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

@@ -198,7 +198,7 @@ theorem areaForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
   by
   convert o.area_form_map φ (φ x) (φ y)
   · symm
-    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ 
+    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
   · simp
   · simp
@@ -427,7 +427,7 @@ theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
   convert (o.right_angle_rotation_map φ (φ x)).symm
   · simp
   · symm
-    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ 
+    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation Orientation.linearIsometryEquiv_comp_rightAngleRotation
 -/

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

@@ -554,7 +554,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
       by
       rw [← (o.basis_right_angle_rotation x hx).sum_repr y]
       simp only [Fin.sum_univ_succ, coe_basis_right_angle_rotation, Matrix.cons_val_zero,
-        Fin.succ_zero_eq_one, Fintype.univ_of_isEmpty, Finset.sum_empty, o.area_form_apply_self,
+        Fin.succ_zero_eq_one, Fintype.univ_ofIsEmpty, Finset.sum_empty, o.area_form_apply_self,
         map_smul, map_add, map_zero, inner_smul_left, inner_smul_right, inner_add_left,
         inner_add_right, inner_zero_right, LinearMap.add_apply, Matrix.cons_val_one,
         Matrix.head_cons, Algebra.id.smul_eq_mul, o.area_form_right_angle_rotation_right,

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

@@ -581,7 +581,7 @@ real part is the inner product and its imaginary part is `orientation.area_form`
 
 On `ℂ` with the standard orientation, `kahler w z = conj w * z`; see `complex.kahler`. -/
 def kahler : E →ₗ[ℝ] E →ₗ[ℝ] ℂ :=
-  LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealClm ∘ₗ innerₛₗ ℝ +
+  LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealCLM ∘ₗ innerₛₗ ℝ +
     LinearMap.llcomp ℝ E ℝ ℂ ((LinearMap.lsmul ℝ ℂ).flip Complex.I) ∘ₗ ω
 #align orientation.kahler Orientation.kahler
 -/

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 -/
-import Mathbin.Analysis.InnerProductSpace.Dual
-import Mathbin.Analysis.InnerProductSpace.Orientation
-import Mathbin.Data.Complex.Orientation
-import Mathbin.Tactic.LinearCombination
+import Analysis.InnerProductSpace.Dual
+import Analysis.InnerProductSpace.Orientation
+import Data.Complex.Orientation
+import Tactic.LinearCombination
 
 #align_import analysis.inner_product_space.two_dim from "leanprover-community/mathlib"@"d07a9c875ed7139abfde6a333b2be205c5bd404e"
 

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

@@ -554,7 +554,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
       by
       rw [← (o.basis_right_angle_rotation x hx).sum_repr y]
       simp only [Fin.sum_univ_succ, coe_basis_right_angle_rotation, Matrix.cons_val_zero,
-        Fin.succ_zero_eq_one', Fintype.univ_of_isEmpty, Finset.sum_empty, o.area_form_apply_self,
+        Fin.succ_zero_eq_one, Fintype.univ_of_isEmpty, Finset.sum_empty, o.area_form_apply_self,
         map_smul, map_add, map_zero, inner_smul_left, inner_smul_right, inner_add_left,
         inner_add_right, inner_zero_right, LinearMap.add_apply, Matrix.cons_val_one,
         Matrix.head_cons, Algebra.id.smul_eq_mul, o.area_form_right_angle_rotation_right,

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit d07a9c875ed7139abfde6a333b2be205c5bd404e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.InnerProductSpace.Dual
 import Mathbin.Analysis.InnerProductSpace.Orientation
 import Mathbin.Data.Complex.Orientation
 import Mathbin.Tactic.LinearCombination
 
+#align_import analysis.inner_product_space.two_dim from "leanprover-community/mathlib"@"d07a9c875ed7139abfde6a333b2be205c5bd404e"
+
 /-!
 # Oriented two-dimensional real inner product spaces
 

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

@@ -134,7 +134,7 @@ theorem areaForm_swap (x y : E) : ω x y = -ω y x :=
 @[simp]
 theorem areaForm_neg_orientation : (-o).areaForm = -o.areaForm :=
   by
-  ext (x y)
+  ext x y
   simp [area_form_to_volume_form]
 #align orientation.area_form_neg_orientation Orientation.areaForm_neg_orientation
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/9f55d0d4363ae59948c33864cbc52e0b12e0e8ce

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit cd8fafa2fac98e1a67097e8a91ad9901cfde48af
+! leanprover-community/mathlib commit d07a9c875ed7139abfde6a333b2be205c5bd404e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Tactic.LinearCombination
 /-!
 # Oriented two-dimensional real inner product spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines constructions specific to the geometry of an oriented two-dimensional real inner
 product space `E`.
 

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

@@ -84,8 +84,6 @@ variable {E : Type _} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [Fact (fi
 
 namespace Orientation
 
-include o
-
 #print Orientation.areaForm /-
 /-- An antisymmetric bilinear form on an oriented real inner product space of dimension 2 (usual
 notation `ω`).  When evaluated on two vectors, it gives the oriented area of the parallelogram they
@@ -100,14 +98,14 @@ irreducible_def areaForm : E →ₗ[ℝ] E →ₗ[ℝ] ℝ :=
 #align orientation.area_form Orientation.areaForm
 -/
 
-omit o
-
--- mathport name: exprω
 local notation "ω" => o.areaForm
 
+#print Orientation.areaForm_to_volumeForm /-
 theorem areaForm_to_volumeForm (x y : E) : ω x y = o.volumeForm ![x, y] := by simp [area_form]
 #align orientation.area_form_to_volume_form Orientation.areaForm_to_volumeForm
+-/
 
+#print Orientation.areaForm_apply_self /-
 @[simp]
 theorem areaForm_apply_self (x : E) : ω x x = 0 :=
   by
@@ -116,7 +114,9 @@ theorem areaForm_apply_self (x : E) : ω x x = 0 :=
   · simp
   · norm_num
 #align orientation.area_form_apply_self Orientation.areaForm_apply_self
+-/
 
+#print Orientation.areaForm_swap /-
 theorem areaForm_swap (x y : E) : ω x y = -ω y x :=
   by
   simp only [area_form_to_volume_form]
@@ -125,13 +125,16 @@ theorem areaForm_swap (x y : E) : ω x y = -ω y x :=
     fin_cases i <;> rfl
   · norm_num
 #align orientation.area_form_swap Orientation.areaForm_swap
+-/
 
+#print Orientation.areaForm_neg_orientation /-
 @[simp]
 theorem areaForm_neg_orientation : (-o).areaForm = -o.areaForm :=
   by
   ext (x y)
   simp [area_form_to_volume_form]
 #align orientation.area_form_neg_orientation Orientation.areaForm_neg_orientation
+-/
 
 #print Orientation.areaForm' /-
 /-- Continuous linear map version of `orientation.area_form`, useful for calculus. -/
@@ -141,19 +144,26 @@ def areaForm' : E →L[ℝ] E →L[ℝ] ℝ :=
 #align orientation.area_form' Orientation.areaForm'
 -/
 
+#print Orientation.areaForm'_apply /-
 @[simp]
 theorem areaForm'_apply (x : E) : o.areaForm' x = (o.areaForm x).toContinuousLinearMap :=
   rfl
 #align orientation.area_form'_apply Orientation.areaForm'_apply
+-/
 
+#print Orientation.abs_areaForm_le /-
 theorem abs_areaForm_le (x y : E) : |ω x y| ≤ ‖x‖ * ‖y‖ := by
   simpa [area_form_to_volume_form, Fin.prod_univ_succ] using o.abs_volume_form_apply_le ![x, y]
 #align orientation.abs_area_form_le Orientation.abs_areaForm_le
+-/
 
+#print Orientation.areaForm_le /-
 theorem areaForm_le (x y : E) : ω x y ≤ ‖x‖ * ‖y‖ := by
   simpa [area_form_to_volume_form, Fin.prod_univ_succ] using o.volume_form_apply_le ![x, y]
 #align orientation.area_form_le Orientation.areaForm_le
+-/
 
+#print Orientation.abs_areaForm_of_orthogonal /-
 theorem abs_areaForm_of_orthogonal {x y : E} (h : ⟪x, y⟫ = 0) : |ω x y| = ‖x‖ * ‖y‖ :=
   by
   rw [o.area_form_to_volume_form, o.abs_volume_form_apply_of_pairwise_orthogonal]
@@ -165,7 +175,9 @@ theorem abs_areaForm_of_orthogonal {x y : E} (h : ⟪x, y⟫ = 0) : |ω x y| = 
   · simpa [real_inner_comm] using h
   · simpa
 #align orientation.abs_area_form_of_orthogonal Orientation.abs_areaForm_of_orthogonal
+-/
 
+#print Orientation.areaForm_map /-
 theorem areaForm_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).areaForm x y = o.areaForm (φ.symm x) (φ.symm y) :=
@@ -176,7 +188,9 @@ theorem areaForm_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ
     fin_cases i <;> rfl
   simp [area_form_to_volume_form, volume_form_map, this]
 #align orientation.area_form_map Orientation.areaForm_map
+-/
 
+#print Orientation.areaForm_comp_linearIsometryEquiv /-
 /-- The area form is invariant under pullback by a positively-oriented isometric automorphism. -/
 theorem areaForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) (x y : E) :
@@ -189,6 +203,7 @@ theorem areaForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
   · simp
   · simp
 #align orientation.area_form_comp_linear_isometry_equiv Orientation.areaForm_comp_linearIsometryEquiv
+-/
 
 #print Orientation.rightAngleRotationAux₁ /-
 /-- Auxiliary construction for `orientation.right_angle_rotation`, rotation by 90 degrees in an
@@ -200,6 +215,7 @@ irreducible_def rightAngleRotationAux₁ : E →ₗ[ℝ] E :=
 #align orientation.right_angle_rotation_aux₁ Orientation.rightAngleRotationAux₁
 -/
 
+#print Orientation.inner_rightAngleRotationAux₁_left /-
 @[simp]
 theorem inner_rightAngleRotationAux₁_left (x y : E) : ⟪o.rightAngleRotationAux₁ x, y⟫ = ω x y := by
   simp only [right_angle_rotation_aux₁, LinearEquiv.trans_symm, LinearEquiv.coe_trans,
@@ -207,13 +223,16 @@ theorem inner_rightAngleRotationAux₁_left (x y : E) : ⟪o.rightAngleRotationA
     LinearMap.coe_toContinuousLinearMap', LinearIsometryEquiv.coe_toLinearEquiv,
     LinearMap.comp_apply, LinearEquiv.symm_symm, LinearIsometryEquiv.toLinearEquiv_symm]
 #align orientation.inner_right_angle_rotation_aux₁_left Orientation.inner_rightAngleRotationAux₁_left
+-/
 
+#print Orientation.inner_rightAngleRotationAux₁_right /-
 @[simp]
 theorem inner_rightAngleRotationAux₁_right (x y : E) : ⟪x, o.rightAngleRotationAux₁ y⟫ = -ω x y :=
   by
   rw [real_inner_comm]
   simp [o.area_form_swap y x]
 #align orientation.inner_right_angle_rotation_aux₁_right Orientation.inner_rightAngleRotationAux₁_right
+-/
 
 #print Orientation.rightAngleRotationAux₂ /-
 /-- Auxiliary construction for `orientation.right_angle_rotation`, rotation by 90 degrees in an
@@ -251,6 +270,7 @@ def rightAngleRotationAux₂ : E →ₗᵢ[ℝ] E :=
 #align orientation.right_angle_rotation_aux₂ Orientation.rightAngleRotationAux₂
 -/
 
+#print Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁ /-
 @[simp]
 theorem rightAngleRotationAux₁_rightAngleRotationAux₁ (x : E) :
     o.rightAngleRotationAux₁ (o.rightAngleRotationAux₁ x) = -x :=
@@ -262,6 +282,7 @@ theorem rightAngleRotationAux₁_rightAngleRotationAux₁ (x : E) :
   rw [o.inner_right_angle_rotation_aux₁_right, ← o.inner_right_angle_rotation_aux₁_left, this,
     inner_neg_right]
 #align orientation.right_angle_rotation_aux₁_right_angle_rotation_aux₁ Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁
+-/
 
 #print Orientation.rightAngleRotation /-
 /-- An isometric automorphism of an oriented real inner product space of dimension 2 (usual notation
@@ -273,29 +294,34 @@ irreducible_def rightAngleRotation : E ≃ₗᵢ[ℝ] E :=
 #align orientation.right_angle_rotation Orientation.rightAngleRotation
 -/
 
--- mathport name: exprJ
 local notation "J" => o.rightAngleRotation
 
+#print Orientation.inner_rightAngleRotation_left /-
 @[simp]
 theorem inner_rightAngleRotation_left (x y : E) : ⟪J x, y⟫ = ω x y :=
   by
   rw [right_angle_rotation]
   exact o.inner_right_angle_rotation_aux₁_left x y
 #align orientation.inner_right_angle_rotation_left Orientation.inner_rightAngleRotation_left
+-/
 
+#print Orientation.inner_rightAngleRotation_right /-
 @[simp]
 theorem inner_rightAngleRotation_right (x y : E) : ⟪x, J y⟫ = -ω x y :=
   by
   rw [right_angle_rotation]
   exact o.inner_right_angle_rotation_aux₁_right x y
 #align orientation.inner_right_angle_rotation_right Orientation.inner_rightAngleRotation_right
+-/
 
+#print Orientation.rightAngleRotation_rightAngleRotation /-
 @[simp]
 theorem rightAngleRotation_rightAngleRotation (x : E) : J (J x) = -x :=
   by
   rw [right_angle_rotation]
   exact o.right_angle_rotation_aux₁_right_angle_rotation_aux₁ x
 #align orientation.right_angle_rotation_right_angle_rotation Orientation.rightAngleRotation_rightAngleRotation
+-/
 
 #print Orientation.rightAngleRotation_symm /-
 @[simp]
@@ -307,34 +333,48 @@ theorem rightAngleRotation_symm :
 #align orientation.right_angle_rotation_symm Orientation.rightAngleRotation_symm
 -/
 
+#print Orientation.inner_rightAngleRotation_self /-
 @[simp]
 theorem inner_rightAngleRotation_self (x : E) : ⟪J x, x⟫ = 0 := by simp
 #align orientation.inner_right_angle_rotation_self Orientation.inner_rightAngleRotation_self
+-/
 
+#print Orientation.inner_rightAngleRotation_swap /-
 theorem inner_rightAngleRotation_swap (x y : E) : ⟪x, J y⟫ = -⟪J x, y⟫ := by simp
 #align orientation.inner_right_angle_rotation_swap Orientation.inner_rightAngleRotation_swap
+-/
 
+#print Orientation.inner_rightAngleRotation_swap' /-
 theorem inner_rightAngleRotation_swap' (x y : E) : ⟪J x, y⟫ = -⟪x, J y⟫ := by
   simp [o.inner_right_angle_rotation_swap x y]
 #align orientation.inner_right_angle_rotation_swap' Orientation.inner_rightAngleRotation_swap'
+-/
 
+#print Orientation.inner_comp_rightAngleRotation /-
 theorem inner_comp_rightAngleRotation (x y : E) : ⟪J x, J y⟫ = ⟪x, y⟫ :=
   LinearIsometryEquiv.inner_map_map J x y
 #align orientation.inner_comp_right_angle_rotation Orientation.inner_comp_rightAngleRotation
+-/
 
+#print Orientation.areaForm_rightAngleRotation_left /-
 @[simp]
 theorem areaForm_rightAngleRotation_left (x y : E) : ω (J x) y = -⟪x, y⟫ := by
   rw [← o.inner_comp_right_angle_rotation, o.inner_right_angle_rotation_right, neg_neg]
 #align orientation.area_form_right_angle_rotation_left Orientation.areaForm_rightAngleRotation_left
+-/
 
+#print Orientation.areaForm_rightAngleRotation_right /-
 @[simp]
 theorem areaForm_rightAngleRotation_right (x y : E) : ω x (J y) = ⟪x, y⟫ := by
   rw [← o.inner_right_angle_rotation_left, o.inner_comp_right_angle_rotation]
 #align orientation.area_form_right_angle_rotation_right Orientation.areaForm_rightAngleRotation_right
+-/
 
+#print Orientation.areaForm_comp_rightAngleRotation /-
 @[simp]
 theorem areaForm_comp_rightAngleRotation (x y : E) : ω (J x) (J y) = ω x y := by simp
 #align orientation.area_form_comp_right_angle_rotation Orientation.areaForm_comp_rightAngleRotation
+-/
 
 #print Orientation.rightAngleRotation_trans_rightAngleRotation /-
 @[simp]
@@ -343,6 +383,7 @@ theorem rightAngleRotation_trans_rightAngleRotation :
 #align orientation.right_angle_rotation_trans_right_angle_rotation Orientation.rightAngleRotation_trans_rightAngleRotation
 -/
 
+#print Orientation.rightAngleRotation_neg_orientation /-
 theorem rightAngleRotation_neg_orientation (x : E) :
     (-o).rightAngleRotation x = -o.rightAngleRotation x :=
   by
@@ -351,13 +392,17 @@ theorem rightAngleRotation_neg_orientation (x : E) :
   rw [inner_right_angle_rotation_left]
   simp
 #align orientation.right_angle_rotation_neg_orientation Orientation.rightAngleRotation_neg_orientation
+-/
 
+#print Orientation.rightAngleRotation_trans_neg_orientation /-
 @[simp]
 theorem rightAngleRotation_trans_neg_orientation :
     (-o).rightAngleRotation = o.rightAngleRotation.trans (LinearIsometryEquiv.neg ℝ) :=
   LinearIsometryEquiv.ext <| o.rightAngleRotation_neg_orientation
 #align orientation.right_angle_rotation_trans_neg_orientation Orientation.rightAngleRotation_trans_neg_orientation
+-/
 
+#print Orientation.rightAngleRotation_map /-
 theorem rightAngleRotation_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).rightAngleRotation x =
@@ -372,7 +417,9 @@ theorem rightAngleRotation_map {F : Type _} [NormedAddCommGroup F] [InnerProduct
   · rw [φ.inner_map_map]
   · simp
 #align orientation.right_angle_rotation_map Orientation.rightAngleRotation_map
+-/
 
+#print Orientation.linearIsometryEquiv_comp_rightAngleRotation /-
 /-- `J` commutes with any positively-oriented isometric automorphism. -/
 theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) (x : E) : φ (J x) = J (φ x) :=
@@ -383,6 +430,7 @@ theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ 
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation Orientation.linearIsometryEquiv_comp_rightAngleRotation
+-/
 
 #print Orientation.rightAngleRotation_map' /-
 theorem rightAngleRotation_map' {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
@@ -393,12 +441,15 @@ theorem rightAngleRotation_map' {F : Type _} [NormedAddCommGroup F] [InnerProduc
 #align orientation.right_angle_rotation_map' Orientation.rightAngleRotation_map'
 -/
 
+#print Orientation.linearIsometryEquiv_comp_rightAngleRotation' /-
 /-- `J` commutes with any positively-oriented isometric automorphism. -/
 theorem linearIsometryEquiv_comp_rightAngleRotation' (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) : LinearIsometryEquiv.trans J φ = φ.trans J :=
   LinearIsometryEquiv.ext <| o.linearIsometryEquiv_comp_rightAngleRotation φ hφ
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation' Orientation.linearIsometryEquiv_comp_rightAngleRotation'
+-/
 
+#print Orientation.basisRightAngleRotation /-
 /-- For a nonzero vector `x` in an oriented two-dimensional real inner product space `E`,
 `![x, J x]` forms an (orthogonal) basis for `E`. -/
 def basisRightAngleRotation (x : E) (hx : x ≠ 0) : Basis (Fin 2) ℝ E :=
@@ -413,13 +464,17 @@ def basisRightAngleRotation (x : E) (hx : x ≠ 0) : Basis (Fin 2) ℝ E :=
         · simpa))
     (Fact.out (finrank ℝ E = 2)).symm
 #align orientation.basis_right_angle_rotation Orientation.basisRightAngleRotation
+-/
 
+#print Orientation.coe_basisRightAngleRotation /-
 @[simp]
 theorem coe_basisRightAngleRotation (x : E) (hx : x ≠ 0) :
     ⇑(o.basisRightAngleRotation x hx) = ![x, J x] :=
   coe_basisOfLinearIndependentOfCardEqFinrank _ _
 #align orientation.coe_basis_right_angle_rotation Orientation.coe_basisRightAngleRotation
+-/
 
+#print Orientation.inner_mul_inner_add_areaForm_mul_areaForm' /-
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫`. (See
 `orientation.inner_mul_inner_add_area_form_mul_area_form` for the "applied" form.)-/
 theorem inner_mul_inner_add_areaForm_mul_areaForm' (a x : E) :
@@ -441,17 +496,23 @@ theorem inner_mul_inner_add_areaForm_mul_areaForm' (a x : E) :
     rw [o.area_form_swap]
     ring
 #align orientation.inner_mul_inner_add_area_form_mul_area_form' Orientation.inner_mul_inner_add_areaForm_mul_areaForm'
+-/
 
+#print Orientation.inner_mul_inner_add_areaForm_mul_areaForm /-
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫`. -/
 theorem inner_mul_inner_add_areaForm_mul_areaForm (a x y : E) :
     ⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫ :=
   congr_arg (fun f : E →ₗ[ℝ] ℝ => f y) (o.inner_mul_inner_add_areaForm_mul_areaForm' a x)
 #align orientation.inner_mul_inner_add_area_form_mul_area_form Orientation.inner_mul_inner_add_areaForm_mul_areaForm
+-/
 
+#print Orientation.inner_sq_add_areaForm_sq /-
 theorem inner_sq_add_areaForm_sq (a b : E) : ⟪a, b⟫ ^ 2 + ω a b ^ 2 = ‖a‖ ^ 2 * ‖b‖ ^ 2 := by
   simpa [sq, real_inner_self_eq_norm_sq] using o.inner_mul_inner_add_area_form_mul_area_form a b b
 #align orientation.inner_sq_add_area_form_sq Orientation.inner_sq_add_areaForm_sq
+-/
 
+#print Orientation.inner_mul_areaForm_sub' /-
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ω a y - ω a x * ⟪a, y⟫ = ‖a‖ ^ 2 * ω x y`. (See
 `orientation.inner_mul_area_form_sub` for the "applied" form.) -/
 theorem inner_mul_areaForm_sub' (a x : E) : ⟪a, x⟫ • ω a - ω a x • innerₛₗ ℝ a = ‖a‖ ^ 2 • ω x :=
@@ -471,12 +532,16 @@ theorem inner_mul_areaForm_sub' (a x : E) : ⟪a, x⟫ • ω a - ω a x • inn
       LinearMap.smul_apply, LinearMap.sub_apply, Matrix.cons_val_one, Matrix.head_cons]
     ring
 #align orientation.inner_mul_area_form_sub' Orientation.inner_mul_areaForm_sub'
+-/
 
+#print Orientation.inner_mul_areaForm_sub /-
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ω a y - ω a x * ⟪a, y⟫ = ‖a‖ ^ 2 * ω x y`. -/
 theorem inner_mul_areaForm_sub (a x y : E) : ⟪a, x⟫ * ω a y - ω a x * ⟪a, y⟫ = ‖a‖ ^ 2 * ω x y :=
   congr_arg (fun f : E →ₗ[ℝ] ℝ => f y) (o.inner_mul_areaForm_sub' a x)
 #align orientation.inner_mul_area_form_sub Orientation.inner_mul_areaForm_sub
+-/
 
+#print Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay /-
 theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
     0 ≤ ⟪x, y⟫ ∧ ω x y = 0 ↔ SameRay ℝ x y :=
   by
@@ -508,7 +573,9 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
       and_true_iff]
     positivity
 #align orientation.nonneg_inner_and_area_form_eq_zero_iff_same_ray Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay
+-/
 
+#print Orientation.kahler /-
 /-- A complex-valued real-bilinear map on an oriented real inner product space of dimension 2. Its
 real part is the inner product and its imaginary part is `orientation.area_form`.
 
@@ -517,23 +584,31 @@ def kahler : E →ₗ[ℝ] E →ₗ[ℝ] ℂ :=
   LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealClm ∘ₗ innerₛₗ ℝ +
     LinearMap.llcomp ℝ E ℝ ℂ ((LinearMap.lsmul ℝ ℂ).flip Complex.I) ∘ₗ ω
 #align orientation.kahler Orientation.kahler
+-/
 
+#print Orientation.kahler_apply_apply /-
 theorem kahler_apply_apply (x y : E) : o.kahler x y = ⟪x, y⟫ + ω x y • Complex.I :=
   rfl
 #align orientation.kahler_apply_apply Orientation.kahler_apply_apply
+-/
 
+#print Orientation.kahler_swap /-
 theorem kahler_swap (x y : E) : o.kahler x y = conj (o.kahler y x) :=
   by
   simp only [kahler_apply_apply]
   rw [real_inner_comm, area_form_swap]
   simp
 #align orientation.kahler_swap Orientation.kahler_swap
+-/
 
+#print Orientation.kahler_apply_self /-
 @[simp]
 theorem kahler_apply_self (x : E) : o.kahler x x = ‖x‖ ^ 2 := by
   simp [kahler_apply_apply, real_inner_self_eq_norm_sq]
 #align orientation.kahler_apply_self Orientation.kahler_apply_self
+-/
 
+#print Orientation.kahler_rightAngleRotation_left /-
 @[simp]
 theorem kahler_rightAngleRotation_left (x y : E) : o.kahler (J x) y = -Complex.I * o.kahler x y :=
   by
@@ -541,7 +616,9 @@ theorem kahler_rightAngleRotation_left (x y : E) : o.kahler (J x) y = -Complex.I
     o.kahler_apply_apply, Complex.ofReal_neg, Complex.real_smul]
   linear_combination ω x y * Complex.I_sq
 #align orientation.kahler_right_angle_rotation_left Orientation.kahler_rightAngleRotation_left
+-/
 
+#print Orientation.kahler_rightAngleRotation_right /-
 @[simp]
 theorem kahler_rightAngleRotation_right (x y : E) : o.kahler x (J y) = Complex.I * o.kahler x y :=
   by
@@ -549,19 +626,25 @@ theorem kahler_rightAngleRotation_right (x y : E) : o.kahler x (J y) = Complex.I
     o.kahler_apply_apply, Complex.ofReal_neg, Complex.real_smul]
   linear_combination -ω x y * Complex.I_sq
 #align orientation.kahler_right_angle_rotation_right Orientation.kahler_rightAngleRotation_right
+-/
 
+#print Orientation.kahler_comp_rightAngleRotation /-
 @[simp]
 theorem kahler_comp_rightAngleRotation (x y : E) : o.kahler (J x) (J y) = o.kahler x y :=
   by
   simp only [kahler_right_angle_rotation_left, kahler_right_angle_rotation_right]
   linear_combination -o.kahler x y * Complex.I_sq
 #align orientation.kahler_comp_right_angle_rotation Orientation.kahler_comp_rightAngleRotation
+-/
 
+#print Orientation.kahler_neg_orientation /-
 @[simp]
 theorem kahler_neg_orientation (x y : E) : (-o).kahler x y = conj (o.kahler x y) := by
   simp [kahler_apply_apply]
 #align orientation.kahler_neg_orientation Orientation.kahler_neg_orientation
+-/
 
+#print Orientation.kahler_mul /-
 theorem kahler_mul (a x y : E) : o.kahler x a * o.kahler a y = ‖a‖ ^ 2 * o.kahler x y :=
   by
   trans (↑(‖a‖ ^ 2) : ℂ) * o.kahler x y
@@ -576,11 +659,15 @@ theorem kahler_mul (a x y : E) : o.kahler x a * o.kahler a y = ‖a‖ ^ 2 * o.k
       linear_combination o.inner_mul_area_form_sub a x y
   · norm_cast
 #align orientation.kahler_mul Orientation.kahler_mul
+-/
 
+#print Orientation.normSq_kahler /-
 theorem normSq_kahler (x y : E) : Complex.normSq (o.kahler x y) = ‖x‖ ^ 2 * ‖y‖ ^ 2 := by
   simpa [kahler_apply_apply, Complex.normSq, sq] using o.inner_sq_add_area_form_sq x y
 #align orientation.norm_sq_kahler Orientation.normSq_kahler
+-/
 
+#print Orientation.abs_kahler /-
 theorem abs_kahler (x y : E) : Complex.abs (o.kahler x y) = ‖x‖ * ‖y‖ :=
   by
   rw [← sq_eq_sq, Complex.sq_abs]
@@ -588,10 +675,14 @@ theorem abs_kahler (x y : E) : Complex.abs (o.kahler x y) = ‖x‖ * ‖y‖ :=
   · positivity
   · positivity
 #align orientation.abs_kahler Orientation.abs_kahler
+-/
 
+#print Orientation.norm_kahler /-
 theorem norm_kahler (x y : E) : ‖o.kahler x y‖ = ‖x‖ * ‖y‖ := by simpa using o.abs_kahler x y
 #align orientation.norm_kahler Orientation.norm_kahler
+-/
 
+#print Orientation.eq_zero_or_eq_zero_of_kahler_eq_zero /-
 theorem eq_zero_or_eq_zero_of_kahler_eq_zero {x y : E} (hx : o.kahler x y = 0) : x = 0 ∨ y = 0 :=
   by
   have : ‖x‖ * ‖y‖ = 0 := by simpa [hx] using (o.norm_kahler x y).symm
@@ -601,19 +692,25 @@ theorem eq_zero_or_eq_zero_of_kahler_eq_zero {x y : E} (hx : o.kahler x y = 0) :
   · right
     simpa using h
 #align orientation.eq_zero_or_eq_zero_of_kahler_eq_zero Orientation.eq_zero_or_eq_zero_of_kahler_eq_zero
+-/
 
+#print Orientation.kahler_eq_zero_iff /-
 theorem kahler_eq_zero_iff (x y : E) : o.kahler x y = 0 ↔ x = 0 ∨ y = 0 :=
   by
   refine' ⟨o.eq_zero_or_eq_zero_of_kahler_eq_zero, _⟩
   rintro (rfl | rfl) <;> simp
 #align orientation.kahler_eq_zero_iff Orientation.kahler_eq_zero_iff
+-/
 
+#print Orientation.kahler_ne_zero /-
 theorem kahler_ne_zero {x y : E} (hx : x ≠ 0) (hy : y ≠ 0) : o.kahler x y ≠ 0 :=
   by
   apply mt o.eq_zero_or_eq_zero_of_kahler_eq_zero
   tauto
 #align orientation.kahler_ne_zero Orientation.kahler_ne_zero
+-/
 
+#print Orientation.kahler_ne_zero_iff /-
 theorem kahler_ne_zero_iff (x y : E) : o.kahler x y ≠ 0 ↔ x ≠ 0 ∧ y ≠ 0 :=
   by
   refine' ⟨_, fun h => o.kahler_ne_zero h.1 h.2⟩
@@ -621,19 +718,24 @@ theorem kahler_ne_zero_iff (x y : E) : o.kahler x y ≠ 0 ↔ x ≠ 0 ∧ y ≠
   simp only [not_and_or, Classical.not_not, kahler_apply_apply, Complex.real_smul]
   rintro (rfl | rfl) <;> simp
 #align orientation.kahler_ne_zero_iff Orientation.kahler_ne_zero_iff
+-/
 
+#print Orientation.kahler_map /-
 theorem kahler_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).kahler x y = o.kahler (φ.symm x) (φ.symm y) := by
   simp [kahler_apply_apply, area_form_map]
 #align orientation.kahler_map Orientation.kahler_map
+-/
 
+#print Orientation.kahler_comp_linearIsometryEquiv /-
 /-- The bilinear map `kahler` is invariant under pullback by a positively-oriented isometric
 automorphism. -/
 theorem kahler_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) (x y : E) : o.kahler (φ x) (φ y) = o.kahler x y :=
   by simp [kahler_apply_apply, o.area_form_comp_linear_isometry_equiv φ hφ]
 #align orientation.kahler_comp_linear_isometry_equiv Orientation.kahler_comp_linearIsometryEquiv
+-/
 
 end Orientation
 
@@ -641,6 +743,7 @@ namespace Complex
 
 attribute [local instance] Complex.finrank_real_complex_fact
 
+#print Complex.areaForm /-
 @[simp]
 protected theorem areaForm (w z : ℂ) : Complex.orientation.areaForm w z = (conj w * z).im :=
   by
@@ -651,7 +754,9 @@ protected theorem areaForm (w z : ℂ) : Complex.orientation.areaForm w z = (con
     conj_re, conj_im]
   ring
 #align complex.area_form Complex.areaForm
+-/
 
+#print Complex.rightAngleRotation /-
 @[simp]
 protected theorem rightAngleRotation (z : ℂ) : Complex.orientation.rightAngleRotation z = I * z :=
   by
@@ -662,26 +767,28 @@ protected theorem rightAngleRotation (z : ℂ) : Complex.orientation.rightAngleR
     neg_re, neg_im, I_re, I_im]
   ring
 #align complex.right_angle_rotation Complex.rightAngleRotation
+-/
 
+#print Complex.kahler /-
 @[simp]
 protected theorem kahler (w z : ℂ) : Complex.orientation.kahler w z = conj w * z :=
   by
   rw [Orientation.kahler_apply_apply]
   ext1 <;> simp
 #align complex.kahler Complex.kahler
+-/
 
 end Complex
 
 namespace Orientation
 
--- mathport name: exprω
 local notation "ω" => o.areaForm
 
--- mathport name: exprJ
 local notation "J" => o.rightAngleRotation
 
 open Complex
 
+#print Orientation.areaForm_map_complex /-
 /-- The area form on an oriented real inner product space of dimension 2 can be evaluated in terms
 of a complex-number representation of the space. -/
 theorem areaForm_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
@@ -691,7 +798,9 @@ theorem areaForm_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
   rw [← Complex.areaForm, ← hf, o.area_form_map]
   simp
 #align orientation.area_form_map_complex Orientation.areaForm_map_complex
+-/
 
+#print Orientation.rightAngleRotation_map_complex /-
 /-- The rotation by 90 degrees on an oriented real inner product space of dimension 2 can be
 evaluated in terms of a complex-number representation of the space. -/
 theorem rightAngleRotation_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
@@ -701,7 +810,9 @@ theorem rightAngleRotation_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
   rw [← Complex.rightAngleRotation, ← hf, o.right_angle_rotation_map]
   simp
 #align orientation.right_angle_rotation_map_complex Orientation.rightAngleRotation_map_complex
+-/
 
+#print Orientation.kahler_map_complex /-
 /-- The Kahler form on an oriented real inner product space of dimension 2 can be evaluated in terms
 of a complex-number representation of the space. -/
 theorem kahler_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
@@ -711,6 +822,7 @@ theorem kahler_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
   rw [← Complex.kahler, ← hf, o.kahler_map]
   simp
 #align orientation.kahler_map_complex Orientation.kahler_map_complex
+-/
 
 end Orientation
 

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

@@ -86,6 +86,7 @@ namespace Orientation
 
 include o
 
+#print Orientation.areaForm /-
 /-- An antisymmetric bilinear form on an oriented real inner product space of dimension 2 (usual
 notation `ω`).  When evaluated on two vectors, it gives the oriented area of the parallelogram they
 span. -/
@@ -97,6 +98,7 @@ irreducible_def areaForm : E →ₗ[ℝ] E →ₗ[ℝ] ℝ :=
     LinearMap.llcomp ℝ E (AlternatingMap ℝ E ℝ (Fin 0)) ℝ z ∘ₗ AlternatingMap.curryLeftLinearMap
   exact y ∘ₗ AlternatingMap.curryLeftLinearMap o.volume_form
 #align orientation.area_form Orientation.areaForm
+-/
 
 omit o
 
@@ -131,11 +133,13 @@ theorem areaForm_neg_orientation : (-o).areaForm = -o.areaForm :=
   simp [area_form_to_volume_form]
 #align orientation.area_form_neg_orientation Orientation.areaForm_neg_orientation
 
+#print Orientation.areaForm' /-
 /-- Continuous linear map version of `orientation.area_form`, useful for calculus. -/
 def areaForm' : E →L[ℝ] E →L[ℝ] ℝ :=
   (↑(LinearMap.toContinuousLinearMap : (E →ₗ[ℝ] ℝ) ≃ₗ[ℝ] E →L[ℝ] ℝ) ∘ₗ
       o.areaForm).toContinuousLinearMap
 #align orientation.area_form' Orientation.areaForm'
+-/
 
 @[simp]
 theorem areaForm'_apply (x : E) : o.areaForm' x = (o.areaForm x).toContinuousLinearMap :=
@@ -186,6 +190,7 @@ theorem areaForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
   · simp
 #align orientation.area_form_comp_linear_isometry_equiv Orientation.areaForm_comp_linearIsometryEquiv
 
+#print Orientation.rightAngleRotationAux₁ /-
 /-- Auxiliary construction for `orientation.right_angle_rotation`, rotation by 90 degrees in an
 oriented real inner product space of dimension 2. -/
 irreducible_def rightAngleRotationAux₁ : E →ₗ[ℝ] E :=
@@ -193,6 +198,7 @@ irreducible_def rightAngleRotationAux₁ : E →ₗ[ℝ] E :=
     (InnerProductSpace.toDual ℝ E).toLinearEquiv ≪≫ₗ LinearMap.toContinuousLinearMap.symm
   ↑to_dual.symm ∘ₗ ω
 #align orientation.right_angle_rotation_aux₁ Orientation.rightAngleRotationAux₁
+-/
 
 @[simp]
 theorem inner_rightAngleRotationAux₁_left (x y : E) : ⟪o.rightAngleRotationAux₁ x, y⟫ = ω x y := by
@@ -209,6 +215,7 @@ theorem inner_rightAngleRotationAux₁_right (x y : E) : ⟪x, o.rightAngleRotat
   simp [o.area_form_swap y x]
 #align orientation.inner_right_angle_rotation_aux₁_right Orientation.inner_rightAngleRotationAux₁_right
 
+#print Orientation.rightAngleRotationAux₂ /-
 /-- Auxiliary construction for `orientation.right_angle_rotation`, rotation by 90 degrees in an
 oriented real inner product space of dimension 2. -/
 def rightAngleRotationAux₂ : E →ₗᵢ[ℝ] E :=
@@ -242,6 +249,7 @@ def rightAngleRotationAux₂ : E →ₗᵢ[ℝ] E :=
         rw [← o.inner_right_angle_rotation_aux₁_left x w]
         exact abs_real_inner_le_norm (o.right_angle_rotation_aux₁ x) w }
 #align orientation.right_angle_rotation_aux₂ Orientation.rightAngleRotationAux₂
+-/
 
 @[simp]
 theorem rightAngleRotationAux₁_rightAngleRotationAux₁ (x : E) :
@@ -255,6 +263,7 @@ theorem rightAngleRotationAux₁_rightAngleRotationAux₁ (x : E) :
     inner_neg_right]
 #align orientation.right_angle_rotation_aux₁_right_angle_rotation_aux₁ Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁
 
+#print Orientation.rightAngleRotation /-
 /-- An isometric automorphism of an oriented real inner product space of dimension 2 (usual notation
 `J`). This automorphism squares to -1.  We will define rotations in such a way that this
 automorphism is equal to rotation by 90 degrees. -/
@@ -262,6 +271,7 @@ irreducible_def rightAngleRotation : E ≃ₗᵢ[ℝ] E :=
   LinearIsometryEquiv.ofLinearIsometry o.rightAngleRotationAux₂ (-o.rightAngleRotationAux₁)
     (by ext <;> simp [right_angle_rotation_aux₂]) (by ext <;> simp [right_angle_rotation_aux₂])
 #align orientation.right_angle_rotation Orientation.rightAngleRotation
+-/
 
 -- mathport name: exprJ
 local notation "J" => o.rightAngleRotation
@@ -287,6 +297,7 @@ theorem rightAngleRotation_rightAngleRotation (x : E) : J (J x) = -x :=
   exact o.right_angle_rotation_aux₁_right_angle_rotation_aux₁ x
 #align orientation.right_angle_rotation_right_angle_rotation Orientation.rightAngleRotation_rightAngleRotation
 
+#print Orientation.rightAngleRotation_symm /-
 @[simp]
 theorem rightAngleRotation_symm :
     LinearIsometryEquiv.symm J = LinearIsometryEquiv.trans J (LinearIsometryEquiv.neg ℝ) :=
@@ -294,6 +305,7 @@ theorem rightAngleRotation_symm :
   rw [right_angle_rotation]
   exact LinearIsometryEquiv.toLinearIsometry_injective rfl
 #align orientation.right_angle_rotation_symm Orientation.rightAngleRotation_symm
+-/
 
 @[simp]
 theorem inner_rightAngleRotation_self (x : E) : ⟪J x, x⟫ = 0 := by simp
@@ -324,10 +336,12 @@ theorem areaForm_rightAngleRotation_right (x y : E) : ω x (J y) = ⟪x, y⟫ :=
 theorem areaForm_comp_rightAngleRotation (x y : E) : ω (J x) (J y) = ω x y := by simp
 #align orientation.area_form_comp_right_angle_rotation Orientation.areaForm_comp_rightAngleRotation
 
+#print Orientation.rightAngleRotation_trans_rightAngleRotation /-
 @[simp]
 theorem rightAngleRotation_trans_rightAngleRotation :
     LinearIsometryEquiv.trans J J = LinearIsometryEquiv.neg ℝ := by ext <;> simp
 #align orientation.right_angle_rotation_trans_right_angle_rotation Orientation.rightAngleRotation_trans_rightAngleRotation
+-/
 
 theorem rightAngleRotation_neg_orientation (x : E) :
     (-o).rightAngleRotation x = -o.rightAngleRotation x :=
@@ -370,18 +384,20 @@ theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation Orientation.linearIsometryEquiv_comp_rightAngleRotation
 
+#print Orientation.rightAngleRotation_map' /-
 theorem rightAngleRotation_map' {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).rightAngleRotation =
       (φ.symm.trans o.rightAngleRotation).trans φ :=
   LinearIsometryEquiv.ext <| o.rightAngleRotation_map φ
 #align orientation.right_angle_rotation_map' Orientation.rightAngleRotation_map'
+-/
 
 /-- `J` commutes with any positively-oriented isometric automorphism. -/
-theorem linearIsometryEquiv_comp_right_angle_rotation' (φ : E ≃ₗᵢ[ℝ] E)
+theorem linearIsometryEquiv_comp_rightAngleRotation' (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) : LinearIsometryEquiv.trans J φ = φ.trans J :=
   LinearIsometryEquiv.ext <| o.linearIsometryEquiv_comp_rightAngleRotation φ hφ
-#align orientation.linear_isometry_equiv_comp_right_angle_rotation' Orientation.linearIsometryEquiv_comp_right_angle_rotation'
+#align orientation.linear_isometry_equiv_comp_right_angle_rotation' Orientation.linearIsometryEquiv_comp_rightAngleRotation'
 
 /-- For a nonzero vector `x` in an oriented two-dimensional real inner product space `E`,
 `![x, J x]` forms an (orthogonal) basis for `E`. -/
@@ -406,7 +422,7 @@ theorem coe_basisRightAngleRotation (x : E) (hx : x ≠ 0) :
 
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫`. (See
 `orientation.inner_mul_inner_add_area_form_mul_area_form` for the "applied" form.)-/
-theorem inner_mul_inner_add_areaForm_mul_area_form' (a x : E) :
+theorem inner_mul_inner_add_areaForm_mul_areaForm' (a x : E) :
     ⟪a, x⟫ • innerₛₗ ℝ a + ω a x • ω a = ‖a‖ ^ 2 • innerₛₗ ℝ x :=
   by
   by_cases ha : a = 0
@@ -424,12 +440,12 @@ theorem inner_mul_inner_add_areaForm_mul_area_form' (a x : E) :
       o.area_form_apply_self, o.inner_right_angle_rotation_right]
     rw [o.area_form_swap]
     ring
-#align orientation.inner_mul_inner_add_area_form_mul_area_form' Orientation.inner_mul_inner_add_areaForm_mul_area_form'
+#align orientation.inner_mul_inner_add_area_form_mul_area_form' Orientation.inner_mul_inner_add_areaForm_mul_areaForm'
 
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫`. -/
 theorem inner_mul_inner_add_areaForm_mul_areaForm (a x y : E) :
     ⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫ :=
-  congr_arg (fun f : E →ₗ[ℝ] ℝ => f y) (o.inner_mul_inner_add_areaForm_mul_area_form' a x)
+  congr_arg (fun f : E →ₗ[ℝ] ℝ => f y) (o.inner_mul_inner_add_areaForm_mul_areaForm' a x)
 #align orientation.inner_mul_inner_add_area_form_mul_area_form Orientation.inner_mul_inner_add_areaForm_mul_areaForm
 
 theorem inner_sq_add_areaForm_sq (a b : E) : ⟪a, b⟫ ^ 2 + ω a b ^ 2 = ‖a‖ ^ 2 * ‖b‖ ^ 2 := by

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

@@ -363,7 +363,7 @@ theorem rightAngleRotation_map {F : Type _} [NormedAddCommGroup F] [InnerProduct
 theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) (x : E) : φ (J x) = J (φ x) :=
   by
-  convert(o.right_angle_rotation_map φ (φ x)).symm
+  convert (o.right_angle_rotation_map φ (φ x)).symm
   · simp
   · symm
     rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ 

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

@@ -180,7 +180,7 @@ theorem areaForm_comp_linearIsometryEquiv (φ : E ≃ₗᵢ[ℝ] E)
   by
   convert o.area_form_map φ (φ x) (φ y)
   · symm
-    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ
+    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ 
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
   · simp
   · simp
@@ -366,7 +366,7 @@ theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
   convert(o.right_angle_rotation_map φ (φ x)).symm
   · simp
   · symm
-    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ
+    rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ 
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation Orientation.linearIsometryEquiv_comp_rightAngleRotation
 

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

@@ -198,7 +198,7 @@ irreducible_def rightAngleRotationAux₁ : E →ₗ[ℝ] E :=
 theorem inner_rightAngleRotationAux₁_left (x y : E) : ⟪o.rightAngleRotationAux₁ x, y⟫ = ω x y := by
   simp only [right_angle_rotation_aux₁, LinearEquiv.trans_symm, LinearEquiv.coe_trans,
     LinearEquiv.coe_coe, InnerProductSpace.toDual_symm_apply, eq_self_iff_true,
-    LinearMap.coe_to_continuous_linear_map', LinearIsometryEquiv.coe_toLinearEquiv,
+    LinearMap.coe_toContinuousLinearMap', LinearIsometryEquiv.coe_toLinearEquiv,
     LinearMap.comp_apply, LinearEquiv.symm_symm, LinearIsometryEquiv.toLinearEquiv_symm]
 #align orientation.inner_right_angle_rotation_aux₁_left Orientation.inner_rightAngleRotationAux₁_left
 

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

@@ -73,7 +73,7 @@ local notation `J` := o.right_angle_rotation
 
 noncomputable section
 
-open RealInnerProductSpace ComplexConjugate
+open scoped RealInnerProductSpace ComplexConjugate
 
 open FiniteDimensional
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit cd8fafa2fac98e1a67097e8a91ad9901cfde48af
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.InnerProductSpace.Dual
 import Mathbin.Analysis.InnerProductSpace.Orientation
+import Mathbin.Data.Complex.Orientation
 import Mathbin.Tactic.LinearCombination
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -78,7 +78,8 @@ open FiniteDimensional
 
 attribute [local instance] fact_finite_dimensional_of_finrank_eq_succ
 
-variable {E : Type _} [InnerProductSpace ℝ E] [Fact (finrank ℝ E = 2)] (o : Orientation ℝ E (Fin 2))
+variable {E : Type _} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [Fact (finrank ℝ E = 2)]
+  (o : Orientation ℝ E (Fin 2))
 
 namespace Orientation
 
@@ -160,8 +161,8 @@ theorem abs_areaForm_of_orthogonal {x y : E} (h : ⟪x, y⟫ = 0) : |ω x y| = 
   · simpa
 #align orientation.abs_area_form_of_orthogonal Orientation.abs_areaForm_of_orthogonal
 
-theorem areaForm_map {F : Type _} [InnerProductSpace ℝ F] [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F)
-    (x y : F) :
+theorem areaForm_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+    [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).areaForm x y = o.areaForm (φ.symm x) (φ.symm y) :=
   by
   have : φ.symm ∘ ![x, y] = ![φ.symm x, φ.symm y] :=
@@ -342,8 +343,8 @@ theorem rightAngleRotation_trans_neg_orientation :
   LinearIsometryEquiv.ext <| o.rightAngleRotation_neg_orientation
 #align orientation.right_angle_rotation_trans_neg_orientation Orientation.rightAngleRotation_trans_neg_orientation
 
-theorem rightAngleRotation_map {F : Type _} [InnerProductSpace ℝ F] [Fact (finrank ℝ F = 2)]
-    (φ : E ≃ₗᵢ[ℝ] F) (x : F) :
+theorem rightAngleRotation_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+    [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).rightAngleRotation x =
       φ (o.rightAngleRotation (φ.symm x)) :=
   by
@@ -368,8 +369,8 @@ theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     rw [Fact.out (finrank ℝ E = 2), Fintype.card_fin]
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation Orientation.linearIsometryEquiv_comp_rightAngleRotation
 
-theorem rightAngleRotation_map' {F : Type _} [InnerProductSpace ℝ F] [Fact (finrank ℝ F = 2)]
-    (φ : E ≃ₗᵢ[ℝ] F) :
+theorem rightAngleRotation_map' {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+    [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).rightAngleRotation =
       (φ.symm.trans o.rightAngleRotation).trans φ :=
   LinearIsometryEquiv.ext <| o.rightAngleRotation_map φ
@@ -604,8 +605,8 @@ theorem kahler_ne_zero_iff (x y : E) : o.kahler x y ≠ 0 ↔ x ≠ 0 ∧ y ≠
   rintro (rfl | rfl) <;> simp
 #align orientation.kahler_ne_zero_iff Orientation.kahler_ne_zero_iff
 
-theorem kahler_map {F : Type _} [InnerProductSpace ℝ F] [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F)
-    (x y : F) :
+theorem kahler_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+    [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).kahler x y = o.kahler (φ.symm x) (φ.symm y) := by
   simp [kahler_apply_apply, area_form_map]
 #align orientation.kahler_map Orientation.kahler_map

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit e65771194f9e923a70dfb49b6ca7be6e400d8b6f
+! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -405,7 +405,7 @@ theorem coe_basisRightAngleRotation (x : E) (hx : x ≠ 0) :
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ⟪a, y⟫ + ω a x * ω a y = ‖a‖ ^ 2 * ⟪x, y⟫`. (See
 `orientation.inner_mul_inner_add_area_form_mul_area_form` for the "applied" form.)-/
 theorem inner_mul_inner_add_areaForm_mul_area_form' (a x : E) :
-    ⟪a, x⟫ • @innerₛₗ ℝ _ _ _ a + ω a x • ω a = ‖a‖ ^ 2 • @innerₛₗ ℝ _ _ _ x :=
+    ⟪a, x⟫ • innerₛₗ ℝ a + ω a x • ω a = ‖a‖ ^ 2 • innerₛₗ ℝ x :=
   by
   by_cases ha : a = 0
   · simp [ha]
@@ -436,8 +436,7 @@ theorem inner_sq_add_areaForm_sq (a b : E) : ⟪a, b⟫ ^ 2 + ω a b ^ 2 = ‖a
 
 /-- For vectors `a x y : E`, the identity `⟪a, x⟫ * ω a y - ω a x * ⟪a, y⟫ = ‖a‖ ^ 2 * ω x y`. (See
 `orientation.inner_mul_area_form_sub` for the "applied" form.) -/
-theorem inner_mul_areaForm_sub' (a x : E) :
-    ⟪a, x⟫ • ω a - ω a x • @innerₛₗ ℝ _ _ _ a = ‖a‖ ^ 2 • ω x :=
+theorem inner_mul_areaForm_sub' (a x : E) : ⟪a, x⟫ • ω a - ω a x • innerₛₗ ℝ a = ‖a‖ ^ 2 • ω x :=
   by
   by_cases ha : a = 0
   · simp [ha]
@@ -497,7 +496,7 @@ real part is the inner product and its imaginary part is `orientation.area_form`
 
 On `ℂ` with the standard orientation, `kahler w z = conj w * z`; see `complex.kahler`. -/
 def kahler : E →ₗ[ℝ] E →ₗ[ℝ] ℂ :=
-  LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealClm ∘ₗ @innerₛₗ ℝ E _ _ +
+  LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealClm ∘ₗ innerₛₗ ℝ +
     LinearMap.llcomp ℝ E ℝ ℂ ((LinearMap.lsmul ℝ ℂ).flip Complex.I) ∘ₗ ω
 #align orientation.kahler Orientation.kahler
 

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

@@ -361,7 +361,7 @@ theorem rightAngleRotation_map {F : Type _} [InnerProductSpace ℝ F] [Fact (fin
 theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < (φ.toLinearEquiv : E →ₗ[ℝ] E).det) (x : E) : φ (J x) = J (φ x) :=
   by
-  convert (o.right_angle_rotation_map φ (φ x)).symm
+  convert(o.right_angle_rotation_map φ (φ x)).symm
   · simp
   · symm
     rwa [← o.map_eq_iff_det_pos φ.to_linear_equiv] at hφ

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -522,7 +522,7 @@ theorem kahler_rightAngleRotation_left (x y : E) : o.kahler (J x) y = -Complex.I
   by
   simp only [o.area_form_right_angle_rotation_left, o.inner_right_angle_rotation_left,
     o.kahler_apply_apply, Complex.ofReal_neg, Complex.real_smul]
-  linear_combination ω x y * Complex.i_sq
+  linear_combination ω x y * Complex.I_sq
 #align orientation.kahler_right_angle_rotation_left Orientation.kahler_rightAngleRotation_left
 
 @[simp]
@@ -530,14 +530,14 @@ theorem kahler_rightAngleRotation_right (x y : E) : o.kahler x (J y) = Complex.I
   by
   simp only [o.area_form_right_angle_rotation_right, o.inner_right_angle_rotation_right,
     o.kahler_apply_apply, Complex.ofReal_neg, Complex.real_smul]
-  linear_combination -ω x y * Complex.i_sq
+  linear_combination -ω x y * Complex.I_sq
 #align orientation.kahler_right_angle_rotation_right Orientation.kahler_rightAngleRotation_right
 
 @[simp]
 theorem kahler_comp_rightAngleRotation (x y : E) : o.kahler (J x) (J y) = o.kahler x y :=
   by
   simp only [kahler_right_angle_rotation_left, kahler_right_angle_rotation_right]
-  linear_combination -o.kahler x y * Complex.i_sq
+  linear_combination -o.kahler x y * Complex.I_sq
 #align orientation.kahler_comp_right_angle_rotation Orientation.kahler_comp_rightAngleRotation
 
 @[simp]
@@ -549,11 +549,11 @@ theorem kahler_mul (a x y : E) : o.kahler x a * o.kahler a y = ‖a‖ ^ 2 * o.k
   by
   trans (↑(‖a‖ ^ 2) : ℂ) * o.kahler x y
   · ext
-    · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.i_im, Complex.i_re,
+    · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.I_im, Complex.I_re,
         Complex.mul_im, Complex.mul_re, Complex.ofReal_im, Complex.ofReal_re, Complex.real_smul]
       rw [real_inner_comm a x, o.area_form_swap x a]
       linear_combination o.inner_mul_inner_add_area_form_mul_area_form a x y
-    · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.i_im, Complex.i_re,
+    · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.I_im, Complex.I_re,
         Complex.mul_im, Complex.mul_re, Complex.ofReal_im, Complex.ofReal_re, Complex.real_smul]
       rw [real_inner_comm a x, o.area_form_swap x a]
       linear_combination o.inner_mul_area_form_sub a x y
@@ -564,7 +564,7 @@ theorem normSq_kahler (x y : E) : Complex.normSq (o.kahler x y) = ‖x‖ ^ 2 *
   simpa [kahler_apply_apply, Complex.normSq, sq] using o.inner_sq_add_area_form_sq x y
 #align orientation.norm_sq_kahler Orientation.normSq_kahler
 
-theorem abs_kahler (x y : E) : Complex.AbsTheory.Complex.abs (o.kahler x y) = ‖x‖ * ‖y‖ :=
+theorem abs_kahler (x y : E) : Complex.abs (o.kahler x y) = ‖x‖ * ‖y‖ :=
   by
   rw [← sq_eq_sq, Complex.sq_abs]
   · linear_combination o.norm_sq_kahler x y

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

@@ -475,9 +475,9 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
         Fin.succ_zero_eq_one', Fintype.univ_of_isEmpty, Finset.sum_empty, o.area_form_apply_self,
         map_smul, map_add, map_zero, inner_smul_left, inner_smul_right, inner_add_left,
         inner_add_right, inner_zero_right, LinearMap.add_apply, Matrix.cons_val_one,
-        Matrix.head_cons, Algebra.id.smul_eq_mul, o.area_form_right_angle_rotation_right, mul_zero,
-        add_zero, zero_add, neg_zero, o.inner_right_angle_rotation_right, o.area_form_apply_self,
-        real_inner_self_eq_norm_sq]
+        Matrix.head_cons, Algebra.id.smul_eq_mul, o.area_form_right_angle_rotation_right,
+        MulZeroClass.mul_zero, add_zero, zero_add, neg_zero, o.inner_right_angle_rotation_right,
+        o.area_form_apply_self, real_inner_self_eq_norm_sq]
       exact this
     rintro ⟨ha, hb⟩
     have hx' : 0 < ‖x‖ := by simpa using hx
@@ -487,7 +487,8 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
   · intro h
     obtain ⟨r, hr, rfl⟩ := h.exists_nonneg_left hx
     simp only [inner_smul_right, real_inner_self_eq_norm_sq, LinearMap.map_smulₛₗ,
-      area_form_apply_self, Algebra.id.smul_eq_mul, mul_zero, eq_self_iff_true, and_true_iff]
+      area_form_apply_self, Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, eq_self_iff_true,
+      and_true_iff]
     positivity
 #align orientation.nonneg_inner_and_area_form_eq_zero_iff_same_ray Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -497,10 +497,10 @@ real part is the inner product and its imaginary part is `orientation.area_form`
 On `ℂ` with the standard orientation, `kahler w z = conj w * z`; see `complex.kahler`. -/
 def kahler : E →ₗ[ℝ] E →ₗ[ℝ] ℂ :=
   LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealClm ∘ₗ @innerₛₗ ℝ E _ _ +
-    LinearMap.llcomp ℝ E ℝ ℂ ((LinearMap.lsmul ℝ ℂ).flip Complex.i) ∘ₗ ω
+    LinearMap.llcomp ℝ E ℝ ℂ ((LinearMap.lsmul ℝ ℂ).flip Complex.I) ∘ₗ ω
 #align orientation.kahler Orientation.kahler
 
-theorem kahler_apply_apply (x y : E) : o.kahler x y = ⟪x, y⟫ + ω x y • Complex.i :=
+theorem kahler_apply_apply (x y : E) : o.kahler x y = ⟪x, y⟫ + ω x y • Complex.I :=
   rfl
 #align orientation.kahler_apply_apply Orientation.kahler_apply_apply
 
@@ -517,18 +517,18 @@ theorem kahler_apply_self (x : E) : o.kahler x x = ‖x‖ ^ 2 := by
 #align orientation.kahler_apply_self Orientation.kahler_apply_self
 
 @[simp]
-theorem kahler_rightAngleRotation_left (x y : E) : o.kahler (J x) y = -Complex.i * o.kahler x y :=
+theorem kahler_rightAngleRotation_left (x y : E) : o.kahler (J x) y = -Complex.I * o.kahler x y :=
   by
   simp only [o.area_form_right_angle_rotation_left, o.inner_right_angle_rotation_left,
-    o.kahler_apply_apply, Complex.of_real_neg, Complex.real_smul]
+    o.kahler_apply_apply, Complex.ofReal_neg, Complex.real_smul]
   linear_combination ω x y * Complex.i_sq
 #align orientation.kahler_right_angle_rotation_left Orientation.kahler_rightAngleRotation_left
 
 @[simp]
-theorem kahler_rightAngleRotation_right (x y : E) : o.kahler x (J y) = Complex.i * o.kahler x y :=
+theorem kahler_rightAngleRotation_right (x y : E) : o.kahler x (J y) = Complex.I * o.kahler x y :=
   by
   simp only [o.area_form_right_angle_rotation_right, o.inner_right_angle_rotation_right,
-    o.kahler_apply_apply, Complex.of_real_neg, Complex.real_smul]
+    o.kahler_apply_apply, Complex.ofReal_neg, Complex.real_smul]
   linear_combination -ω x y * Complex.i_sq
 #align orientation.kahler_right_angle_rotation_right Orientation.kahler_rightAngleRotation_right
 
@@ -549,11 +549,11 @@ theorem kahler_mul (a x y : E) : o.kahler x a * o.kahler a y = ‖a‖ ^ 2 * o.k
   trans (↑(‖a‖ ^ 2) : ℂ) * o.kahler x y
   · ext
     · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.i_im, Complex.i_re,
-        Complex.mul_im, Complex.mul_re, Complex.of_real_im, Complex.of_real_re, Complex.real_smul]
+        Complex.mul_im, Complex.mul_re, Complex.ofReal_im, Complex.ofReal_re, Complex.real_smul]
       rw [real_inner_comm a x, o.area_form_swap x a]
       linear_combination o.inner_mul_inner_add_area_form_mul_area_form a x y
     · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.i_im, Complex.i_re,
-        Complex.mul_im, Complex.mul_re, Complex.of_real_im, Complex.of_real_re, Complex.real_smul]
+        Complex.mul_im, Complex.mul_re, Complex.ofReal_im, Complex.ofReal_re, Complex.real_smul]
       rw [real_inner_comm a x, o.area_form_swap x a]
       linear_combination o.inner_mul_area_form_sub a x y
   · norm_cast
@@ -563,7 +563,7 @@ theorem normSq_kahler (x y : E) : Complex.normSq (o.kahler x y) = ‖x‖ ^ 2 *
   simpa [kahler_apply_apply, Complex.normSq, sq] using o.inner_sq_add_area_form_sq x y
 #align orientation.norm_sq_kahler Orientation.normSq_kahler
 
-theorem abs_kahler (x y : E) : Complex.abs (o.kahler x y) = ‖x‖ * ‖y‖ :=
+theorem abs_kahler (x y : E) : Complex.AbsTheory.Complex.abs (o.kahler x y) = ‖x‖ * ‖y‖ :=
   by
   rw [← sq_eq_sq, Complex.sq_abs]
   · linear_combination o.norm_sq_kahler x y
@@ -635,7 +635,7 @@ protected theorem areaForm (w z : ℂ) : Complex.orientation.areaForm w z = (con
 #align complex.area_form Complex.areaForm
 
 @[simp]
-protected theorem rightAngleRotation (z : ℂ) : Complex.orientation.rightAngleRotation z = i * z :=
+protected theorem rightAngleRotation (z : ℂ) : Complex.orientation.rightAngleRotation z = I * z :=
   by
   apply ext_inner_right ℝ
   intro w
@@ -678,7 +678,7 @@ theorem areaForm_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
 evaluated in terms of a complex-number representation of the space. -/
 theorem rightAngleRotation_map_complex (f : E ≃ₗᵢ[ℝ] ℂ)
     (hf : Orientation.map (Fin 2) f.toLinearEquiv o = Complex.orientation) (x : E) :
-    f (J x) = i * f x :=
+    f (J x) = I * f x :=
   by
   rw [← Complex.rightAngleRotation, ← hf, o.right_angle_rotation_map]
   simp

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit e99e8c8934985b3bed8c6badbd333043a18c49c9
+! leanprover-community/mathlib commit e65771194f9e923a70dfb49b6ca7be6e400d8b6f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -470,16 +470,14 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
     let b : ℝ := (o.basis_right_angle_rotation x hx).repr y 1
     suffices 0 ≤ a * ‖x‖ ^ 2 ∧ b * ‖x‖ ^ 2 = 0 → SameRay ℝ x (a • x + b • J x)
       by
-      -- TODO trace the `dsimp` lemmas in this block to make a single `simp only`
       rw [← (o.basis_right_angle_rotation x hx).sum_repr y]
-      simp only [Fin.sum_univ_succ, coe_basis_right_angle_rotation]
-      dsimp
-      simp only [o.area_form_apply_self, map_smul, map_add, map_zero, inner_smul_left,
-        inner_smul_right, inner_add_left, inner_add_right, inner_zero_right, LinearMap.add_apply,
-        Matrix.cons_val_one]
-      dsimp
-      simp only [o.area_form_right_angle_rotation_right, mul_zero, add_zero, zero_add, neg_zero,
-        o.inner_right_angle_rotation_right, o.area_form_apply_self, real_inner_self_eq_norm_sq]
+      simp only [Fin.sum_univ_succ, coe_basis_right_angle_rotation, Matrix.cons_val_zero,
+        Fin.succ_zero_eq_one', Fintype.univ_of_isEmpty, Finset.sum_empty, o.area_form_apply_self,
+        map_smul, map_add, map_zero, inner_smul_left, inner_smul_right, inner_add_left,
+        inner_add_right, inner_zero_right, LinearMap.add_apply, Matrix.cons_val_one,
+        Matrix.head_cons, Algebra.id.smul_eq_mul, o.area_form_right_angle_rotation_right, mul_zero,
+        add_zero, zero_add, neg_zero, o.inner_right_angle_rotation_right, o.area_form_apply_self,
+        real_inner_self_eq_norm_sq]
       exact this
     rintro ⟨ha, hb⟩
     have hx' : 0 < ‖x‖ := by simpa using hx

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

@@ -485,7 +485,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
     have hx' : 0 < ‖x‖ := by simpa using hx
     have ha' : 0 ≤ a := nonneg_of_mul_nonneg_left ha (by positivity)
     have hb' : b = 0 := eq_zero_of_ne_zero_of_mul_right_eq_zero (pow_ne_zero 2 hx'.ne') hb
-    simpa [hb'] using sameRay_nonneg_smul_right x ha'
+    simpa [hb'] using SameRay.sameRay_nonneg_smul_right x ha'
   · intro h
     obtain ⟨r, hr, rfl⟩ := h.exists_nonneg_left hx
     simp only [inner_smul_right, real_inner_self_eq_norm_sq, LinearMap.map_smulₛₗ,

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

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

Why these changes?

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

@@ -80,7 +80,7 @@ lemma FiniteDimensional.of_fact_finrank_eq_two {K V : Type*} [DivisionRing K]
 
 attribute [local instance] FiniteDimensional.of_fact_finrank_eq_two
 
-@[deprecated] -- Since 2024/02/02
+@[deprecated] -- Since 2024-02-02
 alias FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two :=
   FiniteDimensional.of_fact_finrank_eq_two
 

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

@@ -606,7 +606,7 @@ attribute [local instance] Complex.finrank_real_complex_fact
 protected theorem areaForm (w z : ℂ) : Complex.orientation.areaForm w z = (conj w * z).im := by
   let o := Complex.orientation
   simp only [o.areaForm_to_volumeForm, o.volumeForm_robust Complex.orthonormalBasisOneI rfl,
-    (Basis.det_apply), Matrix.det_fin_two, (Basis.toMatrix_apply), toBasis_orthonormalBasisOneI,
+    Basis.det_apply, Matrix.det_fin_two, Basis.toMatrix_apply, toBasis_orthonormalBasisOneI,
     Matrix.cons_val_zero, coe_basisOneI_repr, Matrix.cons_val_one, Matrix.head_cons, mul_im,
     conj_re, conj_im]
   ring

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -485,7 +485,7 @@ theorem kahler_apply_apply (x y : E) : o.kahler x y = ⟪x, y⟫ + ω x y • Co
 #align orientation.kahler_apply_apply Orientation.kahler_apply_apply
 
 theorem kahler_swap (x y : E) : o.kahler x y = conj (o.kahler y x) := by
-  have : ∀ r : ℝ, Complex.ofReal' r = @IsROrC.ofReal ℂ _ r := fun r => rfl
+  have : ∀ r : ℝ, Complex.ofReal' r = @RCLike.ofReal ℂ _ r := fun r => rfl
   simp only [kahler_apply_apply]
   rw [real_inner_comm, areaForm_swap]
   simp [this]
@@ -524,7 +524,7 @@ theorem kahler_comp_rightAngleRotation' (x y : E) :
 
 @[simp]
 theorem kahler_neg_orientation (x y : E) : (-o).kahler x y = conj (o.kahler x y) := by
-  have : ∀ r : ℝ, Complex.ofReal' r = @IsROrC.ofReal ℂ _ r := fun r => rfl
+  have : ∀ r : ℝ, Complex.ofReal' r = @RCLike.ofReal ℂ _ r := fun r => rfl
   simp [kahler_apply_apply, this]
 #align orientation.kahler_neg_orientation Orientation.kahler_neg_orientation
 

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>

@@ -227,7 +227,7 @@ def rightAngleRotationAux₂ : E →ₗᵢ[ℝ] E :=
           have : Finset.card {x} = 1 := Finset.card_singleton x
           have : finrank ℝ K + finrank ℝ Kᗮ = finrank ℝ E := K.finrank_add_finrank_orthogonal
           have : finrank ℝ E = 2 := Fact.out
-          omega
+          linarith
         obtain ⟨w, hw₀⟩ : ∃ w : Kᗮ, w ≠ 0 := exists_ne 0
         have hw' : ⟪x, (w : E)⟫ = 0 := Submodule.mem_orthogonal_singleton_iff_inner_right.mp w.2
         have hw : (w : E) ≠ 0 := fun h => hw₀ (Submodule.coe_eq_zero.mp h)

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.

@@ -227,7 +227,7 @@ def rightAngleRotationAux₂ : E →ₗᵢ[ℝ] E :=
           have : Finset.card {x} = 1 := Finset.card_singleton x
           have : finrank ℝ K + finrank ℝ Kᗮ = finrank ℝ E := K.finrank_add_finrank_orthogonal
           have : finrank ℝ E = 2 := Fact.out
-          linarith
+          omega
         obtain ⟨w, hw₀⟩ : ∃ w : Kᗮ, w ≠ 0 := exists_ne 0
         have hw' : ⟪x, (w : E)⟫ = 0 := Submodule.mem_orthogonal_singleton_iff_inner_right.mp w.2
         have hw : (w : E) ≠ 0 := fun h => hw₀ (Submodule.coe_eq_zero.mp h)

That is, \bigwedge, not \Lambda

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>

@@ -93,10 +93,10 @@ namespace Orientation
 notation `ω`). When evaluated on two vectors, it gives the oriented area of the parallelogram they
 span. -/
 irreducible_def areaForm : E →ₗ[ℝ] E →ₗ[ℝ] ℝ := by
-  let z : E [Λ^Fin 0]→ₗ[ℝ] ℝ ≃ₗ[ℝ] ℝ :=
+  let z : E [⋀^Fin 0]→ₗ[ℝ] ℝ ≃ₗ[ℝ] ℝ :=
     AlternatingMap.constLinearEquivOfIsEmpty.symm
-  let y : E [Λ^Fin 1]→ₗ[ℝ] ℝ →ₗ[ℝ] E →ₗ[ℝ] ℝ :=
-    LinearMap.llcomp ℝ E (E [Λ^Fin 0]→ₗ[ℝ] ℝ) ℝ z ∘ₗ AlternatingMap.curryLeftLinearMap
+  let y : E [⋀^Fin 1]→ₗ[ℝ] ℝ →ₗ[ℝ] E →ₗ[ℝ] ℝ :=
+    LinearMap.llcomp ℝ E (E [⋀^Fin 0]→ₗ[ℝ] ℝ) ℝ z ∘ₗ AlternatingMap.curryLeftLinearMap
   exact y ∘ₗ AlternatingMap.curryLeftLinearMap (R' := ℝ) o.volumeForm
 #align orientation.area_form Orientation.areaForm
 

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to

• "simp can prove this"
• "simp can simplify this`"
• "was @[simp], now can be proved by simp"
• "was @[simp], but simp can prove it"
• "removed simp attribute as the equality can already be obtained by simp"
• "simp can already prove this"
• "simp already proves this"
• "simp can prove these"

@@ -283,7 +283,7 @@ theorem rightAngleRotation_symm :
   exact LinearIsometryEquiv.toLinearIsometry_injective rfl
 #align orientation.right_angle_rotation_symm Orientation.rightAngleRotation_symm
 
--- @[simp] -- Porting note: simp already proves this
+-- @[simp] -- Porting note (#10618): simp already proves this
 theorem inner_rightAngleRotation_self (x : E) : ⟪J x, x⟫ = 0 := by simp
 #align orientation.inner_right_angle_rotation_self Orientation.inner_rightAngleRotation_self
 
@@ -308,7 +308,7 @@ theorem areaForm_rightAngleRotation_right (x y : E) : ω x (J y) = ⟪x, y⟫ :=
   rw [← o.inner_rightAngleRotation_left, o.inner_comp_rightAngleRotation]
 #align orientation.area_form_right_angle_rotation_right Orientation.areaForm_rightAngleRotation_right
 
--- @[simp] -- Porting note: simp already proves this
+-- @[simp] -- Porting note (#10618): simp already proves this
 theorem areaForm_comp_rightAngleRotation (x y : E) : ω (J x) (J y) = ω x y := by simp
 #align orientation.area_form_comp_right_angle_rotation Orientation.areaForm_comp_rightAngleRotation
 

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -456,7 +456,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
         map_smul, map_add, real_inner_smul_right, inner_add_right, Matrix.cons_val_one,
         Matrix.head_cons, Algebra.id.smul_eq_mul, areaForm_rightAngleRotation_right,
         mul_zero, add_zero, zero_add, neg_zero, inner_rightAngleRotation_right,
-        real_inner_self_eq_norm_sq]
+        real_inner_self_eq_norm_sq, zero_smul, one_smul]
       exact this
     rintro ⟨ha, hb⟩
     have hx' : 0 < ‖x‖ := by simpa using hx

Rename lemmas to enable new-style dot notation or drop repeating FiniteDimensional.finiteDimensional_*. Restore old names as deprecated aliases.

@@ -74,11 +74,15 @@ open scoped RealInnerProductSpace ComplexConjugate
 
 open FiniteDimensional
 
-lemma FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two {K V : Type*} [DivisionRing K]
+lemma FiniteDimensional.of_fact_finrank_eq_two {K V : Type*} [DivisionRing K]
     [AddCommGroup V] [Module K V] [Fact (finrank K V = 2)] : FiniteDimensional K V :=
-  fact_finiteDimensional_of_finrank_eq_succ 1
+  .of_fact_finrank_eq_succ 1
 
-attribute [local instance] FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two
+attribute [local instance] FiniteDimensional.of_fact_finrank_eq_two
+
+@[deprecated] -- Since 2024/02/02
+alias FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two :=
+  FiniteDimensional.of_fact_finrank_eq_two
 
 variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [Fact (finrank ℝ E = 2)]
   (o : Orientation ℝ E (Fin 2))

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -472,7 +472,7 @@ real part is the inner product and its imaginary part is `Orientation.areaForm`.
 
 On `ℂ` with the standard orientation, `kahler w z = conj w * z`; see `Complex.kahler`. -/
 def kahler : E →ₗ[ℝ] E →ₗ[ℝ] ℂ :=
-  LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealClm ∘ₗ innerₛₗ ℝ +
+  LinearMap.llcomp ℝ E ℝ ℂ Complex.ofRealCLM ∘ₗ innerₛₗ ℝ +
     LinearMap.llcomp ℝ E ℝ ℂ ((LinearMap.lsmul ℝ ℂ).flip Complex.I) ∘ₗ ω
 #align orientation.kahler Orientation.kahler
 

From LeanAPAP

@@ -458,7 +458,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
     have hx' : 0 < ‖x‖ := by simpa using hx
     have ha' : 0 ≤ a := nonneg_of_mul_nonneg_left ha (by positivity)
     have hb' : b = 0 := eq_zero_of_ne_zero_of_mul_right_eq_zero (pow_ne_zero 2 hx'.ne') hb
-    simpa [hb'] using SameRay.sameRay_nonneg_smul_right x ha'
+    exact (SameRay.sameRay_nonneg_smul_right x ha').add_right $ by simp [hb']
   · intro h
     obtain ⟨r, hr, rfl⟩ := h.exists_nonneg_left hx
     simp only [inner_smul_right, real_inner_self_eq_norm_sq, LinearMap.map_smulₛₗ,

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

@@ -448,7 +448,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
     suffices ↑0 ≤ a * ‖x‖ ^ 2 ∧ b * ‖x‖ ^ 2 = 0 → SameRay ℝ x (a • x + b • J x) by
       rw [← (o.basisRightAngleRotation x hx).sum_repr y]
       simp only [Fin.sum_univ_succ, coe_basisRightAngleRotation, Matrix.cons_val_zero,
-        Fin.succ_zero_eq_one', Fintype.univ_of_isEmpty, Finset.sum_empty, areaForm_apply_self,
+        Fin.succ_zero_eq_one', Finset.univ_eq_empty, Finset.sum_empty, areaForm_apply_self,
         map_smul, map_add, real_inner_smul_right, inner_add_right, Matrix.cons_val_one,
         Matrix.head_cons, Algebra.id.smul_eq_mul, areaForm_rightAngleRotation_right,
         mul_zero, add_zero, zero_add, neg_zero, inner_rightAngleRotation_right,

In accordance with this Zulip thread, this remove Complex.ext from the global ext attribute list and only enables it locally in certain files.

@@ -526,7 +526,7 @@ theorem kahler_neg_orientation (x y : E) : (-o).kahler x y = conj (o.kahler x y)
 
 theorem kahler_mul (a x y : E) : o.kahler x a * o.kahler a y = ‖a‖ ^ 2 * o.kahler x y := by
   trans ((‖a‖ ^ 2 :) : ℂ) * o.kahler x y
-  · ext
+  · apply Complex.ext
     · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.I_im, Complex.I_re,
         Complex.mul_im, Complex.mul_re, Complex.ofReal_im, Complex.ofReal_re, Complex.real_smul]
       rw [real_inner_comm a x, o.areaForm_swap x a]
@@ -622,7 +622,7 @@ protected theorem rightAngleRotation (z : ℂ) :
 @[simp]
 protected theorem kahler (w z : ℂ) : Complex.orientation.kahler w z = conj w * z := by
   rw [Orientation.kahler_apply_apply]
-  ext1 <;> simp
+  apply Complex.ext <;> simp
 #align complex.kahler Complex.kahler
 
 end Complex

Use M [Λ^ι]→ₗ[R] N for AlternatingMap R M N ι, similarly to the existing notation M [Λ^ι]→L[R] N for ContinuousAlternatingMap R M N ι.

@@ -89,10 +89,10 @@ namespace Orientation
 notation `ω`). When evaluated on two vectors, it gives the oriented area of the parallelogram they
 span. -/
 irreducible_def areaForm : E →ₗ[ℝ] E →ₗ[ℝ] ℝ := by
-  let z : AlternatingMap ℝ E ℝ (Fin 0) ≃ₗ[ℝ] ℝ :=
+  let z : E [Λ^Fin 0]→ₗ[ℝ] ℝ ≃ₗ[ℝ] ℝ :=
     AlternatingMap.constLinearEquivOfIsEmpty.symm
-  let y : AlternatingMap ℝ E ℝ (Fin 1) →ₗ[ℝ] E →ₗ[ℝ] ℝ :=
-    LinearMap.llcomp ℝ E (AlternatingMap ℝ E ℝ (Fin 0)) ℝ z ∘ₗ AlternatingMap.curryLeftLinearMap
+  let y : E [Λ^Fin 1]→ₗ[ℝ] ℝ →ₗ[ℝ] E →ₗ[ℝ] ℝ :=
+    LinearMap.llcomp ℝ E (E [Λ^Fin 0]→ₗ[ℝ] ℝ) ℝ z ∘ₗ AlternatingMap.curryLeftLinearMap
   exact y ∘ₗ AlternatingMap.curryLeftLinearMap (R' := ℝ) o.volumeForm
 #align orientation.area_form Orientation.areaForm
 

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>

@@ -74,8 +74,6 @@ open scoped RealInnerProductSpace ComplexConjugate
 
 open FiniteDimensional
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 lemma FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two {K V : Type*} [DivisionRing K]
     [AddCommGroup V] [Module K V] [Fact (finrank K V = 2)] : FiniteDimensional K V :=
   fact_finiteDimensional_of_finrank_eq_succ 1
@@ -527,7 +525,7 @@ theorem kahler_neg_orientation (x y : E) : (-o).kahler x y = conj (o.kahler x y)
 #align orientation.kahler_neg_orientation Orientation.kahler_neg_orientation
 
 theorem kahler_mul (a x y : E) : o.kahler x a * o.kahler a y = ‖a‖ ^ 2 * o.kahler x y := by
-  trans (↑(‖a‖ ^ 2) : ℂ) * o.kahler x y
+  trans ((‖a‖ ^ 2 :) : ℂ) * o.kahler x y
   · ext
     · simp only [o.kahler_apply_apply, Complex.add_im, Complex.add_re, Complex.I_im, Complex.I_re,
         Complex.mul_im, Complex.mul_re, Complex.ofReal_im, Complex.ofReal_re, Complex.real_smul]

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -346,7 +346,7 @@ theorem rightAngleRotation_map {F : Type*} [NormedAddCommGroup F] [InnerProductS
 /-- `J` commutes with any positively-oriented isometric automorphism. -/
 theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     (hφ : 0 < LinearMap.det (φ.toLinearEquiv : E →ₗ[ℝ] E)) (x : E) : φ (J x) = J (φ x) := by
-  convert(o.rightAngleRotation_map φ (φ x)).symm
+  convert (o.rightAngleRotation_map φ (φ x)).symm
   · simp
   · symm
     rwa [← o.map_eq_iff_det_pos φ.toLinearEquiv] at hφ

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).

@@ -464,7 +464,7 @@ theorem nonneg_inner_and_areaForm_eq_zero_iff_sameRay (x y : E) :
   · intro h
     obtain ⟨r, hr, rfl⟩ := h.exists_nonneg_left hx
     simp only [inner_smul_right, real_inner_self_eq_norm_sq, LinearMap.map_smulₛₗ,
-      areaForm_apply_self, Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, eq_self_iff_true,
+      areaForm_apply_self, Algebra.id.smul_eq_mul, mul_zero, eq_self_iff_true,
       and_true_iff]
     positivity
 #align orientation.nonneg_inner_and_area_form_eq_zero_iff_same_ray Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay

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

This has nice performance benefits.

@@ -76,13 +76,13 @@ open FiniteDimensional
 
 local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
-lemma FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two {K V : Type _} [DivisionRing K]
+lemma FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two {K V : Type*} [DivisionRing K]
     [AddCommGroup V] [Module K V] [Fact (finrank K V = 2)] : FiniteDimensional K V :=
   fact_finiteDimensional_of_finrank_eq_succ 1
 
 attribute [local instance] FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two
 
-variable {E : Type _} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [Fact (finrank ℝ E = 2)]
+variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [Fact (finrank ℝ E = 2)]
   (o : Orientation ℝ E (Fin 2))
 
 namespace Orientation
@@ -156,7 +156,7 @@ theorem abs_areaForm_of_orthogonal {x y : E} (h : ⟪x, y⟫ = 0) : |ω x y| = 
   · simp_all
 #align orientation.abs_area_form_of_orthogonal Orientation.abs_areaForm_of_orthogonal
 
-theorem areaForm_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+theorem areaForm_map {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [hF : Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).areaForm x y =
     o.areaForm (φ.symm x) (φ.symm y) := by
@@ -329,7 +329,7 @@ theorem rightAngleRotation_trans_neg_orientation :
   LinearIsometryEquiv.ext <| o.rightAngleRotation_neg_orientation
 #align orientation.right_angle_rotation_trans_neg_orientation Orientation.rightAngleRotation_trans_neg_orientation
 
-theorem rightAngleRotation_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+theorem rightAngleRotation_map {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [hF : Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).rightAngleRotation x =
       φ (o.rightAngleRotation (φ.symm x)) := by
@@ -353,7 +353,7 @@ theorem linearIsometryEquiv_comp_rightAngleRotation (φ : E ≃ₗᵢ[ℝ] E)
     rw [@Fact.out (finrank ℝ E = 2), Fintype.card_fin]
 #align orientation.linear_isometry_equiv_comp_right_angle_rotation Orientation.linearIsometryEquiv_comp_rightAngleRotation
 
-theorem rightAngleRotation_map' {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+theorem rightAngleRotation_map' {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).rightAngleRotation =
       (φ.symm.trans o.rightAngleRotation).trans φ :=
@@ -580,7 +580,7 @@ theorem kahler_ne_zero_iff (x y : E) : o.kahler x y ≠ 0 ↔ x ≠ 0 ∧ y ≠
   rintro (rfl | rfl) <;> simp
 #align orientation.kahler_ne_zero_iff Orientation.kahler_ne_zero_iff
 
-theorem kahler_map {F : Type _} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
+theorem kahler_map {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
     [hF : Fact (finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F) :
     (Orientation.map (Fin 2) φ.toLinearEquiv o).kahler x y = o.kahler (φ.symm x) (φ.symm y) := by
   simp [kahler_apply_apply, areaForm_map]

@@ -74,9 +74,7 @@ open scoped RealInnerProductSpace ComplexConjugate
 
 open FiniteDimensional
 
--- Porting note: See issue #2220
--- While not strictly necessary, this keeps the file closer to mathlib3 in a few places.
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y)
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 lemma FiniteDimensional.finiteDimensional_of_fact_finrank_eq_two {K V : Type _} [DivisionRing K]
     [AddCommGroup V] [Module K V] [Fact (finrank K V = 2)] : FiniteDimensional K V :=

• 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) 2022 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.two_dim
-! leanprover-community/mathlib commit cd8fafa2fac98e1a67097e8a91ad9901cfde48af
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.InnerProductSpace.Dual
 import Mathlib.Analysis.InnerProductSpace.Orientation
 import Mathlib.Data.Complex.Orientation
 import Mathlib.Tactic.LinearCombination
 
+#align_import analysis.inner_product_space.two_dim from "leanprover-community/mathlib"@"cd8fafa2fac98e1a67097e8a91ad9901cfde48af"
+
 /-!
 # Oriented two-dimensional real inner product spaces
 

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -126,7 +126,7 @@ theorem areaForm_swap (x y : E) : ω x y = -ω y x := by
 
 @[simp]
 theorem areaForm_neg_orientation : (-o).areaForm = -o.areaForm := by
-  ext (x y)
+  ext x y
   simp [areaForm_to_volumeForm]
 #align orientation.area_form_neg_orientation Orientation.areaForm_neg_orientation
 

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