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

@@ -403,7 +403,7 @@ variable {z}
 theorem exists_eq_T_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z :=
   by
   have had := g.det_coe
-  replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had ; linarith
+  replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use↑ₘg 0 1
     suffices g = T ^ ↑ₘg 0 1 by intro z; conv_lhs => rw [this]
@@ -420,7 +420,7 @@ theorem exists_eq_T_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
 theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = T ^ ↑ₘg 0 0 * S * T ^ ↑ₘg 1 1 :=
   by
   have hg := g.det_coe.symm
-  replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1; · rw [det_fin_two, hc] at hg ; linarith
+  replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1; · rw [det_fin_two, hc] at hg; linarith
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two ↑ₘg]
   rw [hc, hg]
@@ -503,10 +503,10 @@ theorem one_lt_normSq_T_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T
 theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) : n = 0 :=
   by
   suffices |(n : ℝ)| < 1 by
-    rwa [← Int.cast_abs, ← Int.cast_one, Int.cast_lt, Int.abs_lt_one_iff] at this 
+    rwa [← Int.cast_abs, ← Int.cast_one, Int.cast_lt, Int.abs_lt_one_iff] at this
   have h₁ := hz.2
   have h₂ := hg.2
-  rw [re_T_zpow_smul] at h₂ 
+  rw [re_T_zpow_smul] at h₂
   calc
     |(n : ℝ)| ≤ |z.re| + |z.re + (n : ℝ)| := abs_add' (n : ℝ) z.re
     _ < 1 / 2 + 1 / 2 := (add_lt_add h₁ h₂)
@@ -563,9 +563,9 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg
   let c : ℝ := (c' : ℝ)
   suffices 3 * c ^ 2 < 4
     by
-    rw [← Int.cast_pow, ← Int.cast_three, ← Int.cast_four, ← Int.cast_mul, Int.cast_lt] at this 
+    rw [← Int.cast_pow, ← Int.cast_three, ← Int.cast_four, ← Int.cast_mul, Int.cast_lt] at this
     replace this : c' ^ 2 ≤ 1 ^ 2; · linarith
-    rwa [sq_le_sq, abs_one] at this 
+    rwa [sq_le_sq, abs_one] at this
   suffices c ≠ 0 → 9 * c ^ 4 < 16
     by
     rcases eq_or_ne c 0 with (hc | hc)

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

@@ -322,7 +322,20 @@ attribute [local simp] coe_smul re_smul
 
 #print ModularGroup.exists_max_im /-
 /-- For `z : ℍ`, there is a `g : SL(2,ℤ)` maximizing `(g•z).im` -/
-theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by classical
+theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by
+  classical
+  let s : Set (Fin 2 → ℤ) := {cd | IsCoprime (cd 0) (cd 1)}
+  have hs : s.nonempty := ⟨![1, 1], isCoprime_one_left⟩
+  obtain ⟨p, hp_coprime, hp⟩ :=
+    Filter.Tendsto.exists_within_forall_le hs (tendsto_norm_sq_coprime_pair z)
+  obtain ⟨g, -, hg⟩ := bottom_row_surj hp_coprime
+  refine' ⟨g, fun g' => _⟩
+  rw [special_linear_group.im_smul_eq_div_norm_sq, special_linear_group.im_smul_eq_div_norm_sq,
+    div_le_div_left]
+  · simpa [← hg] using hp (↑ₘg' 1) (bottom_row_coprime g')
+  · exact z.im_pos
+  · exact norm_sq_denom_pos g' z
+  · exact norm_sq_denom_pos g z
 #align modular_group.exists_max_im ModularGroup.exists_max_im
 -/
 

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

@@ -322,20 +322,7 @@ attribute [local simp] coe_smul re_smul
 
 #print ModularGroup.exists_max_im /-
 /-- For `z : ℍ`, there is a `g : SL(2,ℤ)` maximizing `(g•z).im` -/
-theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by
-  classical
-  let s : Set (Fin 2 → ℤ) := {cd | IsCoprime (cd 0) (cd 1)}
-  have hs : s.nonempty := ⟨![1, 1], isCoprime_one_left⟩
-  obtain ⟨p, hp_coprime, hp⟩ :=
-    Filter.Tendsto.exists_within_forall_le hs (tendsto_norm_sq_coprime_pair z)
-  obtain ⟨g, -, hg⟩ := bottom_row_surj hp_coprime
-  refine' ⟨g, fun g' => _⟩
-  rw [special_linear_group.im_smul_eq_div_norm_sq, special_linear_group.im_smul_eq_div_norm_sq,
-    div_le_div_left]
-  · simpa [← hg] using hp (↑ₘg' 1) (bottom_row_coprime g')
-  · exact z.im_pos
-  · exact norm_sq_denom_pos g' z
-  · exact norm_sq_denom_pos g z
+theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by classical
 #align modular_group.exists_max_im ModularGroup.exists_max_im
 -/
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rig
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
 -/
-import Mathbin.Analysis.Complex.UpperHalfPlane.Basic
-import Mathbin.Analysis.NormedSpace.FiniteDimension
-import Mathbin.LinearAlgebra.GeneralLinearGroup
-import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
+import Analysis.Complex.UpperHalfPlane.Basic
+import Analysis.NormedSpace.FiniteDimension
+import LinearAlgebra.GeneralLinearGroup
+import LinearAlgebra.Matrix.GeneralLinearGroup
 
 #align_import number_theory.modular from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -175,7 +175,7 @@ theorem tendsto_normSq_coprime_pair :
   have hf' : ClosedEmbedding f :=
     by
     -- for some reason we get a timeout if we try and apply this lemma in a more sensible way
-    have := @LinearEquiv.closedEmbedding_of_injective ℝ _ (Fin 2 → ℝ) _ (id _) ℂ _ _ _ _
+    have := @LinearMap.closedEmbedding_of_injective ℝ _ (Fin 2 → ℝ) _ (id _) ℂ _ _ _ _
     rotate_left 2
     exact f
     exact this hf

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

@@ -71,7 +71,7 @@ attribute [-instance] Matrix.GeneralLinearGroup.hasCoeToFun
 
 open Complex hiding abs_two
 
-open Matrix hiding mul_smul
+open Matrix hiding hMul_smul
 
 open Matrix.SpecialLinearGroup UpperHalfPlane
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -96,7 +96,7 @@ section BottomRow
 theorem bottom_row_coprime {R : Type _} [CommRing R] (g : SL(2, R)) :
     IsCoprime ((↑g : Matrix (Fin 2) (Fin 2) R) 1 0) ((↑g : Matrix (Fin 2) (Fin 2) R) 1 1) :=
   by
-  use -(↑g : Matrix (Fin 2) (Fin 2) R) 0 1, (↑g : Matrix (Fin 2) (Fin 2) R) 0 0
+  use-(↑g : Matrix (Fin 2) (Fin 2) R) 0 1, (↑g : Matrix (Fin 2) (Fin 2) R) 0 0
   rw [add_comm, neg_mul, ← sub_eq_add_neg, ← det_fin_two]
   exact g.det_coe
 #align modular_group.bottom_row_coprime ModularGroup.bottom_row_coprime
@@ -405,10 +405,10 @@ theorem exists_eq_T_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
   have had := g.det_coe
   replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had ; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
-  · use ↑ₘg 0 1
+  · use↑ₘg 0 1
     suffices g = T ^ ↑ₘg 0 1 by intro z; conv_lhs => rw [this]
     ext i j; fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
-  · use -↑ₘg 0 1
+  · use-↑ₘg 0 1
     suffices g = -T ^ (-↑ₘg 0 1) by intro z; conv_lhs => rw [this, SL_neg_smul]
     ext i j; fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
 #align modular_group.exists_eq_T_zpow_of_c_eq_zero ModularGroup.exists_eq_T_zpow_of_c_eq_zero

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-
-! This file was ported from Lean 3 source module number_theory.modular
-! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.UpperHalfPlane.Basic
 import Mathbin.Analysis.NormedSpace.FiniteDimension
 import Mathbin.LinearAlgebra.GeneralLinearGroup
 import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
 
+#align_import number_theory.modular from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
 /-!
 # The action of the modular group SL(2, ℤ) on the upper half-plane
 

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: Alex Kontorovich, Heather Macbeth, Marc Masdeu
 
 ! This file was ported from Lean 3 source module number_theory.modular
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
 /-!
 # The action of the modular group SL(2, ℤ) on the upper half-plane
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the action of `SL(2,ℤ)` on `ℍ` (via restriction of the `SL(2,ℝ)` action in
 `analysis.complex.upper_half_plane`). We then define the standard fundamental domain
 (`modular_group.fd`, `𝒟`) for this action and show

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -91,6 +91,7 @@ variable {g : SL(2, ℤ)} (z : ℍ)
 
 section BottomRow
 
+#print ModularGroup.bottom_row_coprime /-
 /-- The two numbers `c`, `d` in the "bottom_row" of `g=[[*,*],[c,d]]` in `SL(2, ℤ)` are coprime. -/
 theorem bottom_row_coprime {R : Type _} [CommRing R] (g : SL(2, R)) :
     IsCoprime ((↑g : Matrix (Fin 2) (Fin 2) R) 1 0) ((↑g : Matrix (Fin 2) (Fin 2) R) 1 1) :=
@@ -99,7 +100,9 @@ theorem bottom_row_coprime {R : Type _} [CommRing R] (g : SL(2, R)) :
   rw [add_comm, neg_mul, ← sub_eq_add_neg, ← det_fin_two]
   exact g.det_coe
 #align modular_group.bottom_row_coprime ModularGroup.bottom_row_coprime
+-/
 
+#print ModularGroup.bottom_row_surj /-
 /-- Every pair `![c, d]` of coprime integers is the "bottom_row" of some element `g=[[*,*],[c,d]]`
 of `SL(2,ℤ)`. -/
 theorem bottom_row_surj {R : Type _} [CommRing R] :
@@ -114,6 +117,7 @@ theorem bottom_row_surj {R : Type _} [CommRing R] :
   refine' ⟨⟨A, det_A_1⟩, Set.mem_univ _, _⟩
   ext <;> simp [A]
 #align modular_group.bottom_row_surj ModularGroup.bottom_row_surj
+-/
 
 end BottomRow
 
@@ -123,6 +127,7 @@ open Filter ContinuousLinearMap
 
 attribute [local simp] coe_smul
 
+#print ModularGroup.tendsto_normSq_coprime_pair /-
 /-- The function `(c,d) → |cz+d|^2` is proper, that is, preimages of bounded-above sets are finite.
 -/
 theorem tendsto_normSq_coprime_pair :
@@ -181,7 +186,9 @@ theorem tendsto_normSq_coprime_pair :
     · rw [Coprod_cocompact]
   exact tendsto_norm_sq_cocompact_at_top.comp (hf'.tendsto_cocompact.comp h₂)
 #align modular_group.tendsto_norm_sq_coprime_pair ModularGroup.tendsto_normSq_coprime_pair
+-/
 
+#print ModularGroup.lcRow0 /-
 /-- Given `coprime_pair` `p=(c,d)`, the matrix `[[a,b],[*,*]]` is sent to `a*c+b*d`.
   This is the linear map version of this operation.
 -/
@@ -189,13 +196,17 @@ def lcRow0 (p : Fin 2 → ℤ) : Matrix (Fin 2) (Fin 2) ℝ →ₗ[ℝ] ℝ :=
   ((p 0 : ℝ) • LinearMap.proj 0 + (p 1 : ℝ) • LinearMap.proj 1 : (Fin 2 → ℝ) →ₗ[ℝ] ℝ).comp
     (LinearMap.proj 0)
 #align modular_group.lc_row0 ModularGroup.lcRow0
+-/
 
+#print ModularGroup.lcRow0_apply /-
 @[simp]
 theorem lcRow0_apply (p : Fin 2 → ℤ) (g : Matrix (Fin 2) (Fin 2) ℝ) :
     lcRow0 p g = p 0 * g 0 0 + p 1 * g 0 1 :=
   rfl
 #align modular_group.lc_row0_apply ModularGroup.lcRow0_apply
+-/
 
+#print ModularGroup.lcRow0Extend /-
 /-- Linear map sending the matrix [a, b; c, d] to the matrix [ac₀ + bd₀, - ad₀ + bc₀; c, d], for
 some fixed `(c₀, d₀)`. -/
 @[simps]
@@ -210,7 +221,9 @@ def lcRow0Extend {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
       rw [neg_sq]
       exact hcd.sq_add_sq_ne_zero, LinearEquiv.refl ℝ (Fin 2 → ℝ)]
 #align modular_group.lc_row0_extend ModularGroup.lcRow0Extend
+-/
 
+#print ModularGroup.tendsto_lcRow0 /-
 /-- The map `lc_row0` is proper, that is, preimages of cocompact sets are finite in
 `[[* , *], [c, d]]`.-/
 theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
@@ -254,7 +267,9 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
     ring
   · rfl
 #align modular_group.tendsto_lc_row0 ModularGroup.tendsto_lcRow0
+-/
 
+#print ModularGroup.smul_eq_lcRow0_add /-
 /-- This replaces `(g•z).re = a/c + *` in the standard theory with the following novel identity:
   `g • z = (a c + b d) / (c^2 + d^2) + (d z - c) / ((c^2 + d^2) (c z + d))`
   which does not need to be decomposed depending on whether `c = 0`. -/
@@ -273,7 +288,9 @@ theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg
     Int.cast_sub, _root_.coe_coe, coe_GL_pos_coe_GL_coe_matrix]
   ring
 #align modular_group.smul_eq_lc_row0_add ModularGroup.smul_eq_lcRow0_add
+-/
 
+#print ModularGroup.tendsto_abs_re_smul /-
 theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
     Tendsto (fun g : { g : SL(2, ℤ) // ↑ₘg 1 = p } => |((g : SL(2, ℤ)) • z).re|) cofinite atTop :=
   by
@@ -295,6 +312,7 @@ theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
         (((p 1 : ℂ) * z - p 0) / ((p 0 ^ 2 + p 1 ^ 2) * (p 0 * z + p 1))).re
   exact_mod_cast congr_arg Complex.re (smul_eq_lc_row0_add z hp g.2)
 #align modular_group.tendsto_abs_re_smul ModularGroup.tendsto_abs_re_smul
+-/
 
 end TendstoLemmas
 
@@ -302,6 +320,7 @@ section FundamentalDomain
 
 attribute [local simp] coe_smul re_smul
 
+#print ModularGroup.exists_max_im /-
 /-- For `z : ℍ`, there is a `g : SL(2,ℤ)` maximizing `(g•z).im` -/
 theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by
   classical
@@ -318,7 +337,9 @@ theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im 
   · exact norm_sq_denom_pos g' z
   · exact norm_sq_denom_pos g z
 #align modular_group.exists_max_im ModularGroup.exists_max_im
+-/
 
+#print ModularGroup.exists_row_one_eq_and_min_re /-
 /-- Given `z : ℍ` and a bottom row `(c,d)`, among the `g : SL(2,ℤ)` with this bottom row, minimize
   `|(g•z).re|`.  -/
 theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
@@ -336,34 +357,50 @@ theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0
       exact Eq.trans hg1.symm (set.mem_singleton_iff.mp (set.mem_preimage.mp g.2))
     exact hg ⟨g1, this⟩
 #align modular_group.exists_row_one_eq_and_min_re ModularGroup.exists_row_one_eq_and_min_re
+-/
 
-theorem coe_t_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n := by simp [coe_T_zpow]
-#align modular_group.coe_T_zpow_smul_eq ModularGroup.coe_t_zpow_smul_eq
+#print ModularGroup.coe_T_zpow_smul_eq /-
+theorem coe_T_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n := by simp [coe_T_zpow]
+#align modular_group.coe_T_zpow_smul_eq ModularGroup.coe_T_zpow_smul_eq
+-/
 
-theorem re_t_zpow_smul (n : ℤ) : (T ^ n • z).re = z.re + n := by
+#print ModularGroup.re_T_zpow_smul /-
+theorem re_T_zpow_smul (n : ℤ) : (T ^ n • z).re = z.re + n := by
   rw [← coe_re, coe_T_zpow_smul_eq, add_re, int_cast_re, coe_re]
-#align modular_group.re_T_zpow_smul ModularGroup.re_t_zpow_smul
+#align modular_group.re_T_zpow_smul ModularGroup.re_T_zpow_smul
+-/
 
-theorem im_t_zpow_smul (n : ℤ) : (T ^ n • z).im = z.im := by
+#print ModularGroup.im_T_zpow_smul /-
+theorem im_T_zpow_smul (n : ℤ) : (T ^ n • z).im = z.im := by
   rw [← coe_im, coe_T_zpow_smul_eq, add_im, int_cast_im, add_zero, coe_im]
-#align modular_group.im_T_zpow_smul ModularGroup.im_t_zpow_smul
+#align modular_group.im_T_zpow_smul ModularGroup.im_T_zpow_smul
+-/
 
-theorem re_t_smul : (T • z).re = z.re + 1 := by simpa using re_T_zpow_smul z 1
-#align modular_group.re_T_smul ModularGroup.re_t_smul
+#print ModularGroup.re_T_smul /-
+theorem re_T_smul : (T • z).re = z.re + 1 := by simpa using re_T_zpow_smul z 1
+#align modular_group.re_T_smul ModularGroup.re_T_smul
+-/
 
-theorem im_t_smul : (T • z).im = z.im := by simpa using im_T_zpow_smul z 1
-#align modular_group.im_T_smul ModularGroup.im_t_smul
+#print ModularGroup.im_T_smul /-
+theorem im_T_smul : (T • z).im = z.im := by simpa using im_T_zpow_smul z 1
+#align modular_group.im_T_smul ModularGroup.im_T_smul
+-/
 
-theorem re_t_inv_smul : (T⁻¹ • z).re = z.re - 1 := by simpa using re_T_zpow_smul z (-1)
-#align modular_group.re_T_inv_smul ModularGroup.re_t_inv_smul
+#print ModularGroup.re_T_inv_smul /-
+theorem re_T_inv_smul : (T⁻¹ • z).re = z.re - 1 := by simpa using re_T_zpow_smul z (-1)
+#align modular_group.re_T_inv_smul ModularGroup.re_T_inv_smul
+-/
 
-theorem im_t_inv_smul : (T⁻¹ • z).im = z.im := by simpa using im_T_zpow_smul z (-1)
-#align modular_group.im_T_inv_smul ModularGroup.im_t_inv_smul
+#print ModularGroup.im_T_inv_smul /-
+theorem im_T_inv_smul : (T⁻¹ • z).im = z.im := by simpa using im_T_zpow_smul z (-1)
+#align modular_group.im_T_inv_smul ModularGroup.im_T_inv_smul
+-/
 
 variable {z}
 
+#print ModularGroup.exists_eq_T_zpow_of_c_eq_zero /-
 -- If instead we had `g` and `T` of type `PSL(2, ℤ)`, then we could simply state `g = T^n`.
-theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z :=
+theorem exists_eq_T_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z :=
   by
   have had := g.det_coe
   replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had ; linarith
@@ -374,9 +411,11 @@ theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
   · use -↑ₘg 0 1
     suffices g = -T ^ (-↑ₘg 0 1) by intro z; conv_lhs => rw [this, SL_neg_smul]
     ext i j; fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
-#align modular_group.exists_eq_T_zpow_of_c_eq_zero ModularGroup.exists_eq_t_zpow_of_c_eq_zero
+#align modular_group.exists_eq_T_zpow_of_c_eq_zero ModularGroup.exists_eq_T_zpow_of_c_eq_zero
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
+#print ModularGroup.g_eq_of_c_eq_one /-
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
 theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = T ^ ↑ₘg 0 0 * S * T ^ ↑ₘg 1 1 :=
   by
@@ -390,14 +429,18 @@ theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = T ^ ↑ₘg 0 0 * S * T ^
       "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]" <;>
     ring
 #align modular_group.g_eq_of_c_eq_one ModularGroup.g_eq_of_c_eq_one
+-/
 
+#print ModularGroup.normSq_S_smul_lt_one /-
 /-- If `1 < |z|`, then `|S • z| < 1`. -/
-theorem normSq_s_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1 := by
+theorem normSq_S_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1 := by
   simpa [coe_S] using (inv_lt_inv z.norm_sq_pos zero_lt_one).mpr h
-#align modular_group.norm_sq_S_smul_lt_one ModularGroup.normSq_s_smul_lt_one
+#align modular_group.norm_sq_S_smul_lt_one ModularGroup.normSq_S_smul_lt_one
+-/
 
+#print ModularGroup.im_lt_im_S_smul /-
 /-- If `|z| < 1`, then applying `S` strictly decreases `im`. -/
-theorem im_lt_im_s_smul (h : normSq z < 1) : z.im < (S • z).im :=
+theorem im_lt_im_S_smul (h : normSq z < 1) : z.im < (S • z).im :=
   by
   have : z.im < z.im / norm_sq (z : ℂ) :=
     by
@@ -407,45 +450,57 @@ theorem im_lt_im_s_smul (h : normSq z < 1) : z.im < (S • z).im :=
   convert this
   simp only [special_linear_group.im_smul_eq_div_norm_sq]
   field_simp [norm_sq_denom_ne_zero, norm_sq_ne_zero, S]
-#align modular_group.im_lt_im_S_smul ModularGroup.im_lt_im_s_smul
+#align modular_group.im_lt_im_S_smul ModularGroup.im_lt_im_S_smul
+-/
 
+#print ModularGroup.fd /-
 /-- The standard (closed) fundamental domain of the action of `SL(2,ℤ)` on `ℍ`. -/
 def fd : Set ℍ :=
   {z | 1 ≤ (z : ℂ).normSq ∧ |z.re| ≤ (1 : ℝ) / 2}
 #align modular_group.fd ModularGroup.fd
+-/
 
+#print ModularGroup.fdo /-
 /-- The standard open fundamental domain of the action of `SL(2,ℤ)` on `ℍ`. -/
 def fdo : Set ℍ :=
   {z | 1 < (z : ℂ).normSq ∧ |z.re| < (1 : ℝ) / 2}
 #align modular_group.fdo ModularGroup.fdo
+-/
 
 scoped[Modular] notation "𝒟" => ModularGroup.fd
 
 scoped[Modular] notation "𝒟ᵒ" => ModularGroup.fdo
 
+#print ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo /-
 theorem abs_two_mul_re_lt_one_of_mem_fdo (h : z ∈ 𝒟ᵒ) : |2 * z.re| < 1 :=
   by
   rw [abs_mul, abs_two, ← lt_div_iff' (zero_lt_two' ℝ)]
   exact h.2
 #align modular_group.abs_two_mul_re_lt_one_of_mem_fdo ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo
+-/
 
+#print ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo /-
 theorem three_lt_four_mul_im_sq_of_mem_fdo (h : z ∈ 𝒟ᵒ) : 3 < 4 * z.im ^ 2 :=
   by
   have : 1 < z.re * z.re + z.im * z.im := by simpa [Complex.normSq_apply] using h.1
   have := h.2
   cases abs_cases z.re <;> nlinarith
 #align modular_group.three_lt_four_mul_im_sq_of_mem_fdo ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo
+-/
 
+#print ModularGroup.one_lt_normSq_T_zpow_smul /-
 /-- If `z ∈ 𝒟ᵒ`, and `n : ℤ`, then `|z + n| > 1`. -/
-theorem one_lt_normSq_t_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T ^ n • z : ℍ) :=
+theorem one_lt_normSq_T_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T ^ n • z : ℍ) :=
   by
   have hz₁ : 1 < z.re * z.re + z.im * z.im := hz.1
   have hzn := Int.nneg_mul_add_sq_of_abs_le_one n (abs_two_mul_re_lt_one_of_mem_fdo hz).le
   have : 1 < (z.re + ↑n) * (z.re + ↑n) + z.im * z.im := by linarith
   simpa [coe_T_zpow, norm_sq]
-#align modular_group.one_lt_norm_sq_T_zpow_smul ModularGroup.one_lt_normSq_t_zpow_smul
+#align modular_group.one_lt_norm_sq_T_zpow_smul ModularGroup.one_lt_normSq_T_zpow_smul
+-/
 
-theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) : n = 0 :=
+#print ModularGroup.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo /-
+theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) : n = 0 :=
   by
   suffices |(n : ℝ)| < 1 by
     rwa [← Int.cast_abs, ← Int.cast_one, Int.cast_lt, Int.abs_lt_one_iff] at this 
@@ -456,8 +511,10 @@ theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg
     |(n : ℝ)| ≤ |z.re| + |z.re + (n : ℝ)| := abs_add' (n : ℝ) z.re
     _ < 1 / 2 + 1 / 2 := (add_lt_add h₁ h₂)
     _ = 1 := add_halves 1
-#align modular_group.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo ModularGroup.eq_zero_of_mem_fdo_of_t_zpow_mem_fdo
+#align modular_group.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo ModularGroup.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo
+-/
 
+#print ModularGroup.exists_smul_mem_fd /-
 /-- Any `z : ℍ` can be moved to `𝒟` by an element of `SL(2,ℤ)`  -/
 theorem exists_smul_mem_fd (z : ℍ) : ∃ g : SL(2, ℤ), g • z ∈ 𝒟 :=
   by
@@ -492,11 +549,13 @@ theorem exists_smul_mem_fd (z : ℍ) : ∃ g : SL(2, ℤ), g • z ∈ 𝒟 :=
       rw [mul_smul, re_T_inv_smul]
       cases abs_cases ((g • z).re - 1) <;> cases abs_cases (g • z).re <;> linarith
 #align modular_group.exists_smul_mem_fd ModularGroup.exists_smul_mem_fd
+-/
 
 section UniqueRepresentative
 
 variable {z}
 
+#print ModularGroup.abs_c_le_one /-
 /-- An auxiliary result en route to `modular_group.c_eq_zero`. -/
 theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg 1 0| ≤ 1 :=
   by
@@ -534,7 +593,9 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg
       ring
     _ ≤ 16 := by rw [← mul_pow]; linarith
 #align modular_group.abs_c_le_one ModularGroup.abs_c_le_one
+-/
 
+#print ModularGroup.c_eq_zero /-
 /-- An auxiliary result en route to `modular_group.eq_smul_self_of_mem_fdo_mem_fdo`. -/
 theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : ↑ₘg 1 0 = 0 :=
   by
@@ -558,7 +619,9 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : ↑ₘg 1 0
   specialize hp hg
   rcases int.abs_le_one_iff.mp <| abs_c_le_one hz hg with ⟨⟩ <;> tauto
 #align modular_group.c_eq_zero ModularGroup.c_eq_zero
+-/
 
+#print ModularGroup.eq_smul_self_of_mem_fdo_mem_fdo /-
 /-- Second Main Fundamental Domain Lemma: if both `z` and `g • z` are in the open domain `𝒟ᵒ`,
 where `z : ℍ` and `g : SL(2,ℤ)`, then `z = g • z`. -/
 theorem eq_smul_self_of_mem_fdo_mem_fdo (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : z = g • z :=
@@ -567,6 +630,7 @@ theorem eq_smul_self_of_mem_fdo_mem_fdo (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 
   rw [hn] at hg ⊢
   simp [eq_zero_of_mem_fdo_of_T_zpow_mem_fdo hz hg, one_smul]
 #align modular_group.eq_smul_self_of_mem_fdo_mem_fdo ModularGroup.eq_smul_self_of_mem_fdo_mem_fdo
+-/
 
 end UniqueRepresentative
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -237,7 +237,7 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
   have hf₂ : ClosedEmbedding (lc_row0_extend hcd) :=
     (lc_row0_extend hcd).toContinuousLinearEquiv.toHomeomorph.ClosedEmbedding
   convert hf₂.tendsto_cocompact.comp (hf₁.comp subtype.coe_injective.tendsto_cofinite) using 1
-  ext (⟨g, rfl⟩i j) : 3
+  ext ⟨g, rfl⟩ i j : 3
   fin_cases i <;> [fin_cases j; skip]
   -- the following are proved by `simp`, but it is replaced by `simp only` to avoid timeouts.
   ·
@@ -370,10 +370,10 @@ theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use ↑ₘg 0 1
     suffices g = T ^ ↑ₘg 0 1 by intro z; conv_lhs => rw [this]
-    ext (i j); fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
+    ext i j; fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
   · use -↑ₘg 0 1
     suffices g = -T ^ (-↑ₘg 0 1) by intro z; conv_lhs => rw [this, SL_neg_smul]
-    ext (i j); fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
+    ext i j; fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
 #align modular_group.exists_eq_T_zpow_of_c_eq_zero ModularGroup.exists_eq_t_zpow_of_c_eq_zero
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/

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

@@ -77,10 +77,8 @@ open Matrix.SpecialLinearGroup UpperHalfPlane
 
 noncomputable section
 
--- mathport name: «exprSL( , )»
 local notation "SL(" n ", " R ")" => SpecialLinearGroup (Fin n) R
 
--- mathport name: «expr↑ₘ »
 local prefix:1024 "↑ₘ" => @coe _ (Matrix (Fin 2) (Fin 2) ℤ) _
 
 open scoped UpperHalfPlane ComplexConjugate
@@ -421,10 +419,8 @@ def fdo : Set ℍ :=
   {z | 1 < (z : ℂ).normSq ∧ |z.re| < (1 : ℝ) / 2}
 #align modular_group.fdo ModularGroup.fdo
 
--- mathport name: modular_group.fd
 scoped[Modular] notation "𝒟" => ModularGroup.fd
 
--- mathport name: modular_group.fdo
 scoped[Modular] notation "𝒟ᵒ" => ModularGroup.fdo
 
 theorem abs_two_mul_re_lt_one_of_mem_fdo (h : z ∈ 𝒟ᵒ) : |2 * z.re| < 1 :=

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

@@ -460,7 +460,6 @@ theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg
     |(n : ℝ)| ≤ |z.re| + |z.re + (n : ℝ)| := abs_add' (n : ℝ) z.re
     _ < 1 / 2 + 1 / 2 := (add_lt_add h₁ h₂)
     _ = 1 := add_halves 1
-    
 #align modular_group.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo ModularGroup.eq_zero_of_mem_fdo_of_t_zpow_mem_fdo
 
 /-- Any `z : ℍ` can be moved to `𝒟` by an element of `SL(2,ℤ)`  -/
@@ -538,7 +537,6 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg
       rw [special_linear_group.im_smul_eq_div_norm_sq, div_pow]
       ring
     _ ≤ 16 := by rw [← mul_pow]; linarith
-    
 #align modular_group.abs_c_le_one ModularGroup.abs_c_le_one
 
 /-- An auxiliary result en route to `modular_group.eq_smul_self_of_mem_fdo_mem_fdo`. -/

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

@@ -106,7 +106,7 @@ theorem bottom_row_coprime {R : Type _} [CommRing R] (g : SL(2, R)) :
 of `SL(2,ℤ)`. -/
 theorem bottom_row_surj {R : Type _} [CommRing R] :
     Set.SurjOn (fun g : SL(2, R) => @coe _ (Matrix (Fin 2) (Fin 2) R) _ g 1) Set.univ
-      { cd | IsCoprime (cd 0) (cd 1) } :=
+      {cd | IsCoprime (cd 0) (cd 1)} :=
   by
   rintro cd ⟨b₀, a, gcd_eqn⟩
   let A := of ![![a, -b₀], cd]
@@ -289,7 +289,7 @@ theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
     exact_mod_cast hp.sq_add_sq_ne_zero
   let f := Homeomorph.mulRight₀ _ this
   let ff := Homeomorph.addRight (((p 1 : ℂ) * z - p 0) / ((p 0 ^ 2 + p 1 ^ 2) * (p 0 * z + p 1))).re
-  convert(f.trans ff).ClosedEmbedding.tendsto_cocompact.comp (tendsto_lc_row0 hp)
+  convert (f.trans ff).ClosedEmbedding.tendsto_cocompact.comp (tendsto_lc_row0 hp)
   ext g
   change
     ((g : SL(2, ℤ)) • z).re =
@@ -307,18 +307,18 @@ attribute [local simp] coe_smul re_smul
 /-- For `z : ℍ`, there is a `g : SL(2,ℤ)` maximizing `(g•z).im` -/
 theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by
   classical
-    let s : Set (Fin 2 → ℤ) := { cd | IsCoprime (cd 0) (cd 1) }
-    have hs : s.nonempty := ⟨![1, 1], isCoprime_one_left⟩
-    obtain ⟨p, hp_coprime, hp⟩ :=
-      Filter.Tendsto.exists_within_forall_le hs (tendsto_norm_sq_coprime_pair z)
-    obtain ⟨g, -, hg⟩ := bottom_row_surj hp_coprime
-    refine' ⟨g, fun g' => _⟩
-    rw [special_linear_group.im_smul_eq_div_norm_sq, special_linear_group.im_smul_eq_div_norm_sq,
-      div_le_div_left]
-    · simpa [← hg] using hp (↑ₘg' 1) (bottom_row_coprime g')
-    · exact z.im_pos
-    · exact norm_sq_denom_pos g' z
-    · exact norm_sq_denom_pos g z
+  let s : Set (Fin 2 → ℤ) := {cd | IsCoprime (cd 0) (cd 1)}
+  have hs : s.nonempty := ⟨![1, 1], isCoprime_one_left⟩
+  obtain ⟨p, hp_coprime, hp⟩ :=
+    Filter.Tendsto.exists_within_forall_le hs (tendsto_norm_sq_coprime_pair z)
+  obtain ⟨g, -, hg⟩ := bottom_row_surj hp_coprime
+  refine' ⟨g, fun g' => _⟩
+  rw [special_linear_group.im_smul_eq_div_norm_sq, special_linear_group.im_smul_eq_div_norm_sq,
+    div_le_div_left]
+  · simpa [← hg] using hp (↑ₘg' 1) (bottom_row_coprime g')
+  · exact z.im_pos
+  · exact norm_sq_denom_pos g' z
+  · exact norm_sq_denom_pos g z
 #align modular_group.exists_max_im ModularGroup.exists_max_im
 
 /-- Given `z : ℍ` and a bottom row `(c,d)`, among the `g : SL(2,ℤ)` with this bottom row, minimize
@@ -413,12 +413,12 @@ theorem im_lt_im_s_smul (h : normSq z < 1) : z.im < (S • z).im :=
 
 /-- The standard (closed) fundamental domain of the action of `SL(2,ℤ)` on `ℍ`. -/
 def fd : Set ℍ :=
-  { z | 1 ≤ (z : ℂ).normSq ∧ |z.re| ≤ (1 : ℝ) / 2 }
+  {z | 1 ≤ (z : ℂ).normSq ∧ |z.re| ≤ (1 : ℝ) / 2}
 #align modular_group.fd ModularGroup.fd
 
 /-- The standard open fundamental domain of the action of `SL(2,ℤ)` on `ℍ`. -/
 def fdo : Set ℍ :=
-  { z | 1 < (z : ℂ).normSq ∧ |z.re| < (1 : ℝ) / 2 }
+  {z | 1 < (z : ℂ).normSq ∧ |z.re| < (1 : ℝ) / 2}
 #align modular_group.fdo ModularGroup.fdo
 
 -- mathport name: modular_group.fd

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

@@ -240,7 +240,7 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
     (lc_row0_extend hcd).toContinuousLinearEquiv.toHomeomorph.ClosedEmbedding
   convert hf₂.tendsto_cocompact.comp (hf₁.comp subtype.coe_injective.tendsto_cofinite) using 1
   ext (⟨g, rfl⟩i j) : 3
-  fin_cases i <;> [fin_cases j;skip]
+  fin_cases i <;> [fin_cases j; skip]
   -- the following are proved by `simp`, but it is replaced by `simp only` to avoid timeouts.
   ·
     simp only [mB, mul_vec, dot_product, Fin.sum_univ_two, _root_.coe_coe, coe_matrix_coe,
@@ -368,7 +368,7 @@ variable {z}
 theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z :=
   by
   have had := g.det_coe
-  replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had; linarith
+  replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had ; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use ↑ₘg 0 1
     suffices g = T ^ ↑ₘg 0 1 by intro z; conv_lhs => rw [this]
@@ -383,7 +383,7 @@ theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
 theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = T ^ ↑ₘg 0 0 * S * T ^ ↑ₘg 1 1 :=
   by
   have hg := g.det_coe.symm
-  replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1; · rw [det_fin_two, hc] at hg; linarith
+  replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1; · rw [det_fin_two, hc] at hg ; linarith
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two ↑ₘg]
   rw [hc, hg]
@@ -452,10 +452,10 @@ theorem one_lt_normSq_t_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T
 theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) : n = 0 :=
   by
   suffices |(n : ℝ)| < 1 by
-    rwa [← Int.cast_abs, ← Int.cast_one, Int.cast_lt, Int.abs_lt_one_iff] at this
+    rwa [← Int.cast_abs, ← Int.cast_one, Int.cast_lt, Int.abs_lt_one_iff] at this 
   have h₁ := hz.2
   have h₂ := hg.2
-  rw [re_T_zpow_smul] at h₂
+  rw [re_T_zpow_smul] at h₂ 
   calc
     |(n : ℝ)| ≤ |z.re| + |z.re + (n : ℝ)| := abs_add' (n : ℝ) z.re
     _ < 1 / 2 + 1 / 2 := (add_lt_add h₁ h₂)
@@ -509,9 +509,9 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg
   let c : ℝ := (c' : ℝ)
   suffices 3 * c ^ 2 < 4
     by
-    rw [← Int.cast_pow, ← Int.cast_three, ← Int.cast_four, ← Int.cast_mul, Int.cast_lt] at this
+    rw [← Int.cast_pow, ← Int.cast_three, ← Int.cast_four, ← Int.cast_mul, Int.cast_lt] at this 
     replace this : c' ^ 2 ≤ 1 ^ 2; · linarith
-    rwa [sq_le_sq, abs_one] at this
+    rwa [sq_le_sq, abs_one] at this 
   suffices c ≠ 0 → 9 * c ^ 4 < 16
     by
     rcases eq_or_ne c 0 with (hc | hc)
@@ -570,7 +570,7 @@ where `z : ℍ` and `g : SL(2,ℤ)`, then `z = g • z`. -/
 theorem eq_smul_self_of_mem_fdo_mem_fdo (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : z = g • z :=
   by
   obtain ⟨n, hn⟩ := exists_eq_T_zpow_of_c_eq_zero (c_eq_zero hz hg)
-  rw [hn] at hg⊢
+  rw [hn] at hg ⊢
   simp [eq_zero_of_mem_fdo_of_T_zpow_mem_fdo hz hg, one_smul]
 #align modular_group.eq_smul_self_of_mem_fdo_mem_fdo ModularGroup.eq_smul_self_of_mem_fdo_mem_fdo
 

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

@@ -83,7 +83,7 @@ local notation "SL(" n ", " R ")" => SpecialLinearGroup (Fin n) R
 -- mathport name: «expr↑ₘ »
 local prefix:1024 "↑ₘ" => @coe _ (Matrix (Fin 2) (Fin 2) ℤ) _
 
-open UpperHalfPlane ComplexConjugate
+open scoped UpperHalfPlane ComplexConjugate
 
 attribute [local instance] Fintype.card_fin_even
 

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

@@ -368,22 +368,14 @@ variable {z}
 theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z :=
   by
   have had := g.det_coe
-  replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1;
-  · rw [det_fin_two, hc] at had
-    linarith
+  replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1; · rw [det_fin_two, hc] at had; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use ↑ₘg 0 1
-    suffices g = T ^ ↑ₘg 0 1 by
-      intro z
-      conv_lhs => rw [this]
-    ext (i j)
-    fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
+    suffices g = T ^ ↑ₘg 0 1 by intro z; conv_lhs => rw [this]
+    ext (i j); fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
   · use -↑ₘg 0 1
-    suffices g = -T ^ (-↑ₘg 0 1) by
-      intro z
-      conv_lhs => rw [this, SL_neg_smul]
-    ext (i j)
-    fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
+    suffices g = -T ^ (-↑ₘg 0 1) by intro z; conv_lhs => rw [this, SL_neg_smul]
+    ext (i j); fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
 #align modular_group.exists_eq_T_zpow_of_c_eq_zero ModularGroup.exists_eq_t_zpow_of_c_eq_zero
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
@@ -391,9 +383,7 @@ theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
 theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = T ^ ↑ₘg 0 0 * S * T ^ ↑ₘg 1 1 :=
   by
   have hg := g.det_coe.symm
-  replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1;
-  · rw [det_fin_two, hc] at hg
-    linarith
+  replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1; · rw [det_fin_two, hc] at hg; linarith
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two ↑ₘg]
   rw [hc, hg]
@@ -520,20 +510,17 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg
   suffices 3 * c ^ 2 < 4
     by
     rw [← Int.cast_pow, ← Int.cast_three, ← Int.cast_four, ← Int.cast_mul, Int.cast_lt] at this
-    replace this : c' ^ 2 ≤ 1 ^ 2
-    · linarith
+    replace this : c' ^ 2 ≤ 1 ^ 2; · linarith
     rwa [sq_le_sq, abs_one] at this
   suffices c ≠ 0 → 9 * c ^ 4 < 16
     by
     rcases eq_or_ne c 0 with (hc | hc)
-    · rw [hc]
-      norm_num
+    · rw [hc]; norm_num
     · refine' (abs_lt_of_sq_lt_sq' _ (by norm_num)).2
       specialize this hc
       linarith
   intro hc
-  replace hc : 0 < c ^ 4
-  · rw [pow_bit0_pos_iff] <;> trivial
+  replace hc : 0 < c ^ 4; · rw [pow_bit0_pos_iff] <;> trivial
   have h₁ :=
     mul_lt_mul_of_pos_right
       (mul_lt_mul'' (three_lt_four_mul_im_sq_of_mem_fdo hg) (three_lt_four_mul_im_sq_of_mem_fdo hz)
@@ -550,9 +537,7 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |↑ₘg
       by
       rw [special_linear_group.im_smul_eq_div_norm_sq, div_pow]
       ring
-    _ ≤ 16 := by
-      rw [← mul_pow]
-      linarith
+    _ ≤ 16 := by rw [← mul_pow]; linarith
     
 #align modular_group.abs_c_le_one ModularGroup.abs_c_le_one
 
@@ -565,10 +550,7 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : ↑ₘg 1 0
     by_contra hc
     let a := ↑ₘg' 0 0
     let d := ↑ₘg' 1 1
-    have had : T ^ (-a) * g' = S * T ^ d :=
-      by
-      rw [g_eq_of_c_eq_one hc]
-      group
+    have had : T ^ (-a) * g' = S * T ^ d := by rw [g_eq_of_c_eq_one hc]; group
     let w := T ^ (-a) • g' • z
     have h₁ : w = S • T ^ d • z := by simp only [w, ← mul_smul, had]
     replace h₁ : norm_sq w < 1 := h₁.symm ▸ norm_sq_S_smul_lt_one (one_lt_norm_sq_T_zpow_smul hz d)
@@ -576,8 +558,7 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : ↑ₘg 1 0
     linarith
   have hn : ↑ₘg 1 0 ≠ -1 := by
     intro hc
-    replace hc : ↑ₘ(-g) 1 0 = 1
-    · simp [← neg_eq_iff_eq_neg.mpr hc]
+    replace hc : ↑ₘ(-g) 1 0 = 1; · simp [← neg_eq_iff_eq_neg.mpr hc]
     replace hg : -g • z ∈ 𝒟ᵒ := (SL_neg_smul g z).symm ▸ hg
     exact hp hg hc
   specialize hp hg

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

@@ -240,7 +240,7 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
     (lc_row0_extend hcd).toContinuousLinearEquiv.toHomeomorph.ClosedEmbedding
   convert hf₂.tendsto_cocompact.comp (hf₁.comp subtype.coe_injective.tendsto_cofinite) using 1
   ext (⟨g, rfl⟩i j) : 3
-  fin_cases i <;> [fin_cases j, skip]
+  fin_cases i <;> [fin_cases j;skip]
   -- the following are proved by `simp`, but it is replaced by `simp only` to avoid timeouts.
   ·
     simp only [mB, mul_vec, dot_product, Fin.sum_univ_two, _root_.coe_coe, coe_matrix_coe,

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -339,33 +339,33 @@ theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0
     exact hg ⟨g1, this⟩
 #align modular_group.exists_row_one_eq_and_min_re ModularGroup.exists_row_one_eq_and_min_re
 
-theorem coe_t_zpow_smul_eq {n : ℤ} : (↑(t ^ n • z) : ℂ) = z + n := by simp [coe_T_zpow]
+theorem coe_t_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n := by simp [coe_T_zpow]
 #align modular_group.coe_T_zpow_smul_eq ModularGroup.coe_t_zpow_smul_eq
 
-theorem re_t_zpow_smul (n : ℤ) : (t ^ n • z).re = z.re + n := by
+theorem re_t_zpow_smul (n : ℤ) : (T ^ n • z).re = z.re + n := by
   rw [← coe_re, coe_T_zpow_smul_eq, add_re, int_cast_re, coe_re]
 #align modular_group.re_T_zpow_smul ModularGroup.re_t_zpow_smul
 
-theorem im_t_zpow_smul (n : ℤ) : (t ^ n • z).im = z.im := by
+theorem im_t_zpow_smul (n : ℤ) : (T ^ n • z).im = z.im := by
   rw [← coe_im, coe_T_zpow_smul_eq, add_im, int_cast_im, add_zero, coe_im]
 #align modular_group.im_T_zpow_smul ModularGroup.im_t_zpow_smul
 
-theorem re_t_smul : (t • z).re = z.re + 1 := by simpa using re_T_zpow_smul z 1
+theorem re_t_smul : (T • z).re = z.re + 1 := by simpa using re_T_zpow_smul z 1
 #align modular_group.re_T_smul ModularGroup.re_t_smul
 
-theorem im_t_smul : (t • z).im = z.im := by simpa using im_T_zpow_smul z 1
+theorem im_t_smul : (T • z).im = z.im := by simpa using im_T_zpow_smul z 1
 #align modular_group.im_T_smul ModularGroup.im_t_smul
 
-theorem re_t_inv_smul : (t⁻¹ • z).re = z.re - 1 := by simpa using re_T_zpow_smul z (-1)
+theorem re_t_inv_smul : (T⁻¹ • z).re = z.re - 1 := by simpa using re_T_zpow_smul z (-1)
 #align modular_group.re_T_inv_smul ModularGroup.re_t_inv_smul
 
-theorem im_t_inv_smul : (t⁻¹ • z).im = z.im := by simpa using im_T_zpow_smul z (-1)
+theorem im_t_inv_smul : (T⁻¹ • z).im = z.im := by simpa using im_T_zpow_smul z (-1)
 #align modular_group.im_T_inv_smul ModularGroup.im_t_inv_smul
 
 variable {z}
 
 -- If instead we had `g` and `T` of type `PSL(2, ℤ)`, then we could simply state `g = T^n`.
-theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = t ^ n • z :=
+theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z :=
   by
   have had := g.det_coe
   replace had : ↑ₘg 0 0 * ↑ₘg 1 1 = 1;
@@ -388,7 +388,7 @@ theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
-theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = t ^ ↑ₘg 0 0 * s * t ^ ↑ₘg 1 1 :=
+theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = T ^ ↑ₘg 0 0 * S * T ^ ↑ₘg 1 1 :=
   by
   have hg := g.det_coe.symm
   replace hg : ↑ₘg 0 1 = ↑ₘg 0 0 * ↑ₘg 1 1 - 1;
@@ -404,12 +404,12 @@ theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = t ^ ↑ₘg 0 0 * s * t ^
 #align modular_group.g_eq_of_c_eq_one ModularGroup.g_eq_of_c_eq_one
 
 /-- If `1 < |z|`, then `|S • z| < 1`. -/
-theorem normSq_s_smul_lt_one (h : 1 < normSq z) : normSq ↑(s • z) < 1 := by
+theorem normSq_s_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1 := by
   simpa [coe_S] using (inv_lt_inv z.norm_sq_pos zero_lt_one).mpr h
 #align modular_group.norm_sq_S_smul_lt_one ModularGroup.normSq_s_smul_lt_one
 
 /-- If `|z| < 1`, then applying `S` strictly decreases `im`. -/
-theorem im_lt_im_s_smul (h : normSq z < 1) : z.im < (s • z).im :=
+theorem im_lt_im_s_smul (h : normSq z < 1) : z.im < (S • z).im :=
   by
   have : z.im < z.im / norm_sq (z : ℂ) :=
     by
@@ -451,7 +451,7 @@ theorem three_lt_four_mul_im_sq_of_mem_fdo (h : z ∈ 𝒟ᵒ) : 3 < 4 * z.im ^
 #align modular_group.three_lt_four_mul_im_sq_of_mem_fdo ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo
 
 /-- If `z ∈ 𝒟ᵒ`, and `n : ℤ`, then `|z + n| > 1`. -/
-theorem one_lt_normSq_t_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (t ^ n • z : ℍ) :=
+theorem one_lt_normSq_t_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T ^ n • z : ℍ) :=
   by
   have hz₁ : 1 < z.re * z.re + z.im * z.im := hz.1
   have hzn := Int.nneg_mul_add_sq_of_abs_le_one n (abs_two_mul_re_lt_one_of_mem_fdo hz).le
@@ -459,7 +459,7 @@ theorem one_lt_normSq_t_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (t
   simpa [coe_T_zpow, norm_sq]
 #align modular_group.one_lt_norm_sq_T_zpow_smul ModularGroup.one_lt_normSq_t_zpow_smul
 
-theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : t ^ n • z ∈ 𝒟ᵒ) : n = 0 :=
+theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) : n = 0 :=
   by
   suffices |(n : ℝ)| < 1 by
     rwa [← Int.cast_abs, ← Int.cast_one, Int.cast_lt, Int.abs_lt_one_iff] at this

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -289,7 +289,7 @@ theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
     exact_mod_cast hp.sq_add_sq_ne_zero
   let f := Homeomorph.mulRight₀ _ this
   let ff := Homeomorph.addRight (((p 1 : ℂ) * z - p 0) / ((p 0 ^ 2 + p 1 ^ 2) * (p 0 * z + p 1))).re
-  convert (f.trans ff).ClosedEmbedding.tendsto_cocompact.comp (tendsto_lc_row0 hp)
+  convert(f.trans ff).ClosedEmbedding.tendsto_cocompact.comp (tendsto_lc_row0 hp)
   ext g
   change
     ((g : SL(2, ℤ)) • z).re =

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
 
 ! This file was ported from Lean 3 source module number_theory.modular
-! leanprover-community/mathlib commit f06058e64b7e8397234455038f3f8aec83aaba5a
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -577,7 +577,7 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : ↑ₘg 1 0
   have hn : ↑ₘg 1 0 ≠ -1 := by
     intro hc
     replace hc : ↑ₘ(-g) 1 0 = 1
-    · simp [eq_neg_of_eq_neg hc]
+    · simp [← neg_eq_iff_eq_neg.mpr hc]
     replace hg : -g • z ∈ 𝒟ᵒ := (SL_neg_smul g z).symm ▸ hg
     exact hp hg hc
   specialize hp hg

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

@@ -168,7 +168,7 @@ theorem tendsto_normSq_coprime_pair :
     · show (z : ℂ).im⁻¹ * ((z : ℂ) * conj (f c)).im = c 1
       rw [f_def, RingHom.map_add, RingHom.map_mul, mul_add, mul_left_comm, mul_conj, conj_of_real,
         conj_of_real, ← of_real_mul, add_im, of_real_im, zero_add, inv_mul_eq_iff_eq_mul₀ hz]
-      simp only [of_real_im, of_real_re, mul_im, zero_add, mul_zero]
+      simp only [of_real_im, of_real_re, mul_im, zero_add, MulZeroClass.mul_zero]
   have hf' : ClosedEmbedding f :=
     by
     -- for some reason we get a timeout if we try and apply this lemma in a more sensible way

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
 
 ! This file was ported from Lean 3 source module number_theory.modular
-! leanprover-community/mathlib commit 2705404e701abc6b3127da906f40bae062a169c9
+! leanprover-community/mathlib commit f06058e64b7e8397234455038f3f8aec83aaba5a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -339,87 +339,6 @@ theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0
     exact hg ⟨g1, this⟩
 #align modular_group.exists_row_one_eq_and_min_re ModularGroup.exists_row_one_eq_and_min_re
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-/-- The matrix `T = [[1,1],[0,1]]` as an element of `SL(2,ℤ)` -/
-def t : SL(2, ℤ) :=
-  ⟨«expr!![ »
-      "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation",
-    by norm_num [Matrix.det_fin_two_of] ⟩
-#align modular_group.T ModularGroup.t
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-/-- The matrix `S = [[0,-1],[1,0]]` as an element of `SL(2,ℤ)` -/
-def s : SL(2, ℤ) :=
-  ⟨«expr!![ »
-      "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation",
-    by norm_num [Matrix.det_fin_two_of] ⟩
-#align modular_group.S ModularGroup.s
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-theorem coe_s :
-    ↑ₘs =
-      «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
-  rfl
-#align modular_group.coe_S ModularGroup.coe_s
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-theorem coe_t :
-    ↑ₘt =
-      «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
-  rfl
-#align modular_group.coe_T ModularGroup.coe_t
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-theorem coe_t_inv :
-    ↑ₘt⁻¹ =
-      «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
-  by simp [coe_inv, coe_T, adjugate_fin_two]
-#align modular_group.coe_T_inv ModularGroup.coe_t_inv
-
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-theorem coe_t_zpow (n : ℤ) :
-    ↑ₘ(t ^ n) =
-      «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
-  by
-  induction' n using Int.induction_on with n h n h
-  · rw [zpow_zero, coe_one, Matrix.one_fin_two]
-  · simp_rw [zpow_add, zpow_one, coe_mul, h, coe_T, Matrix.mul_fin_two]
-    trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]"
-    rw [mul_one, mul_one, add_comm]
-  · simp_rw [zpow_sub, zpow_one, coe_mul, h, coe_T_inv, Matrix.mul_fin_two]
-    trace
-        "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]" <;>
-      ring
-#align modular_group.coe_T_zpow ModularGroup.coe_t_zpow
-
-@[simp]
-theorem t_pow_mul_apply_one (n : ℤ) (g : SL(2, ℤ)) : ↑ₘ(t ^ n * g) 1 = ↑ₘg 1 := by
-  simp [coe_T_zpow, Matrix.mul, Matrix.dotProduct, Fin.sum_univ_succ]
-#align modular_group.T_pow_mul_apply_one ModularGroup.t_pow_mul_apply_one
-
-@[simp]
-theorem t_mul_apply_one (g : SL(2, ℤ)) : ↑ₘ(t * g) 1 = ↑ₘg 1 := by
-  simpa using T_pow_mul_apply_one 1 g
-#align modular_group.T_mul_apply_one ModularGroup.t_mul_apply_one
-
-@[simp]
-theorem t_inv_mul_apply_one (g : SL(2, ℤ)) : ↑ₘ(t⁻¹ * g) 1 = ↑ₘg 1 := by
-  simpa using T_pow_mul_apply_one (-1) g
-#align modular_group.T_inv_mul_apply_one ModularGroup.t_inv_mul_apply_one
-
 theorem coe_t_zpow_smul_eq {n : ℤ} : (↑(t ^ n • z) : ℂ) = z + n := by simp [coe_T_zpow]
 #align modular_group.coe_T_zpow_smul_eq ModularGroup.coe_t_zpow_smul_eq
 

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

@@ -340,68 +340,68 @@ theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0
 #align modular_group.exists_row_one_eq_and_min_re ModularGroup.exists_row_one_eq_and_min_re
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 /-- The matrix `T = [[1,1],[0,1]]` as an element of `SL(2,ℤ)` -/
 def t : SL(2, ℤ) :=
   ⟨«expr!![ »
-      "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation",
+      "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation",
     by norm_num [Matrix.det_fin_two_of] ⟩
 #align modular_group.T ModularGroup.t
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 /-- The matrix `S = [[0,-1],[1,0]]` as an element of `SL(2,ℤ)` -/
 def s : SL(2, ℤ) :=
   ⟨«expr!![ »
-      "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation",
+      "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation",
     by norm_num [Matrix.det_fin_two_of] ⟩
 #align modular_group.S ModularGroup.s
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 theorem coe_s :
     ↑ₘs =
       «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation" :=
+        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
   rfl
 #align modular_group.coe_S ModularGroup.coe_s
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 theorem coe_t :
     ↑ₘt =
       «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation" :=
+        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
   rfl
 #align modular_group.coe_T ModularGroup.coe_t
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 theorem coe_t_inv :
     ↑ₘt⁻¹ =
       «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation" :=
+        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
   by simp [coe_inv, coe_T, adjugate_fin_two]
 #align modular_group.coe_T_inv ModularGroup.coe_t_inv
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 theorem coe_t_zpow (n : ℤ) :
     ↑ₘ(t ^ n) =
       «expr!![ »
-        "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation" :=
+        "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
   by
   induction' n using Int.induction_on with n h n h
   · rw [zpow_zero, coe_one, Matrix.one_fin_two]
   · simp_rw [zpow_add, zpow_one, coe_mul, h, coe_T, Matrix.mul_fin_two]
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]"
     rw [mul_one, mul_one, add_comm]
   · simp_rw [zpow_sub, zpow_one, coe_mul, h, coe_T_inv, Matrix.mul_fin_two]
     trace
-        "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]" <;>
+        "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]" <;>
       ring
 #align modular_group.coe_T_zpow ModularGroup.coe_t_zpow
 
@@ -467,7 +467,7 @@ theorem exists_eq_t_zpow_of_c_eq_zero (hc : ↑ₘg 1 0 = 0) : ∃ n : ℤ, ∀
     fin_cases i <;> fin_cases j <;> simp [ha, hc, hd, coe_T_zpow]
 #align modular_group.exists_eq_T_zpow_of_c_eq_zero ModularGroup.exists_eq_t_zpow_of_c_eq_zero
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, ",", expr _, ";", expr _, ",", expr _, "]"] [])]] -/
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
 theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = t ^ ↑ₘg 0 0 * s * t ^ ↑ₘg 1 1 :=
   by
@@ -480,7 +480,7 @@ theorem g_eq_of_c_eq_one (hc : ↑ₘg 1 0 = 1) : g = t ^ ↑ₘg 0 0 * s * t ^
   rw [hc, hg]
   simp only [coe_mul, coe_T_zpow, coe_S, mul_fin_two]
   trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]" <;>
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr!![ »(matrix.notation [expr _, \",\", expr _, \";\", expr _, \",\", expr _, \"]\"] [])]]" <;>
     ring
 #align modular_group.g_eq_of_c_eq_one ModularGroup.g_eq_of_c_eq_one
 
@@ -549,7 +549,7 @@ theorem eq_zero_of_mem_fdo_of_t_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg
   rw [re_T_zpow_smul] at h₂
   calc
     |(n : ℝ)| ≤ |z.re| + |z.re + (n : ℝ)| := abs_add' (n : ℝ) z.re
-    _ < 1 / 2 + 1 / 2 := add_lt_add h₁ h₂
+    _ < 1 / 2 + 1 / 2 := (add_lt_add h₁ h₂)
     _ = 1 := add_halves 1
     
 #align modular_group.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo ModularGroup.eq_zero_of_mem_fdo_of_t_zpow_mem_fdo

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.

@@ -490,7 +490,7 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |(↑ₘg
       linarith
   intro hc
   replace hc : 0 < c ^ 4 := by
-    change 0 < c ^ (2 * 2); rw [pow_mul]; apply sq_pos_of_pos (sq_pos_of_ne_zero _ hc)
+    change 0 < c ^ (2 * 2); rw [pow_mul]; apply sq_pos_of_pos (sq_pos_of_ne_zero hc)
   have h₁ :=
     mul_lt_mul_of_pos_right
       (mul_lt_mul'' (three_lt_four_mul_im_sq_of_mem_fdo hg) (three_lt_four_mul_im_sq_of_mem_fdo hz)

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.

@@ -133,7 +133,7 @@ theorem tendsto_normSq_coprime_pair :
     ext1
     rw [f_def]
     dsimp only [Function.comp_def]
-    rw [ofReal_int_cast, ofReal_int_cast]
+    rw [ofReal_intCast, ofReal_intCast]
   rw [this]
   have hf : LinearMap.ker f = ⊥ := by
     let g : ℂ →ₗ[ℝ] Fin 2 → ℝ :=
@@ -250,7 +250,7 @@ theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg
   rw [(by simp :
     (p 1 : ℂ) * z - p 0 = (p 1 * z - p 0) * ↑(Matrix.det (↑g : Matrix (Fin 2) (Fin 2) ℤ)))]
   rw [← hg, det_fin_two]
-  simp only [Int.coe_castRingHom, coe_matrix_coe, Int.cast_mul, ofReal_int_cast, map_apply, denom,
+  simp only [Int.coe_castRingHom, coe_matrix_coe, Int.cast_mul, ofReal_intCast, map_apply, denom,
     Int.cast_sub, coe_GLPos_coe_GL_coe_matrix, coe'_apply_complex]
   ring
 #align modular_group.smul_eq_lc_row0_add ModularGroup.smul_eq_lcRow0_add
@@ -324,11 +324,11 @@ theorem coe_T_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n := by
 #align modular_group.coe_T_zpow_smul_eq ModularGroup.coe_T_zpow_smul_eq
 
 theorem re_T_zpow_smul (n : ℤ) : (T ^ n • z).re = z.re + n := by
-  rw [← coe_re, coe_T_zpow_smul_eq, add_re, int_cast_re, coe_re]
+  rw [← coe_re, coe_T_zpow_smul_eq, add_re, intCast_re, coe_re]
 #align modular_group.re_T_zpow_smul ModularGroup.re_T_zpow_smul
 
 theorem im_T_zpow_smul (n : ℤ) : (T ^ n • z).im = z.im := by
-  rw [← coe_im, coe_T_zpow_smul_eq, add_im, int_cast_im, add_zero, coe_im]
+  rw [← coe_im, coe_T_zpow_smul_eq, add_im, intCast_im, add_zero, coe_im]
 #align modular_group.im_T_zpow_smul ModularGroup.im_T_zpow_smul
 
 theorem re_T_smul : (T • z).re = z.re + 1 := by simpa using re_T_zpow_smul z 1

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

@@ -434,7 +434,7 @@ theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg
   rw [re_T_zpow_smul] at h₂
   calc
     |(n : ℝ)| ≤ |z.re| + |z.re + (n : ℝ)| := abs_add' (n : ℝ) z.re
-    _ < 1 / 2 + 1 / 2 := (add_lt_add h₁ h₂)
+    _ < 1 / 2 + 1 / 2 := add_lt_add h₁ h₂
     _ = 1 := add_halves 1
 #align modular_group.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo ModularGroup.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo
 

Added a class HasRankNullity consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file LinearAlgebra.Dimension.RankNullity.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -191,6 +191,9 @@ def lcRow0Extend {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
       exact hcd.sq_add_sq_ne_zero, LinearEquiv.refl ℝ (Fin 2 → ℝ)]
 #align modular_group.lc_row0_extend ModularGroup.lcRow0Extend
 
+-- `simpNF` times out, but only in CI where all of `Mathlib` is imported
+attribute [nolint simpNF] lcRow0Extend_apply lcRow0Extend_symm_apply
+
 /-- The map `lcRow0` is proper, that is, preimages of cocompact sets are finite in
 `[[* , *], [c, d]]`. -/
 theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -192,7 +192,7 @@ def lcRow0Extend {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
 #align modular_group.lc_row0_extend ModularGroup.lcRow0Extend
 
 /-- The map `lcRow0` is proper, that is, preimages of cocompact sets are finite in
-`[[* , *], [c, d]]`.-/
+`[[* , *], [c, d]]`. -/
 theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
     Tendsto (fun g : { g : SL(2, ℤ) // (↑ₘg) 1 = cd } => lcRow0 cd ↑(↑g : SL(2, ℝ))) cofinite
       (cocompact ℝ) := by

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

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

@@ -346,7 +346,7 @@ variable {z}
 theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
     ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z := by
   have had := g.det_coe
-  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1 := by rw [det_fin_two, hc] at had; omega
+  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1 := by rw [det_fin_two, hc] at had; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use (↑ₘg) 0 1
     suffices g = T ^ (↑ₘg) 0 1 by intro z; conv_lhs => rw [this]
@@ -361,7 +361,7 @@ theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
 theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S * T ^ (↑ₘg) 1 1 := by
   have hg := g.det_coe.symm
-  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1 := by rw [det_fin_two, hc] at hg; omega
+  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1 := by rw [det_fin_two, hc] at hg; linarith
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two (↑ₘg)]
   rw [hc, hg]

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -346,7 +346,7 @@ variable {z}
 theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
     ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z := by
   have had := g.det_coe
-  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1 := by rw [det_fin_two, hc] at had; linarith
+  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1 := by rw [det_fin_two, hc] at had; omega
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use (↑ₘg) 0 1
     suffices g = T ^ (↑ₘg) 0 1 by intro z; conv_lhs => rw [this]
@@ -361,7 +361,7 @@ theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
 theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S * T ^ (↑ₘg) 1 1 := by
   have hg := g.det_coe.symm
-  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1 := by rw [det_fin_two, hc] at hg; linarith
+  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1 := by rw [det_fin_two, hc] at hg; omega
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two (↑ₘg)]
   rw [hc, hg]

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -99,9 +99,9 @@ theorem bottom_row_surj {R : Type*} [CommRing R] :
   have det_A_1 : det A = 1 := by
     convert gcd_eqn
     rw [det_fin_two]
-    simp [(by ring : a * cd 1 + b₀ * cd 0 = b₀ * cd 0 + a * cd 1)]
+    simp [A, (by ring : a * cd 1 + b₀ * cd 0 = b₀ * cd 0 + a * cd 1)]
   refine' ⟨⟨A, det_A_1⟩, Set.mem_univ _, _⟩
-  ext; simp
+  ext; simp [A]
 #align modular_group.bottom_row_surj ModularGroup.bottom_row_surj
 
 end BottomRow
@@ -124,7 +124,8 @@ theorem tendsto_normSq_coprime_pair :
   let f : (Fin 2 → ℝ) →ₗ[ℝ] ℂ := π₀.smulRight (z : ℂ) + π₁.smulRight 1
   have f_def : ⇑f = fun p : Fin 2 → ℝ => (p 0 : ℂ) * ↑z + p 1 := by
     ext1
-    dsimp only [LinearMap.coe_proj, real_smul, LinearMap.coe_smulRight, LinearMap.add_apply]
+    dsimp only [π₀, π₁, f, LinearMap.coe_proj, real_smul, LinearMap.coe_smulRight,
+      LinearMap.add_apply]
     rw [mul_one]
   have :
     (fun p : Fin 2 → ℤ => normSq ((p 0 : ℂ) * ↑z + ↑(p 1))) =
@@ -198,7 +199,7 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
   let mB : ℝ → Matrix (Fin 2) (Fin 2) ℝ := fun t => of ![![t, (-(1 : ℤ) : ℝ)], (↑) ∘ cd]
   have hmB : Continuous mB := by
     refine' continuous_matrix _
-    simp only [Fin.forall_fin_two, continuous_const, continuous_id', of_apply, cons_val_zero,
+    simp only [mB, Fin.forall_fin_two, continuous_const, continuous_id', of_apply, cons_val_zero,
       cons_val_one, and_self_iff]
   refine' Filter.Tendsto.of_tendsto_comp _ (comap_cocompact_le hmB)
   let f₁ : SL(2, ℤ) → Matrix (Fin 2) (Fin 2) ℝ := fun g =>
@@ -217,13 +218,13 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
   ext ⟨g, rfl⟩ i j : 3
   fin_cases i <;> [fin_cases j; skip]
   -- the following are proved by `simp`, but it is replaced by `simp only` to avoid timeouts.
-  · simp only [mulVec, dotProduct, Fin.sum_univ_two, coe_matrix_coe,
+  · simp only [mB, mulVec, dotProduct, Fin.sum_univ_two, coe_matrix_coe,
       Int.coe_castRingHom, lcRow0_apply, Function.comp_apply, cons_val_zero, lcRow0Extend_apply,
       LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, GeneralLinearGroup.coe_toLinear,
       val_planeConformalMatrix, neg_neg, mulVecLin_apply, cons_val_one, head_cons, of_apply,
       Fin.mk_zero, Fin.mk_one]
   · convert congr_arg (fun n : ℤ => (-n : ℝ)) g.det_coe.symm using 1
-    simp only [mulVec, dotProduct, Fin.sum_univ_two, Matrix.det_fin_two, Function.comp_apply,
+    simp only [f₁, mulVec, dotProduct, Fin.sum_univ_two, Matrix.det_fin_two, Function.comp_apply,
       Subtype.coe_mk, lcRow0Extend_apply, cons_val_zero,
       LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, GeneralLinearGroup.coe_toLinear,
       val_planeConformalMatrix, mulVecLin_apply, cons_val_one, head_cons, map_apply, neg_mul,
@@ -514,7 +515,7 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : (↑ₘg) 1
     let d := (↑ₘg') 1 1
     have had : T ^ (-a) * g' = S * T ^ d := by rw [g_eq_of_c_eq_one hc]; group
     let w := T ^ (-a) • g' • z
-    have h₁ : w = S • T ^ d • z := by simp only [← mul_smul, had]
+    have h₁ : w = S • T ^ d • z := by simp only [w, ← mul_smul, had]
     replace h₁ : normSq w < 1 := h₁.symm ▸ normSq_S_smul_lt_one (one_lt_normSq_T_zpow_smul hz d)
     have h₂ : 1 < normSq w := one_lt_normSq_T_zpow_smul hg' (-a)
     linarith

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

This follows on from #6964.

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

@@ -345,7 +345,7 @@ variable {z}
 theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
     ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z := by
   have had := g.det_coe
-  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1; · rw [det_fin_two, hc] at had; linarith
+  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1 := by rw [det_fin_two, hc] at had; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use (↑ₘg) 0 1
     suffices g = T ^ (↑ₘg) 0 1 by intro z; conv_lhs => rw [this]
@@ -360,7 +360,7 @@ theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
 theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S * T ^ (↑ₘg) 1 1 := by
   have hg := g.det_coe.symm
-  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1; · rw [det_fin_two, hc] at hg; linarith
+  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1 := by rw [det_fin_two, hc] at hg; linarith
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two (↑ₘg)]
   rw [hc, hg]
@@ -476,7 +476,7 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |(↑ₘg
   let c : ℝ := (c' : ℝ)
   suffices 3 * c ^ 2 < 4 by
     rw [← Int.cast_pow, ← Int.cast_three, ← Int.cast_four, ← Int.cast_mul, Int.cast_lt] at this
-    replace this : c' ^ 2 ≤ 1 ^ 2; · linarith
+    replace this : c' ^ 2 ≤ 1 ^ 2 := by linarith
     rwa [sq_le_sq, abs_one] at this
   suffices c ≠ 0 → 9 * c ^ 4 < 16 by
     rcases eq_or_ne c 0 with (hc | hc)
@@ -485,8 +485,8 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |(↑ₘg
       specialize this hc
       linarith
   intro hc
-  replace hc : 0 < c ^ 4;
-  · change 0 < c ^ (2 * 2); rw [pow_mul]; apply sq_pos_of_pos (sq_pos_of_ne_zero _ hc)
+  replace hc : 0 < c ^ 4 := by
+    change 0 < c ^ (2 * 2); rw [pow_mul]; apply sq_pos_of_pos (sq_pos_of_ne_zero _ hc)
   have h₁ :=
     mul_lt_mul_of_pos_right
       (mul_lt_mul'' (three_lt_four_mul_im_sq_of_mem_fdo hg) (three_lt_four_mul_im_sq_of_mem_fdo hz)
@@ -520,7 +520,7 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : (↑ₘg) 1
     linarith
   have hn : (↑ₘg) 1 0 ≠ -1 := by
     intro hc
-    replace hc : (↑ₘ(-g)) 1 0 = 1; · simp [← neg_eq_iff_eq_neg.mpr hc]
+    replace hc : (↑ₘ(-g)) 1 0 = 1 := by simp [← neg_eq_iff_eq_neg.mpr hc]
     replace hg : -g • z ∈ 𝒟ᵒ := (SL_neg_smul g z).symm ▸ hg
     exact hp hg hc
   specialize hp hg

Rename some definitions and theorems about $SL(2, ℤ)$ in Analysis/Complex/UpperHalfPlane/Basic.lean to place them in the namespace UpperHalfPlane.ModularGroup, in order to avoid the confusion with definitions and theorems about $SL(2, ℝ)$. For example, UpperHalfPlane.det_coe' is renamed to UpperHalfPlane.ModularGroup.det_coe', because we will have UpperHalfPlane.SL2R.det_coe'.

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

@@ -65,7 +65,7 @@ open Complex hiding abs_two
 
 open Matrix hiding mul_smul
 
-open Matrix.SpecialLinearGroup UpperHalfPlane
+open Matrix.SpecialLinearGroup UpperHalfPlane ModularGroup
 
 noncomputable section
 
@@ -289,7 +289,7 @@ theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im 
     Filter.Tendsto.exists_within_forall_le hs (tendsto_normSq_coprime_pair z)
   obtain ⟨g, -, hg⟩ := bottom_row_surj hp_coprime
   refine' ⟨g, fun g' => _⟩
-  rw [SpecialLinearGroup.im_smul_eq_div_normSq, SpecialLinearGroup.im_smul_eq_div_normSq,
+  rw [ModularGroup.im_smul_eq_div_normSq, ModularGroup.im_smul_eq_div_normSq,
     div_le_div_left]
   · simpa [← hg] using hp ((↑ₘg') 1) (bottom_row_coprime g')
   · exact z.im_pos
@@ -380,7 +380,7 @@ theorem im_lt_im_S_smul (h : normSq z < 1) : z.im < (S • z).im := by
     apply (lt_div_iff z.normSq_pos).mpr
     nlinarith
   convert this
-  simp only [SpecialLinearGroup.im_smul_eq_div_normSq]
+  simp only [ModularGroup.im_smul_eq_div_normSq]
   simp [denom, coe_S]
 #align modular_group.im_lt_im_S_smul ModularGroup.im_lt_im_S_smul
 
@@ -445,7 +445,7 @@ theorem exists_smul_mem_fd (z : ℍ) : ∃ g : SL(2, ℤ), g • z ∈ 𝒟 := b
   -- `g` has same max im property as `g₀`
   have hg₀' : ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im := by
     have hg'' : (g • z).im = (g₀ • z).im := by
-      rw [SpecialLinearGroup.im_smul_eq_div_normSq, SpecialLinearGroup.im_smul_eq_div_normSq,
+      rw [ModularGroup.im_smul_eq_div_normSq, ModularGroup.im_smul_eq_div_normSq,
         denom_apply, denom_apply, hg]
     simpa only [hg''] using hg₀
   constructor
@@ -500,7 +500,7 @@ theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |(↑ₘg
   calc
     9 * c ^ 4 < c ^ 4 * z.im ^ 2 * (g • z).im ^ 2 * 16 := by linarith
     _ = c ^ 4 * z.im ^ 4 / nsq ^ 2 * 16 := by
-      rw [SpecialLinearGroup.im_smul_eq_div_normSq, div_pow]
+      rw [ModularGroup.im_smul_eq_div_normSq, div_pow]
       ring
     _ ≤ 16 := by rw [← mul_pow]; linarith
 #align modular_group.abs_c_le_one ModularGroup.abs_c_le_one

This instance was meant to apply to even literal numbers. Because Lean 4 no longer uses bit0/bit1 for literals, it no longer serves that purpose. Instead, a specific instance for Fin 2 is added.

@@ -75,8 +75,6 @@ local macro "↑ₘ" t:term:80 : term => `(term| ($t : Matrix (Fin 2) (Fin 2) 
 
 open scoped UpperHalfPlane ComplexConjugate
 
-attribute [local instance] Fintype.card_fin_even
-
 namespace ModularGroup
 
 variable {g : SL(2, ℤ)} (z : ℍ)

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

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

@@ -4,9 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
 -/
 import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
-import Mathlib.Analysis.NormedSpace.FiniteDimension
 import Mathlib.LinearAlgebra.GeneralLinearGroup
 import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup
+import Mathlib.Topology.Instances.Matrix
+import Mathlib.Topology.Algebra.Module.FiniteDimension
 
 #align_import number_theory.modular from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
 

and rename ofReal_mul_re → re_mul_ofReal, ofReal_mul_im → im_mul_ofReal.

From LeanAPAP

@@ -147,7 +147,7 @@ theorem tendsto_normSq_coprime_pair :
     dsimp only [Pi.smul_apply, LinearMap.pi_apply, smul_eq_mul]
     fin_cases i
     · show (z : ℂ).im⁻¹ * (f c).im = c 0
-      rw [f_def, add_im, ofReal_mul_im, ofReal_im, add_zero, mul_left_comm, inv_mul_cancel hz,
+      rw [f_def, add_im, im_ofReal_mul, ofReal_im, add_zero, mul_left_comm, inv_mul_cancel hz,
         mul_one]
     · show (z : ℂ).im⁻¹ * ((z : ℂ) * conj (f c)).im = c 1
       rw [f_def, RingHom.map_add, RingHom.map_mul, mul_add, mul_left_comm, mul_conj, conj_ofReal,

@@ -435,7 +435,8 @@ theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg
     _ = 1 := add_halves 1
 #align modular_group.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo ModularGroup.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo
 
-/-- Any `z : ℍ` can be moved to `𝒟` by an element of `SL(2,ℤ)`  -/
+/-- First Fundamental Domain Lemma: Any `z : ℍ` can be moved to `𝒟` by an element of
+`SL(2,ℤ)` -/
 theorem exists_smul_mem_fd (z : ℍ) : ∃ g : SL(2, ℤ), g • z ∈ 𝒟 := by
   -- obtain a g₀ which maximizes im (g • z),
   obtain ⟨g₀, hg₀⟩ := exists_max_im z
@@ -527,7 +528,7 @@ theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : (↑ₘg) 1
   rcases Int.abs_le_one_iff.mp <| abs_c_le_one hz hg with ⟨⟩ <;> tauto
 #align modular_group.c_eq_zero ModularGroup.c_eq_zero
 
-/-- Second Main Fundamental Domain Lemma: if both `z` and `g • z` are in the open domain `𝒟ᵒ`,
+/-- Second Fundamental Domain Lemma: if both `z` and `g • z` are in the open domain `𝒟ᵒ`,
 where `z : ℍ` and `g : SL(2,ℤ)`, then `z = g • z`. -/
 theorem eq_smul_self_of_mem_fdo_mem_fdo (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : z = g • z := by
   obtain ⟨n, hn⟩ := exists_eq_T_zpow_of_c_eq_zero (c_eq_zero hz hg)

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>

@@ -240,7 +240,7 @@ theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg
     ↑(g • z) =
       (lcRow0 p ↑(g : SL(2, ℝ)) : ℂ) / ((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) +
         ((p 1 : ℂ) * z - p 0) / (((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) * (p 0 * z + p 1)) := by
-  have nonZ1 : (p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2 ≠ 0 := by exact_mod_cast hp.sq_add_sq_ne_zero
+  have nonZ1 : (p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2 ≠ 0 := mod_cast hp.sq_add_sq_ne_zero
   have : ((↑) : ℤ → ℝ) ∘ p ≠ 0 := fun h => hp.ne_zero (by ext i; simpa using congr_fun h i)
   have nonZ2 : (p 0 : ℂ) * z + p 1 ≠ 0 := by simpa using linear_ne_zero _ z this
   field_simp [nonZ1, nonZ2, denom_ne_zero, num]
@@ -261,7 +261,7 @@ theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
     by exact tendsto_norm_cocompact_atTop.comp this
   have : ((p 0 : ℝ) ^ 2 + (p 1 : ℝ) ^ 2)⁻¹ ≠ 0 := by
     apply inv_ne_zero
-    exact_mod_cast hp.sq_add_sq_ne_zero
+    exact mod_cast hp.sq_add_sq_ne_zero
   let f := Homeomorph.mulRight₀ _ this
   let ff := Homeomorph.addRight
     (((p 1 : ℂ) * z - p 0) / (((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) * (p 0 * z + p 1))).re
@@ -270,7 +270,7 @@ theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :
     ((g : SL(2, ℤ)) • z).re =
       lcRow0 p ↑(↑g : SL(2, ℝ)) / ((p 0 : ℝ) ^ 2 + (p 1 : ℝ) ^ 2) +
         Complex.re (((p 1 : ℂ) * z - p 0) / (((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) * (p 0 * z + p 1)))
-  exact_mod_cast congr_arg Complex.re (smul_eq_lcRow0_add z hp g.2)
+  exact mod_cast congr_arg Complex.re (smul_eq_lcRow0_add z hp g.2)
 #align modular_group.tendsto_abs_re_smul ModularGroup.tendsto_abs_re_smul
 
 end TendstoLemmas

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>

@@ -132,7 +132,7 @@ theorem tendsto_normSq_coprime_pair :
       normSq ∘ f ∘ fun p : Fin 2 → ℤ => ((↑) : ℤ → ℝ) ∘ p := by
     ext1
     rw [f_def]
-    dsimp only [Function.comp]
+    dsimp only [Function.comp_def]
     rw [ofReal_int_cast, ofReal_int_cast]
   rw [this]
   have hf : LinearMap.ker f = ⊥ := by

Due to recent changes in core we can reduce or remove many set_option maxHeartbeats statements.

I have tried to be careful to not leave anything too close to the line, so don't be surprised if some of these can still be reduced further.

This reduces us from 96 maxHeartbeats statements to 44. (There are 10 false positives in meta or testing code.)

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

@@ -369,7 +369,6 @@ theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S *
   congrm !![?_, ?_; ?_, ?_] <;> ring
 #align modular_group.g_eq_of_c_eq_one ModularGroup.g_eq_of_c_eq_one
 
-set_option maxHeartbeats 250000 in
 /-- If `1 < |z|`, then `|S • z| < 1`. -/
 theorem normSq_S_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1 := by
   simpa [coe_S, num, denom] using (inv_lt_inv z.normSq_pos zero_lt_one).mpr h
@@ -415,7 +414,6 @@ theorem three_lt_four_mul_im_sq_of_mem_fdo (h : z ∈ 𝒟ᵒ) : 3 < 4 * z.im ^
   cases abs_cases z.re <;> nlinarith
 #align modular_group.three_lt_four_mul_im_sq_of_mem_fdo ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo
 
-set_option maxHeartbeats 260000 in
 /-- If `z ∈ 𝒟ᵒ`, and `n : ℤ`, then `|z + n| > 1`. -/
 theorem one_lt_normSq_T_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T ^ n • z : ℍ) := by
   have hz₁ : 1 < z.re * z.re + z.im * z.im := hz.1

• Generalize FiniteDimensional.complete, Submodule.complete_of_finiteDimensional from a normed space over 𝕜 to a uniform additive commutative group that is a TVS over 𝕜.
• Generalize Submodule.closed_of_finiteDimensional, LinearMap.closedEmbedding_of_injective, closedEmbedding_smul_left isClosedMap_smul_left, and ContinuousLinearMap.exists_right_inverse_of_surjective from a normed space to a TVS.
• Rename finiteDimensional_of_isCompact_closed_ball₀ to finiteDimensional_of_isCompact_closedBall₀.

Co-authored-by: ADedecker <anatolededecker@gmail.com>

@@ -153,9 +153,7 @@ theorem tendsto_normSq_coprime_pair :
       rw [f_def, RingHom.map_add, RingHom.map_mul, mul_add, mul_left_comm, mul_conj, conj_ofReal,
         conj_ofReal, ← ofReal_mul, add_im, ofReal_im, zero_add, inv_mul_eq_iff_eq_mul₀ hz]
       simp only [ofReal_im, ofReal_re, mul_im, zero_add, mul_zero]
-  have hf' : ClosedEmbedding f := by
-    have := @LinearEquiv.closedEmbedding_of_injective ℝ _ (Fin 2 → ℝ) _ _ ℂ _ _ _ f
-    exact this hf
+  have hf' : ClosedEmbedding f := f.closedEmbedding_of_injective hf
   have h₂ : Tendsto (fun p : Fin 2 → ℤ => ((↑) : ℤ → ℝ) ∘ p) cofinite (cocompact _) := by
     convert Tendsto.pi_map_coprodᵢ fun _ => Int.tendsto_coe_cofinite
     · rw [coprodᵢ_cofinite]

Adds a term elaborator for congr(...) "congruence quotations". For example, if hf : f = f' and hx : x = x', then we have congr($hf $x) : f x = f' x'. This supports the functions having implicit arguments, and it has support for subsingleton instance arguments. So for example, if s t : Set X are sets with Fintype instances and h : s = t then congr(Fintype.card $h) : Fintype.card s = Fintype.card t works.

Ports the congrm tactic as a convenient frontend for applying a congruence quotation to the goal. Holes are turned into congruence holes. For example, congrm 1 + ?_ uses congr(1 + $(?_)). Placeholders (_) do not turn into congruence holes; that's not to say they have to be identical on the LHS and RHS, but congrm itself is responsible for finding a congruence lemma for such arguments.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>

@@ -368,8 +368,7 @@ theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S *
   conv_lhs => rw [Matrix.eta_fin_two (↑ₘg)]
   rw [hc, hg]
   simp only [coe_mul, coe_T_zpow, coe_S, mul_fin_two]
-  -- Porting note: Was `congrm !![_, _; _, _] <;> ring`.
-  congr! 3 <;> [skip; congr! 1; congr! 2] <;> ring
+  congrm !![?_, ?_; ?_, ?_] <;> ring
 #align modular_group.g_eq_of_c_eq_one ModularGroup.g_eq_of_c_eq_one
 
 set_option maxHeartbeats 250000 in

@@ -223,13 +223,13 @@ theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :
   · simp only [mulVec, dotProduct, Fin.sum_univ_two, coe_matrix_coe,
       Int.coe_castRingHom, lcRow0_apply, Function.comp_apply, cons_val_zero, lcRow0Extend_apply,
       LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, GeneralLinearGroup.coe_toLinear,
-      planeConformalMatrix_val, neg_neg, mulVecLin_apply, cons_val_one, head_cons, of_apply,
+      val_planeConformalMatrix, neg_neg, mulVecLin_apply, cons_val_one, head_cons, of_apply,
       Fin.mk_zero, Fin.mk_one]
   · convert congr_arg (fun n : ℤ => (-n : ℝ)) g.det_coe.symm using 1
     simp only [mulVec, dotProduct, Fin.sum_univ_two, Matrix.det_fin_two, Function.comp_apply,
       Subtype.coe_mk, lcRow0Extend_apply, cons_val_zero,
       LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, GeneralLinearGroup.coe_toLinear,
-      planeConformalMatrix_val, mulVecLin_apply, cons_val_one, head_cons, map_apply, neg_mul,
+      val_planeConformalMatrix, mulVecLin_apply, cons_val_one, head_cons, map_apply, neg_mul,
       Int.cast_sub, Int.cast_mul, neg_sub, of_apply, Fin.mk_zero, Fin.mk_one]
     ring
   · rfl

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

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

@@ -152,7 +152,7 @@ theorem tendsto_normSq_coprime_pair :
     · show (z : ℂ).im⁻¹ * ((z : ℂ) * conj (f c)).im = c 1
       rw [f_def, RingHom.map_add, RingHom.map_mul, mul_add, mul_left_comm, mul_conj, conj_ofReal,
         conj_ofReal, ← ofReal_mul, add_im, ofReal_im, zero_add, inv_mul_eq_iff_eq_mul₀ hz]
-      simp only [ofReal_im, ofReal_re, mul_im, zero_add, MulZeroClass.mul_zero]
+      simp only [ofReal_im, ofReal_re, mul_im, zero_add, mul_zero]
   have hf' : ClosedEmbedding f := by
     have := @LinearEquiv.closedEmbedding_of_injective ℝ _ (Fin 2 → ℝ) _ _ ℂ _ _ _ f
     exact this hf

@@ -245,13 +245,12 @@ theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg
   have nonZ1 : (p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2 ≠ 0 := by exact_mod_cast hp.sq_add_sq_ne_zero
   have : ((↑) : ℤ → ℝ) ∘ p ≠ 0 := fun h => hp.ne_zero (by ext i; simpa using congr_fun h i)
   have nonZ2 : (p 0 : ℂ) * z + p 1 ≠ 0 := by simpa using linear_ne_zero _ z this
-  -- Porting note: `SMul.smul, smulAux, smulAux'` are required to unfold `SMul.smul` in `sl_moeb`.
-  field_simp [nonZ1, nonZ2, denom_ne_zero, SMul.smul, smulAux, smulAux', num]
+  field_simp [nonZ1, nonZ2, denom_ne_zero, num]
   rw [(by simp :
     (p 1 : ℂ) * z - p 0 = (p 1 * z - p 0) * ↑(Matrix.det (↑g : Matrix (Fin 2) (Fin 2) ℤ)))]
   rw [← hg, det_fin_two]
   simp only [Int.coe_castRingHom, coe_matrix_coe, Int.cast_mul, ofReal_int_cast, map_apply, denom,
-    Int.cast_sub, coe_GLPos_coe_GL_coe_matrix]
+    Int.cast_sub, coe_GLPos_coe_GL_coe_matrix, coe'_apply_complex]
   ring
 #align modular_group.smul_eq_lc_row0_add ModularGroup.smul_eq_lcRow0_add
 
@@ -319,8 +318,7 @@ theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0
 #align modular_group.exists_row_one_eq_and_min_re ModularGroup.exists_row_one_eq_and_min_re
 
 theorem coe_T_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n := by
-  -- Porting note: This line is required due to `SMul.smul` in `sl_moeb`.
-  erw [sl_moeb, UpperHalfPlane.coe_smul]
+  rw [sl_moeb, UpperHalfPlane.coe_smul]
   simp [coe_T_zpow, denom, num, -map_zpow]
 #align modular_group.coe_T_zpow_smul_eq ModularGroup.coe_T_zpow_smul_eq
 
@@ -377,9 +375,7 @@ theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S *
 set_option maxHeartbeats 250000 in
 /-- If `1 < |z|`, then `|S • z| < 1`. -/
 theorem normSq_S_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1 := by
-  -- Porting note: `SMul.smul, smulAux, smulAux'` are required to unfold `SMul.smul` in `sl_moeb`.
-  simpa [coe_S, SMul.smul, smulAux, smulAux', num, denom]
-    using (inv_lt_inv z.normSq_pos zero_lt_one).mpr h
+  simpa [coe_S, num, denom] using (inv_lt_inv z.normSq_pos zero_lt_one).mpr h
 #align modular_group.norm_sq_S_smul_lt_one ModularGroup.normSq_S_smul_lt_one
 
 /-- If `|z| < 1`, then applying `S` strictly decreases `im`. -/
@@ -390,7 +386,7 @@ theorem im_lt_im_S_smul (h : normSq z < 1) : z.im < (S • z).im := by
     nlinarith
   convert this
   simp only [SpecialLinearGroup.im_smul_eq_div_normSq]
-  field_simp [normSq_denom_ne_zero, normSq_ne_zero, S, denom]
+  simp [denom, coe_S]
 #align modular_group.im_lt_im_S_smul ModularGroup.im_lt_im_S_smul
 
 /-- The standard (closed) fundamental domain of the action of `SL(2,ℤ)` on `ℍ`. -/
@@ -428,8 +424,7 @@ theorem one_lt_normSq_T_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T
   have hz₁ : 1 < z.re * z.re + z.im * z.im := hz.1
   have hzn := Int.nneg_mul_add_sq_of_abs_le_one n (abs_two_mul_re_lt_one_of_mem_fdo hz).le
   have : 1 < (z.re + ↑n) * (z.re + ↑n) + z.im * z.im := by linarith
-  -- Porting note: `SMul.smul, smulAux, smulAux'` are required to unfold `SMul.smul` in `sl_moeb`.
-  simpa [coe_T_zpow, normSq, SMul.smul, smulAux, smulAux', num, denom, -map_zpow]
+  simpa [coe_T_zpow, normSq, num, denom, -map_zpow]
 #align modular_group.one_lt_norm_sq_T_zpow_smul ModularGroup.one_lt_normSq_T_zpow_smul
 
 theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) :

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

This has nice performance benefits.

@@ -83,7 +83,7 @@ variable {g : SL(2, ℤ)} (z : ℍ)
 section BottomRow
 
 /-- The two numbers `c`, `d` in the "bottom_row" of `g=[[*,*],[c,d]]` in `SL(2, ℤ)` are coprime. -/
-theorem bottom_row_coprime {R : Type _} [CommRing R] (g : SL(2, R)) :
+theorem bottom_row_coprime {R : Type*} [CommRing R] (g : SL(2, R)) :
     IsCoprime ((↑g : Matrix (Fin 2) (Fin 2) R) 1 0) ((↑g : Matrix (Fin 2) (Fin 2) R) 1 1) := by
   use -(↑g : Matrix (Fin 2) (Fin 2) R) 0 1, (↑g : Matrix (Fin 2) (Fin 2) R) 0 0
   rw [add_comm, neg_mul, ← sub_eq_add_neg, ← det_fin_two]
@@ -92,7 +92,7 @@ theorem bottom_row_coprime {R : Type _} [CommRing R] (g : SL(2, R)) :
 
 /-- Every pair `![c, d]` of coprime integers is the "bottom_row" of some element `g=[[*,*],[c,d]]`
 of `SL(2,ℤ)`. -/
-theorem bottom_row_surj {R : Type _} [CommRing R] :
+theorem bottom_row_surj {R : Type*} [CommRing R] :
     Set.SurjOn (fun g : SL(2, R) => (↑g : Matrix (Fin 2) (Fin 2) R) 1) Set.univ
       {cd | IsCoprime (cd 0) (cd 1)} := by
   rintro cd ⟨b₀, a, gcd_eqn⟩

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-
-! This file was ported from Lean 3 source module number_theory.modular
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
 import Mathlib.Analysis.NormedSpace.FiniteDimension
 import Mathlib.LinearAlgebra.GeneralLinearGroup
 import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup
 
+#align_import number_theory.modular from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
+
 /-!
 # The action of the modular group SL(2, ℤ) on the upper half-plane
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -353,7 +353,7 @@ variable {z}
 theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
     ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z := by
   have had := g.det_coe
-  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1; · rw [det_fin_two, hc] at had ; linarith
+  replace had : (↑ₘg) 0 0 * (↑ₘg) 1 1 = 1; · rw [det_fin_two, hc] at had; linarith
   rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
   · use (↑ₘg) 0 1
     suffices g = T ^ (↑ₘg) 0 1 by intro z; conv_lhs => rw [this]

Also define UpperHalfPlane.coe so that type synonym doesn't leak through API.

@@ -368,7 +368,7 @@ theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :
 -- If `c = 1`, then `g` factorises into a product terms involving only `T` and `S`.
 theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S * T ^ (↑ₘg) 1 1 := by
   have hg := g.det_coe.symm
-  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1; · rw [det_fin_two, hc] at hg ; linarith
+  replace hg : (↑ₘg) 0 1 = (↑ₘg) 0 0 * (↑ₘg) 1 1 - 1; · rw [det_fin_two, hc] at hg; linarith
   refine' Subtype.ext _
   conv_lhs => rw [Matrix.eta_fin_two (↑ₘg)]
   rw [hc, hg]