts) :
     (4 : ℝ) ^ P.parts.card * m ≤ u.card := by
   norm_cast
   rw [step_bound, ← Nat.div_div_eq_div_mul]
   exact (Nat.mul_div_le _ _).trans (hP.average_le_card_part hu)
 #align szemeredi_regularity.pow_mul_m_le_card_part SzemerediRegularity.pow_mul_m_le_card_part
+-/
 
 variable (P ε) (l : ℕ)
 
+#print SzemerediRegularity.initialBound /-
 /-- Auxiliary function for Szemerédi's regularity lemma. The size of the partition by which we start
 blowing. -/
 noncomputable def initialBound : ℕ :=
   max 7 <| max l <| ⌊log (100 / ε ^ 5) / log 4⌋₊ + 1
 #align szemeredi_regularity.initial_bound SzemerediRegularity.initialBound
+-/
 
+#print SzemerediRegularity.le_initialBound /-
 theorem le_initialBound : l ≤ initialBound ε l :=
   (le_max_left _ _).trans <| le_max_right _ _
 #align szemeredi_regularity.le_initial_bound SzemerediRegularity.le_initialBound
+-/
 
+#print SzemerediRegularity.seven_le_initialBound /-
 theorem seven_le_initialBound : 7 ≤ initialBound ε l :=
   le_max_left _ _
 #align szemeredi_regularity.seven_le_initial_bound SzemerediRegularity.seven_le_initialBound
+-/
 
+#print SzemerediRegularity.initialBound_pos /-
 theorem initialBound_pos : 0 < initialBound ε l :=
   Nat.succ_pos'.trans_le <| seven_le_initialBound _ _
 #align szemeredi_regularity.initial_bound_pos SzemerediRegularity.initialBound_pos
+-/
 
+#print SzemerediRegularity.hundred_lt_pow_initialBound_mul /-
 theorem hundred_lt_pow_initialBound_mul {ε : ℝ} (hε : 0 < ε) (l : ℕ) :
     100 < 4 ^ initialBound ε l * ε ^ 5 :=
   by
@@ -225,36 +264,48 @@ theorem hundred_lt_pow_initialBound_mul {ε : ℝ} (hε : 0 < ε) (l : ℕ) :
   · exact log_pos (by norm_num)
   · exact div_pos (by norm_num) (pow_pos hε 5)
 #align szemeredi_regularity.hundred_lt_pow_initial_bound_mul SzemerediRegularity.hundred_lt_pow_initialBound_mul
+-/
 
+#print SzemerediRegularity.bound /-
 /-- An explicit bound on the size of the equipartition whose existence is given by Szemerédi's
 regularity lemma. -/
 noncomputable def bound : ℕ :=
   (stepBound^[⌊4 / ε ^ 5⌋₊] <| initialBound ε l) *
     16 ^ (stepBound^[⌊4 / ε ^ 5⌋₊] <| initialBound ε l)
 #align szemeredi_regularity.bound SzemerediRegularity.bound
+-/
 
+#print SzemerediRegularity.initialBound_le_bound /-
 theorem initialBound_le_bound : initialBound ε l ≤ bound ε l :=
   (id_le_iterate_of_id_le le_stepBound _ _).trans <| Nat.le_mul_of_pos_right <| by positivity
 #align szemeredi_regularity.initial_bound_le_bound SzemerediRegularity.initialBound_le_bound
+-/
 
+#print SzemerediRegularity.le_bound /-
 theorem le_bound : l ≤ bound ε l :=
   (le_initialBound ε l).trans <| initialBound_le_bound ε l
 #align szemeredi_regularity.le_bound SzemerediRegularity.le_bound
+-/
 
+#print SzemerediRegularity.bound_pos /-
 theorem bound_pos : 0 < bound ε l :=
   (initialBound_pos ε l).trans_le <| initialBound_le_bound ε l
 #align szemeredi_regularity.bound_pos SzemerediRegularity.bound_pos
+-/
 
 variable {ι 𝕜 : Type _} [LinearOrderedField 𝕜] (r : ι → ι → Prop) [DecidableRel r] {s t : Finset ι}
   {x : 𝕜}
 
+#print SzemerediRegularity.mul_sq_le_sum_sq /-
 theorem mul_sq_le_sum_sq (hst : s ⊆ t) (f : ι → 𝕜) (hs : x ^ 2 ≤ ((∑ i in s, f i) / s.card) ^ 2)
     (hs' : (s.card : 𝕜) ≠ 0) : (s.card : 𝕜) * x ^ 2 ≤ ∑ i in t, f i ^ 2 :=
   (mul_le_mul_of_nonneg_left (hs.trans sum_div_card_sq_le_sum_sq_div_card) <|
         Nat.cast_nonneg _).trans <|
     (mul_div_cancel' _ hs').le.trans <| sum_le_sum_of_subset_of_nonneg hst fun i _ _ => sq_nonneg _
 #align szemeredi_regularity.mul_sq_le_sum_sq SzemerediRegularity.mul_sq_le_sum_sq
+-/
 
+#print SzemerediRegularity.add_div_le_sum_sq_div_card /-
 theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜) (hx : 0 ≤ x)
     (hs : x ≤ |(∑ i in s, f i) / s.card - (∑ i in t, f i) / t.card|)
     (ht : d ≤ ((∑ i in t, f i) / t.card) ^ 2) :
@@ -278,6 +329,7 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
     mul_sum]
   ring_nf
 #align szemeredi_regularity.add_div_le_sum_sq_div_card SzemerediRegularity.add_div_le_sum_sq_div_card
+-/
 
 end SzemerediRegularity
 

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

@@ -66,10 +66,8 @@ open SzemerediRegularity
 variable {α : Type _} [DecidableEq α] [Fintype α] {P : Finpartition (univ : Finset α)}
   {u : Finset α} {ε : ℝ}
 
--- mathport name: exprm
 local notation "m" => (card α / stepBound P.parts.card : ℕ)
 
--- mathport name: expra
 local notation "a" => (card α / P.parts.card - m * 4 ^ P.parts.card : ℕ)
 
 namespace Tactic

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

@@ -267,7 +267,7 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
   have htcard : (0 : 𝕜) < t.card := hscard.trans_le (Nat.cast_le.2 (card_le_of_subset hst))
   have h₁ : x ^ 2 ≤ ((∑ i in s, f i) / s.card - (∑ i in t, f i) / t.card) ^ 2 :=
     sq_le_sq.2 (by rwa [abs_of_nonneg hx])
-  have h₂ : x ^ 2 ≤ ((∑ i in s, f i - (∑ j in t, f j) / t.card) / s.card) ^ 2 :=
+  have h₂ : x ^ 2 ≤ ((∑ i in s, (f i - (∑ j in t, f j) / t.card)) / s.card) ^ 2 :=
     by
     apply h₁.trans
     rw [sum_sub_distrib, sum_const, nsmul_eq_mul, sub_div, mul_div_cancel_left _ hscard.ne']

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -83,6 +83,7 @@ private theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤
   Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_of_le_left (by norm_num) _).trans hPα) <|
     stepBound_pos (P.parts_nonempty <| univ_nonempty.ne_empty).card_pos
 
+-- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
 -- failed to format: unknown constant 'term.pseudo.antiquot'
 /--
       Local extension for the `positivity` tactic: A few facts that are needed many times for the

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

@@ -184,7 +184,7 @@ theorem card_aux₂ (hP : P.IsEquipartition) (hu : u ∈ P.parts)
     by
     rw [step_bound, ← Nat.div_div_eq_div_mul]
     exact Nat.div_mul_le_self _ _
-  rw [Nat.add_sub_of_le this] at hucard
+  rw [Nat.add_sub_of_le this] at hucard 
   rw [(hP.card_parts_eq_average hu).resolve_left hucard, mul_add, mul_one, ← add_assoc, ← add_mul,
     Nat.sub_add_cancel a_add_one_le_four_pow_parts_card, ← add_assoc, mul_comm,
     Nat.add_sub_of_le this, card_univ]

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

@@ -35,7 +35,7 @@ This entire file is internal to the proof of Szemerédi Regularity Lemma.
 
 open Finset Fintype Function Real
 
-open BigOperators
+open scoped BigOperators
 
 namespace SzemerediRegularity
 

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

@@ -222,8 +222,7 @@ theorem hundred_lt_pow_initialBound_mul {ε : ℝ} (hε : 0 < ε) (l : ℕ) :
   by
   rw [← rpow_nat_cast 4, ← div_lt_iff (pow_pos hε 5), lt_rpow_iff_log_lt _ zero_lt_four, ←
     div_lt_iff, initial_bound, Nat.cast_max, Nat.cast_max]
-  · push_cast
-    exact lt_max_of_lt_right (lt_max_of_lt_right <| Nat.lt_floor_add_one _)
+  · push_cast ; exact lt_max_of_lt_right (lt_max_of_lt_right <| Nat.lt_floor_add_one _)
   · exact log_pos (by norm_num)
   · exact div_pos (by norm_num) (pow_pos hε 5)
 #align szemeredi_regularity.hundred_lt_pow_initial_bound_mul SzemerediRegularity.hundred_lt_pow_initialBound_mul

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

@@ -78,12 +78,10 @@ open Positivity
 
 private theorem eps_pos {ε : ℝ} {n : ℕ} (h : 100 ≤ 4 ^ n * ε ^ 5) : 0 < ε :=
   pow_bit1_pos_iff.1 <| pos_of_mul_pos_right (h.trans_lt' <| by norm_num) <| by positivity
-#align tactic.eps_pos tactic.eps_pos
 
 private theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m :=
   Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_of_le_left (by norm_num) _).trans hPα) <|
     stepBound_pos (P.parts_nonempty <| univ_nonempty.ne_empty).card_pos
-#align tactic.m_pos tactic.m_pos
 
 -- failed to format: unknown constant 'term.pseudo.antiquot'
 /--

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit 4fa54b337f7d52805480306db1b1439c741848c8
+! leanprover-community/mathlib commit bf7ef0e83e5b7e6c1169e97f055e58a2e4e9d52d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -26,6 +26,10 @@ This entire file is internal to the proof of Szemerédi Regularity Lemma.
 * `szemeredi_regularity.initial_bound`: The size of the partition we start the induction with.
 * `szemeredi_regularity.bound`: The upper bound on the size of the partition produced by our version
   of Szemerédi's regularity lemma.
+
+## References
+
+[Yaël Dillies, Bhavik Mehta, *Formalising Szemerédi’s Regularity Lemma in Lean*][srl_itp]
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 4fa54b337f7d52805480306db1b1439c741848c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Chebyshev
-import Mathbin.Analysis.SpecialFunctions.Pow.Tactic
+import Mathbin.Analysis.SpecialFunctions.Pow.Real
 import Mathbin.Order.Partition.Equipartition
 
 /-!

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

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit 7a0dd7b2466948ac029d671c2701df3b1f134b3c
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Chebyshev
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Tactic
 import Mathbin.Order.Partition.Equipartition
 
 /-!

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit b7399344324326918d65d0c74e9571e3a8cb9199
+! leanprover-community/mathlib commit 7a0dd7b2466948ac029d671c2701df3b1f134b3c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -55,6 +55,10 @@ theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
 alias step_bound_pos_iff ↔ _ step_bound_pos
 #align szemeredi_regularity.step_bound_pos SzemerediRegularity.stepBound_pos
 
+end SzemerediRegularity
+
+open SzemerediRegularity
+
 variable {α : Type _} [DecidableEq α] [Fintype α] {P : Finpartition (univ : Finset α)}
   {u : Finset α} {ε : ℝ}
 
@@ -64,17 +68,67 @@ local notation "m" => (card α / stepBound P.parts.card : ℕ)
 -- mathport name: expra
 local notation "a" => (card α / P.parts.card - m * 4 ^ P.parts.card : ℕ)
 
-theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m :=
+namespace Tactic
+
+open Positivity
+
+private theorem eps_pos {ε : ℝ} {n : ℕ} (h : 100 ≤ 4 ^ n * ε ^ 5) : 0 < ε :=
+  pow_bit1_pos_iff.1 <| pos_of_mul_pos_right (h.trans_lt' <| by norm_num) <| by positivity
+#align tactic.eps_pos tactic.eps_pos
+
+private theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m :=
   Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_of_le_left (by norm_num) _).trans hPα) <|
     stepBound_pos (P.parts_nonempty <| univ_nonempty.ne_empty).card_pos
-#align szemeredi_regularity.m_pos SzemerediRegularity.m_pos
+#align tactic.m_pos tactic.m_pos
+
+-- failed to format: unknown constant 'term.pseudo.antiquot'
+/--
+      Local extension for the `positivity` tactic: A few facts that are needed many times for the
+      proof of Szemerédi's regularity lemma. -/
+    unsafe
+  def
+    positivity_szemeredi_regularity
+    : expr → tactic strictness
+    |
+        q( $ ( n ) / stepBound ( Finpartition.parts $ ( P ) ) . card )
+        =>
+        do
+          let
+              p
+                ←
+                to_expr
+                    `
+                      `(
+                        ( Finpartition.parts $ ( P ) ) . card
+                            *
+                            16 ^ ( Finpartition.parts $ ( P ) ) . card
+                          ≤
+                          $ ( n )
+                        )
+                  >>=
+                  find_assumption
+            positive <$> mk_app ` ` m_pos [ p ]
+      |
+        ε
+        =>
+        do
+          let typ ← infer_type ε
+            unify typ q( ℝ )
+            let p ← to_expr ` `( 100 ≤ 4 ^ _ * $ ( ε ) ^ 5 ) >>= find_assumption
+            positive <$> mk_app ` ` eps_pos [ p ]
+#align tactic.positivity_szemeredi_regularity tactic.positivity_szemeredi_regularity
+
+end Tactic
+
+attribute [local positivity] tactic.positivity_szemeredi_regularity
 
-theorem m_coe_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : (0 : ℝ) < m :=
-  Nat.cast_pos.2 <| m_pos hPα
-#align szemeredi_regularity.m_coe_pos SzemerediRegularity.m_coe_pos
+namespace SzemerediRegularity
+
+theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m := by
+  positivity
+#align szemeredi_regularity.m_pos SzemerediRegularity.m_pos
 
-theorem coe_m_add_one_pos : 0 < (m : ℝ) + 1 :=
-  Nat.cast_add_one_pos _
+theorem coe_m_add_one_pos : 0 < (m : ℝ) + 1 := by positivity
 #align szemeredi_regularity.coe_m_add_one_pos SzemerediRegularity.coe_m_add_one_pos
 
 theorem one_le_m_coe [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : (1 : ℝ) ≤ m :=
@@ -102,8 +156,8 @@ theorem hundred_div_ε_pow_five_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P
 theorem hundred_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)
     (hPε : 100 ≤ 4 ^ P.parts.card * ε ^ 5) (hε : ε ≤ 1) : 100 ≤ m := by
   exact_mod_cast
-    (le_div_self (by norm_num) (eps_pow_five_pos hPε) <| pow_le_one _ (eps_pos hPε).le hε).trans
-      (hundred_div_ε_pow_five_le_m hPα hPε)
+    (hundred_div_ε_pow_five_le_m hPα hPε).trans'
+      (le_div_self (by norm_num) (by positivity) <| pow_le_one _ (by positivity) hε)
 #align szemeredi_regularity.hundred_le_m SzemerediRegularity.hundred_le_m
 
 theorem a_add_one_le_four_pow_parts_card : a + 1 ≤ 4 ^ P.parts.card :=

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

This matches our general policy and zpow_two_pos_of_ne_zero.

Also define sq_pos_of_ne_zero as an alias.

@@ -254,12 +254,12 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
   apply (add_le_add_left h₃ _).trans
   -- Porting note: was
   -- `simp [← mul_div_right_comm _ (t.card : 𝕜), sub_div' _ _ _ htcard.ne', ← sum_div, ← add_div,`
-  -- `  mul_pow, div_le_iff (sq_pos_of_ne_zero _ htcard.ne'), sub_sq, sum_add_distrib, ← sum_mul,`
+  -- `  mul_pow, div_le_iff (sq_pos_of_ne_zero htcard.ne'), sub_sq, sum_add_distrib, ← sum_mul,`
   -- `  ← mul_sum]`
   simp_rw [sub_div' _ _ _ htcard.ne']
   conv_lhs => enter [2, 2, x]; rw [div_pow]
   rw [div_pow, ← sum_div, ← mul_div_right_comm _ (t.card : 𝕜), ← add_div,
-    div_le_iff (sq_pos_of_ne_zero _ htcard.ne')]
+    div_le_iff (sq_pos_of_ne_zero htcard.ne')]
   simp_rw [sub_sq, sum_add_distrib, sum_const, nsmul_eq_mul, sum_sub_distrib, mul_pow, ← sum_mul,
     ← mul_sum, ← sum_mul]
   ring_nf; rfl

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.

@@ -199,7 +199,7 @@ theorem initialBound_pos : 0 < initialBound ε l :=
 
 theorem hundred_lt_pow_initialBound_mul {ε : ℝ} (hε : 0 < ε) (l : ℕ) :
     100 < ↑4 ^ initialBound ε l * ε ^ 5 := by
-  rw [← rpow_nat_cast 4, ← div_lt_iff (pow_pos hε 5), lt_rpow_iff_log_lt _ zero_lt_four, ←
+  rw [← rpow_natCast 4, ← div_lt_iff (pow_pos hε 5), lt_rpow_iff_log_lt _ zero_lt_four, ←
     div_lt_iff, initialBound, Nat.cast_max, Nat.cast_max]
   · push_cast
     exact lt_max_of_lt_right (lt_max_of_lt_right <| Nat.lt_floor_add_one _)

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

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

| Statement | New name | Old name | |

@@ -232,7 +232,7 @@ variable {ι 𝕜 : Type*} [LinearOrderedField 𝕜] (r : ι → ι → Prop) [D
 theorem mul_sq_le_sum_sq (hst : s ⊆ t) (f : ι → 𝕜) (hs : x ^ 2 ≤ ((∑ i in s, f i) / s.card) ^ 2)
     (hs' : (s.card : 𝕜) ≠ 0) : (s.card : 𝕜) * x ^ 2 ≤ ∑ i in t, f i ^ 2 :=
   (mul_le_mul_of_nonneg_left (hs.trans sum_div_card_sq_le_sum_sq_div_card) <|
-    Nat.cast_nonneg _).trans <| (mul_div_cancel' _ hs').le.trans <|
+    Nat.cast_nonneg _).trans <| (mul_div_cancel₀ _ hs').le.trans <|
       sum_le_sum_of_subset_of_nonneg hst fun _ _ _ => sq_nonneg _
 #align szemeredi_regularity.mul_sq_le_sum_sq SzemerediRegularity.mul_sq_le_sum_sq
 
@@ -247,9 +247,9 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
     sq_le_sq.2 (by rwa [abs_of_nonneg hx])
   have h₂ : x ^ 2 ≤ ((∑ i in s, (f i - (∑ j in t, f j) / t.card)) / s.card) ^ 2 := by
     apply h₁.trans
-    rw [sum_sub_distrib, sum_const, nsmul_eq_mul, sub_div, mul_div_cancel_left _ hscard.ne']
+    rw [sum_sub_distrib, sum_const, nsmul_eq_mul, sub_div, mul_div_cancel_left₀ _ hscard.ne']
   apply (add_le_add_right ht _).trans
-  rw [← mul_div_right_comm, le_div_iff htcard, add_mul, div_mul_cancel _ htcard.ne']
+  rw [← mul_div_right_comm, le_div_iff htcard, add_mul, div_mul_cancel₀ _ htcard.ne']
   have h₃ := mul_sq_le_sum_sq hst (fun i => (f i - (∑ j in t, f j) / t.card)) h₂ hscard.ne'
   apply (add_le_add_left h₃ _).trans
   -- Porting note: was

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.

@@ -273,17 +273,24 @@ open Lean.Meta Qq
 
 /-- Extension for the `positivity` tactic: `SzemerediRegularity.initialBound` is always positive. -/
 @[positivity SzemerediRegularity.initialBound _ _]
-def evalInitialBound : PositivityExt where eval {_ _} _ _ e := do
-  let (.app (.app _ (ε : Q(ℝ))) (l : Q(ℕ))) ← whnfR e | throwError "not initialBound"
-  pure (.positive (q(SzemerediRegularity.initialBound_pos $ε $l) : Lean.Expr))
+def evalInitialBound : PositivityExt where eval {u α} _ _ e := do
+  match u, α, e with
+  | 0, ~q(ℕ), ~q(SzemerediRegularity.initialBound $ε $l) =>
+    assertInstancesCommute
+    pure (.positive q(SzemerediRegularity.initialBound_pos $ε $l))
+  | _, _, _ => throwError "not initialBound"
+
 
 example (ε : ℝ) (l : ℕ) : 0 < SzemerediRegularity.initialBound ε l := by positivity
 
 /-- Extension for the `positivity` tactic: `SzemerediRegularity.bound` is always positive. -/
 @[positivity SzemerediRegularity.bound _ _]
-def evalBound : PositivityExt where eval {_ _} _ _ e := do
-  let (.app (.app _ (ε : Q(ℝ))) (l : Q(ℕ))) ← whnfR e | throwError "not bound"
-  pure (.positive (q(SzemerediRegularity.bound_pos $ε $l) : Lean.Expr))
+def evalBound : PositivityExt where eval {u α} _ _ e := do
+  match u, α, e with
+  | 0, ~q(ℕ), ~q(SzemerediRegularity.bound $ε $l) =>
+    assertInstancesCommute
+    pure (.positive q(SzemerediRegularity.bound_pos $ε $l))
+  | _, _, _ => throwError "not bound"
 
 example (ε : ℝ) (l : ℕ) : 0 < SzemerediRegularity.bound ε l := by positivity
 

@@ -267,13 +267,13 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
 
 end SzemerediRegularity
 
-namespace Tactic
+namespace Mathlib.Meta.Positivity
 
 open Lean.Meta Qq
 
 /-- Extension for the `positivity` tactic: `SzemerediRegularity.initialBound` is always positive. -/
 @[positivity SzemerediRegularity.initialBound _ _]
-def evalInitialBound : Mathlib.Meta.Positivity.PositivityExt where eval {_ _} _ _ e := do
+def evalInitialBound : PositivityExt where eval {_ _} _ _ e := do
   let (.app (.app _ (ε : Q(ℝ))) (l : Q(ℕ))) ← whnfR e | throwError "not initialBound"
   pure (.positive (q(SzemerediRegularity.initialBound_pos $ε $l) : Lean.Expr))
 
@@ -281,10 +281,10 @@ example (ε : ℝ) (l : ℕ) : 0 < SzemerediRegularity.initialBound ε l := by p
 
 /-- Extension for the `positivity` tactic: `SzemerediRegularity.bound` is always positive. -/
 @[positivity SzemerediRegularity.bound _ _]
-def evalBound : Mathlib.Meta.Positivity.PositivityExt where eval {_ _} _ _ e := do
+def evalBound : PositivityExt where eval {_ _} _ _ e := do
   let (.app (.app _ (ε : Q(ℝ))) (l : Q(ℕ))) ← whnfR e | throwError "not bound"
   pure (.positive (q(SzemerediRegularity.bound_pos $ε $l) : Lean.Expr))
 
 example (ε : ℝ) (l : ℕ) : 0 < SzemerediRegularity.bound ε l := by positivity
 
-end Tactic
+end Mathlib.Meta.Positivity

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

@@ -42,7 +42,8 @@ def stepBound (n : ℕ) : ℕ :=
   n * 4 ^ n
 #align szemeredi_regularity.step_bound SzemerediRegularity.stepBound
 
-theorem le_stepBound : id ≤ stepBound := fun n => Nat.le_mul_of_pos_right <| pow_pos (by norm_num) n
+theorem le_stepBound : id ≤ stepBound := fun n =>
+  Nat.le_mul_of_pos_right _ <| pow_pos (by norm_num) n
 #align szemeredi_regularity.le_step_bound SzemerediRegularity.le_stepBound
 
 theorem stepBound_mono : Monotone stepBound := fun a b h =>
@@ -214,7 +215,7 @@ noncomputable def bound : ℕ :=
 #align szemeredi_regularity.bound SzemerediRegularity.bound
 
 theorem initialBound_le_bound : initialBound ε l ≤ bound ε l :=
-  (id_le_iterate_of_id_le le_stepBound _ _).trans <| Nat.le_mul_of_pos_right <| by positivity
+  (id_le_iterate_of_id_le le_stepBound _ _).trans <| Nat.le_mul_of_pos_right _ <| by positivity
 #align szemeredi_regularity.initial_bound_le_bound SzemerediRegularity.initialBound_le_bound
 
 theorem le_bound : l ≤ bound ε l :=

@@ -130,11 +130,10 @@ theorem eps_pos (hPε : 100 ≤ (4 : ℝ) ^ P.parts.card * ε ^ 5) : 0 < ε :=
 
 theorem hundred_div_ε_pow_five_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)
     (hPε : 100 ≤ (4 : ℝ) ^ P.parts.card * ε ^ 5) : 100 / ε ^ 5 ≤ m :=
-  (div_le_of_nonneg_of_le_mul (eps_pow_five_pos hPε).le (by positivity) hPε).trans
-    (by
-      norm_cast
-      rwa [Nat.le_div_iff_mul_le' (stepBound_pos (P.parts_nonempty <|
-        univ_nonempty.ne_empty).card_pos), stepBound, mul_left_comm, ← mul_pow])
+  (div_le_of_nonneg_of_le_mul (eps_pow_five_pos hPε).le (by positivity) hPε).trans <| by
+    norm_cast
+    rwa [Nat.le_div_iff_mul_le' (stepBound_pos (P.parts_nonempty <|
+      univ_nonempty.ne_empty).card_pos), stepBound, mul_left_comm, ← mul_pow]
 #align szemeredi_regularity.hundred_div_ε_pow_five_le_m SzemerediRegularity.hundred_div_ε_pow_five_le_m
 
 theorem hundred_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)

Change a few lemma names that have historically bothered me.

• Finset.card_le_of_subset → Finset.card_le_card
• Multiset.card_le_of_le → Multiset.card_le_card
• Multiset.card_lt_of_lt → Multiset.card_lt_card
• Set.ncard_le_of_subset → Set.ncard_le_ncard
• Finset.image_filter → Finset.filter_image
• CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

@@ -242,7 +242,7 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
     d + s.card / t.card * x ^ 2 ≤ (∑ i in t, f i ^ 2) / t.card := by
   obtain hscard | hscard := (s.card.cast_nonneg : (0 : 𝕜) ≤ s.card).eq_or_lt
   · simpa [← hscard] using ht.trans sum_div_card_sq_le_sum_sq_div_card
-  have htcard : (0 : 𝕜) < t.card := hscard.trans_le (Nat.cast_le.2 (card_le_of_subset hst))
+  have htcard : (0 : 𝕜) < t.card := hscard.trans_le (Nat.cast_le.2 (card_le_card hst))
   have h₁ : x ^ 2 ≤ ((∑ i in s, f i) / s.card - (∑ i in t, f i) / t.card) ^ 2 :=
     sq_le_sq.2 (by rwa [abs_of_nonneg hx])
   have h₂ : x ^ 2 ≤ ((∑ i in s, (f i - (∑ j in t, f j) / t.card)) / s.card) ^ 2 := by

by using calc, gcongr and positivity. This should be much more maintainable now.

Nicely enough, this reduces the total number of lines.

@@ -56,6 +56,9 @@ theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
 alias ⟨_, stepBound_pos⟩ := stepBound_pos_iff
 #align szemeredi_regularity.step_bound_pos SzemerediRegularity.stepBound_pos
 
+@[norm_cast] lemma coe_stepBound {α : Type*} [Semiring α] (n : ℕ) :
+    (stepBound n : α) = n * 4 ^ n := by unfold stepBound; norm_cast
+
 end SzemerediRegularity
 
 open SzemerediRegularity

I had a slightly logic-heavy argument that was nicely simplified by stating this lemma. Also fix a few lemma names.

From LeanAPAP and LeanCamCombi

@@ -50,7 +50,7 @@ theorem stepBound_mono : Monotone stepBound := fun a b h =>
 #align szemeredi_regularity.step_bound_mono SzemerediRegularity.stepBound_mono
 
 theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
-  zero_lt_mul_right <| by positivity
+  mul_pos_iff_of_pos_right <| by positivity
 #align szemeredi_regularity.step_bound_pos_iff SzemerediRegularity.stepBound_pos_iff
 
 alias ⟨_, stepBound_pos⟩ := stepBound_pos_iff

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -74,7 +74,7 @@ private theorem eps_pos {ε : ℝ} {n : ℕ} (h : 100 ≤ (4 : ℝ) ^ n * ε ^ 5
     (pos_of_mul_pos_right ((show 0 < (100 : ℝ) by norm_num).trans_le h) (by positivity))
 
 private theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m :=
-  Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_of_le_left (by norm_num) _).trans hPα) <|
+  Nat.div_pos ((Nat.mul_le_mul_left _ <| Nat.pow_le_pow_left (by norm_num) _).trans hPα) <|
     stepBound_pos (P.parts_nonempty <| univ_nonempty.ne_empty).card_pos
 
 /-- Local extension for the `positivity` tactic: A few facts that are needed many times for the

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

@@ -251,8 +251,8 @@ theorem add_div_le_sum_sq_div_card (hst : s ⊆ t) (f : ι → 𝕜) (d : 𝕜)
   apply (add_le_add_left h₃ _).trans
   -- Porting note: was
   -- `simp [← mul_div_right_comm _ (t.card : 𝕜), sub_div' _ _ _ htcard.ne', ← sum_div, ← add_div,`
-  -- `  mul_pow, div_le_iff (sq_pos_of_ne_zero _ htcard.ne'), sub_sq, sum_add_distrib, ← sum_mul, ←`
-  -- `  mul_sum]`
+  -- `  mul_pow, div_le_iff (sq_pos_of_ne_zero _ htcard.ne'), sub_sq, sum_add_distrib, ← sum_mul,`
+  -- `  ← mul_sum]`
   simp_rw [sub_div' _ _ _ htcard.ne']
   conv_lhs => enter [2, 2, x]; rw [div_pow]
   rw [div_pow, ← sum_div, ← mul_div_right_comm _ (t.card : 𝕜), ← add_div,

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>

@@ -135,8 +135,8 @@ theorem hundred_div_ε_pow_five_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P
 #align szemeredi_regularity.hundred_div_ε_pow_five_le_m SzemerediRegularity.hundred_div_ε_pow_five_le_m
 
 theorem hundred_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)
-    (hPε : 100 ≤ (4 : ℝ) ^ P.parts.card * ε ^ 5) (hε : ε ≤ 1) : 100 ≤ m := by
-  exact_mod_cast
+    (hPε : 100 ≤ (4 : ℝ) ^ P.parts.card * ε ^ 5) (hε : ε ≤ 1) : 100 ≤ m :=
+  mod_cast
     (hundred_div_ε_pow_five_le_m hPα hPε).trans'
       (le_div_self (by norm_num) (by sz_positivity) <| pow_le_one _ (by sz_positivity) hε)
 #align szemeredi_regularity.hundred_le_m SzemerediRegularity.hundred_le_m

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

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

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -32,8 +32,6 @@ This entire file is internal to the proof of Szemerédi Regularity Lemma.
 
 open Finset Fintype Function Real
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open BigOperators
 
 namespace SzemerediRegularity
@@ -72,7 +70,7 @@ local notation3 "a" => (card α / P.parts.card - m * 4 ^ P.parts.card : ℕ)
 namespace SzemerediRegularity.Positivity
 
 private theorem eps_pos {ε : ℝ} {n : ℕ} (h : 100 ≤ (4 : ℝ) ^ n * ε ^ 5) : 0 < ε :=
-  (Odd.pow_pos_iff (by norm_num)).mp
+  (Odd.pow_pos_iff (by decide)).mp
     (pos_of_mul_pos_right ((show 0 < (100 : ℝ) by norm_num).trans_le h) (by positivity))
 
 private theorem m_pos [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α) : 0 < m :=
@@ -124,7 +122,7 @@ theorem eps_pow_five_pos (hPε : 100 ≤ (4 : ℝ) ^ P.parts.card * ε ^ 5) : 
 #align szemeredi_regularity.eps_pow_five_pos SzemerediRegularity.eps_pow_five_pos
 
 theorem eps_pos (hPε : 100 ≤ (4 : ℝ) ^ P.parts.card * ε ^ 5) : 0 < ε :=
-  (Odd.pow_pos_iff (by norm_num)).mp (eps_pow_five_pos hPε)
+  (Odd.pow_pos_iff (by decide)).mp (eps_pow_five_pos hPε)
 #align szemeredi_regularity.eps_pos SzemerediRegularity.eps_pos
 
 theorem hundred_div_ε_pow_five_le_m [Nonempty α] (hPα : P.parts.card * 16 ^ P.parts.card ≤ card α)

@@ -148,7 +148,7 @@ theorem a_add_one_le_four_pow_parts_card : a + 1 ≤ 4 ^ P.parts.card := by
   rw [stepBound, ← Nat.div_div_eq_div_mul]
   conv_rhs => rw [← Nat.sub_add_cancel h]
   rw [add_le_add_iff_right, tsub_le_iff_left, ← Nat.add_sub_assoc h]
-  exact Nat.le_pred_of_lt (Nat.lt_div_mul_add h)
+  exact Nat.le_sub_one_of_lt (Nat.lt_div_mul_add h)
 #align szemeredi_regularity.a_add_one_le_four_pow_parts_card SzemerediRegularity.a_add_one_le_four_pow_parts_card
 
 theorem card_aux₁ (hucard : u.card = m * 4 ^ P.parts.card + a) :

notation3 was generating matchers directly from syntax, which included a half-baked implementation of a term elaborator. This switches to elaborating the term and then generating matchers from the elaborated term. This

1. is more robust and consistent, since it uses the main elaborator and one can make use of other notations
2. has the nice side effect of adding term info to expansions in the notation3 command
3. can unfortunately generate matchers that are more restrictive than before since they also match against elaborated features such as implicit arguments.

We now also generate matchers for expansions that have pi types and lambda expressions.

@@ -65,11 +65,9 @@ open SzemerediRegularity
 variable {α : Type*} [DecidableEq α] [Fintype α] {P : Finpartition (univ : Finset α)}
   {u : Finset α} {ε : ℝ}
 
-local notation3 (prettyPrint := false)
-  "m" => (card α / stepBound P.parts.card : ℕ)
+local notation3 "m" => (card α / stepBound P.parts.card : ℕ)
 
-local notation3 (prettyPrint := false)
-  "a" => (card α / P.parts.card - m * 4 ^ P.parts.card : ℕ)
+local notation3 "a" => (card α / P.parts.card - m * 4 ^ P.parts.card : ℕ)
 
 namespace SzemerediRegularity.Positivity
 

@@ -55,7 +55,7 @@ theorem stepBound_pos_iff {n : ℕ} : 0 < stepBound n ↔ 0 < n :=
   zero_lt_mul_right <| by positivity
 #align szemeredi_regularity.step_bound_pos_iff SzemerediRegularity.stepBound_pos_iff
 
-alias stepBound_pos_iff ↔ _ stepBound_pos
+alias ⟨_, stepBound_pos⟩ := stepBound_pos_iff
 #align szemeredi_regularity.step_bound_pos SzemerediRegularity.stepBound_pos
 
 end SzemerediRegularity

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

This has nice performance benefits.

@@ -62,7 +62,7 @@ end SzemerediRegularity
 
 open SzemerediRegularity
 
-variable {α : Type _} [DecidableEq α] [Fintype α] {P : Finpartition (univ : Finset α)}
+variable {α : Type*} [DecidableEq α] [Fintype α] {P : Finpartition (univ : Finset α)}
   {u : Finset α} {ε : ℝ}
 
 local notation3 (prettyPrint := false)
@@ -227,7 +227,7 @@ theorem bound_pos : 0 < bound ε l :=
   (initialBound_pos ε l).trans_le <| initialBound_le_bound ε l
 #align szemeredi_regularity.bound_pos SzemerediRegularity.bound_pos
 
-variable {ι 𝕜 : Type _} [LinearOrderedField 𝕜] (r : ι → ι → Prop) [DecidableRel r] {s t : Finset ι}
+variable {ι 𝕜 : Type*} [LinearOrderedField 𝕜] (r : ι → ι → Prop) [DecidableRel r] {s t : Finset ι}
   {x : 𝕜}
 
 theorem mul_sq_le_sum_sq (hst : s ⊆ t) (f : ι → 𝕜) (hs : x ^ 2 ≤ ((∑ i in s, f i) / s.card) ^ 2)

@@ -32,7 +32,7 @@ This entire file is internal to the proof of Szemerédi Regularity Lemma.
 
 open Finset Fintype Function Real
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 open BigOperators
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
-
-! This file was ported from Lean 3 source module combinatorics.simple_graph.regularity.bound
-! leanprover-community/mathlib commit bf7ef0e83e5b7e6c1169e97f055e58a2e4e9d52d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Order.Chebyshev
 import Mathlib.Analysis.SpecialFunctions.Pow.Real
 import Mathlib.Order.Partition.Equipartition
 
+#align_import combinatorics.simple_graph.regularity.bound from "leanprover-community/mathlib"@"bf7ef0e83e5b7e6c1169e97f055e58a2e4e9d52d"
+
 /-!
 # Numerical bounds for Szemerédi Regularity Lemma
 

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com>