analysis.quaternion ⟷ Mathlib.Analysis.Quaternion

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

@@ -217,7 +217,7 @@ theorem norm_piLp_equiv_symm_equivTuple (x : ℍ) :
   by
   rw [norm_eq_sqrt_real_inner, norm_eq_sqrt_real_inner, inner_self, norm_sq_def', PiLp.inner_apply,
     Fin.sum_univ_four]
-  simp_rw [IsROrC.inner_apply, starRingEnd_apply, star_trivial, ← sq]
+  simp_rw [RCLike.inner_apply, starRingEnd_apply, star_trivial, ← sq]
   rfl
 #align quaternion.norm_pi_Lp_equiv_symm_equiv_tuple Quaternion.norm_piLp_equiv_symm_equivTuple
 -/

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 -/
-import Mathbin.Algebra.Quaternion
-import Mathbin.Analysis.InnerProductSpace.Basic
-import Mathbin.Analysis.InnerProductSpace.PiL2
-import Mathbin.Topology.Algebra.Algebra
+import Algebra.Quaternion
+import Analysis.InnerProductSpace.Basic
+import Analysis.InnerProductSpace.PiL2
+import Topology.Algebra.Algebra
 
 #align_import analysis.quaternion from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
 

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

@@ -119,7 +119,7 @@ instance : NormedAlgebra ℝ ℍ where
   toAlgebra := (Quaternion.algebra : Algebra ℝ ℍ)
 
 instance : CstarRing ℍ
-    where norm_star_mul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) (norm_star x)
+    where norm_star_hMul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) (norm_star x)
 
 instance : Coe ℂ ℍ :=
   ⟨fun z => ⟨z.re, z.im, 0, 0⟩⟩

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Quaternion
 import Mathbin.Analysis.InnerProductSpace.Basic
 import Mathbin.Analysis.InnerProductSpace.PiL2
 import Mathbin.Topology.Algebra.Algebra
 
+#align_import analysis.quaternion from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
+
 /-!
 # Quaternions as a normed algebra
 

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

@@ -39,7 +39,6 @@ quaternion, normed ring, normed space, normed algebra
 -/
 
 
--- mathport name: quaternion.real
 scoped[Quaternion] notation "ℍ" => Quaternion ℝ
 
 open scoped RealInnerProductSpace
@@ -49,13 +48,17 @@ namespace Quaternion
 instance : Inner ℝ ℍ :=
   ⟨fun a b => (a * star b).re⟩
 
+#print Quaternion.inner_self /-
 theorem inner_self (a : ℍ) : ⟪a, a⟫ = normSq a :=
   rfl
 #align quaternion.inner_self Quaternion.inner_self
+-/
 
+#print Quaternion.inner_def /-
 theorem inner_def (a b : ℍ) : ⟪a, b⟫ = (a * star b).re :=
   rfl
 #align quaternion.inner_def Quaternion.inner_def
+-/
 
 noncomputable instance : NormedAddCommGroup ℍ :=
   @InnerProductSpace.Core.toNormedAddCommGroup ℝ ℍ _ _ _
@@ -69,32 +72,42 @@ noncomputable instance : NormedAddCommGroup ℍ :=
 noncomputable instance : InnerProductSpace ℝ ℍ :=
   InnerProductSpace.ofCore _
 
+#print Quaternion.normSq_eq_norm_mul_self /-
 theorem normSq_eq_norm_mul_self (a : ℍ) : normSq a = ‖a‖ * ‖a‖ := by
   rw [← inner_self, real_inner_self_eq_norm_mul_norm]
 #align quaternion.norm_sq_eq_norm_sq Quaternion.normSq_eq_norm_mul_self
+-/
 
 instance : NormOneClass ℍ :=
   ⟨by rw [norm_eq_sqrt_real_inner, inner_self, norm_sq.map_one, Real.sqrt_one]⟩
 
+#print Quaternion.norm_coe /-
 @[simp, norm_cast]
 theorem norm_coe (a : ℝ) : ‖(a : ℍ)‖ = ‖a‖ := by
   rw [norm_eq_sqrt_real_inner, inner_self, norm_sq_coe, Real.sqrt_sq_eq_abs, Real.norm_eq_abs]
 #align quaternion.norm_coe Quaternion.norm_coe
+-/
 
+#print Quaternion.nnnorm_coe /-
 @[simp, norm_cast]
 theorem nnnorm_coe (a : ℝ) : ‖(a : ℍ)‖₊ = ‖a‖₊ :=
   Subtype.ext <| norm_coe a
 #align quaternion.nnnorm_coe Quaternion.nnnorm_coe
+-/
 
+#print Quaternion.norm_star /-
 @[simp]
 theorem norm_star (a : ℍ) : ‖star a‖ = ‖a‖ := by
   simp_rw [norm_eq_sqrt_real_inner, inner_self, norm_sq_star]
 #align quaternion.norm_star Quaternion.norm_star
+-/
 
+#print Quaternion.nnnorm_star /-
 @[simp]
 theorem nnnorm_star (a : ℍ) : ‖star a‖₊ = ‖a‖₊ :=
   Subtype.ext <| norm_star a
 #align quaternion.nnnorm_star Quaternion.nnnorm_star
+-/
 
 noncomputable instance : NormedDivisionRing ℍ
     where
@@ -128,43 +141,60 @@ theorem coeComplex_imI (z : ℂ) : (z : ℍ).imI = z.im :=
 #align quaternion.coe_complex_im_i Quaternion.coeComplex_imI
 -/
 
+#print Quaternion.coeComplex_imJ /-
 @[simp, norm_cast]
 theorem coeComplex_imJ (z : ℂ) : (z : ℍ).imJ = 0 :=
   rfl
 #align quaternion.coe_complex_im_j Quaternion.coeComplex_imJ
+-/
 
+#print Quaternion.coeComplex_imK /-
 @[simp, norm_cast]
 theorem coeComplex_imK (z : ℂ) : (z : ℍ).imK = 0 :=
   rfl
 #align quaternion.coe_complex_im_k Quaternion.coeComplex_imK
+-/
 
+#print Quaternion.coeComplex_add /-
 @[simp, norm_cast]
 theorem coeComplex_add (z w : ℂ) : ↑(z + w) = (z + w : ℍ) := by ext <;> simp
 #align quaternion.coe_complex_add Quaternion.coeComplex_add
+-/
 
+#print Quaternion.coeComplex_mul /-
 @[simp, norm_cast]
 theorem coeComplex_mul (z w : ℂ) : ↑(z * w) = (z * w : ℍ) := by ext <;> simp
 #align quaternion.coe_complex_mul Quaternion.coeComplex_mul
+-/
 
+#print Quaternion.coeComplex_zero /-
 @[simp, norm_cast]
 theorem coeComplex_zero : ((0 : ℂ) : ℍ) = 0 :=
   rfl
 #align quaternion.coe_complex_zero Quaternion.coeComplex_zero
+-/
 
+#print Quaternion.coeComplex_one /-
 @[simp, norm_cast]
 theorem coeComplex_one : ((1 : ℂ) : ℍ) = 1 :=
   rfl
 #align quaternion.coe_complex_one Quaternion.coeComplex_one
+-/
 
+#print Quaternion.coe_real_complex_mul /-
 @[simp, norm_cast]
 theorem coe_real_complex_mul (r : ℝ) (z : ℂ) : (r • z : ℍ) = ↑r * ↑z := by ext <;> simp
 #align quaternion.coe_real_complex_mul Quaternion.coe_real_complex_mul
+-/
 
+#print Quaternion.coeComplex_coe /-
 @[simp, norm_cast]
 theorem coeComplex_coe (r : ℝ) : ((r : ℂ) : ℍ) = r :=
   rfl
 #align quaternion.coe_complex_coe Quaternion.coeComplex_coe
+-/
 
+#print Quaternion.ofComplex /-
 /-- Coercion `ℂ →ₐ[ℝ] ℍ` as an algebra homomorphism. -/
 def ofComplex : ℂ →ₐ[ℝ] ℍ where
   toFun := coe
@@ -174,12 +204,16 @@ def ofComplex : ℂ →ₐ[ℝ] ℍ where
   map_mul' := coeComplex_mul
   commutes' x := rfl
 #align quaternion.of_complex Quaternion.ofComplex
+-/
 
+#print Quaternion.coe_ofComplex /-
 @[simp]
 theorem coe_ofComplex : ⇑ofComplex = coe :=
   rfl
 #align quaternion.coe_of_complex Quaternion.coe_ofComplex
+-/
 
+#print Quaternion.norm_piLp_equiv_symm_equivTuple /-
 /-- The norm of the components as a euclidean vector equals the norm of the quaternion. -/
 theorem norm_piLp_equiv_symm_equivTuple (x : ℍ) :
     ‖(PiLp.equiv 2 fun _ : Fin 4 => _).symm (equivTuple ℝ x)‖ = ‖x‖ :=
@@ -189,7 +223,9 @@ theorem norm_piLp_equiv_symm_equivTuple (x : ℍ) :
   simp_rw [IsROrC.inner_apply, starRingEnd_apply, star_trivial, ← sq]
   rfl
 #align quaternion.norm_pi_Lp_equiv_symm_equiv_tuple Quaternion.norm_piLp_equiv_symm_equivTuple
+-/
 
+#print Quaternion.linearIsometryEquivTuple /-
 /-- `quaternion_algebra.linear_equiv_tuple` as a `linear_isometry_equiv`. -/
 @[simps apply symm_apply]
 noncomputable def linearIsometryEquivTuple : ℍ ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin 4) :=
@@ -201,42 +237,57 @@ noncomputable def linearIsometryEquivTuple : ℍ ≃ₗᵢ[ℝ] EuclideanSpace 
     invFun := fun a => ⟨a 0, a 1, a 2, a 3⟩
     norm_map' := norm_piLp_equiv_symm_equivTuple }
 #align quaternion.linear_isometry_equiv_tuple Quaternion.linearIsometryEquivTuple
+-/
 
+#print Quaternion.continuous_coe /-
 @[continuity]
 theorem continuous_coe : Continuous (coe : ℝ → ℍ) :=
   continuous_algebraMap ℝ ℍ
 #align quaternion.continuous_coe Quaternion.continuous_coe
+-/
 
+#print Quaternion.continuous_normSq /-
 @[continuity]
 theorem continuous_normSq : Continuous (normSq : ℍ → ℝ) := by
   simpa [← norm_sq_eq_norm_sq] using
     (continuous_norm.mul continuous_norm : Continuous fun q : ℍ => ‖q‖ * ‖q‖)
 #align quaternion.continuous_norm_sq Quaternion.continuous_normSq
+-/
 
+#print Quaternion.continuous_re /-
 @[continuity]
 theorem continuous_re : Continuous fun q : ℍ => q.re :=
   (continuous_apply 0).comp linearIsometryEquivTuple.Continuous
 #align quaternion.continuous_re Quaternion.continuous_re
+-/
 
+#print Quaternion.continuous_imI /-
 @[continuity]
 theorem continuous_imI : Continuous fun q : ℍ => q.imI :=
   (continuous_apply 1).comp linearIsometryEquivTuple.Continuous
 #align quaternion.continuous_im_i Quaternion.continuous_imI
+-/
 
+#print Quaternion.continuous_imJ /-
 @[continuity]
 theorem continuous_imJ : Continuous fun q : ℍ => q.imJ :=
   (continuous_apply 2).comp linearIsometryEquivTuple.Continuous
 #align quaternion.continuous_im_j Quaternion.continuous_imJ
+-/
 
+#print Quaternion.continuous_imK /-
 @[continuity]
 theorem continuous_imK : Continuous fun q : ℍ => q.imK :=
   (continuous_apply 3).comp linearIsometryEquivTuple.Continuous
 #align quaternion.continuous_im_k Quaternion.continuous_imK
+-/
 
+#print Quaternion.continuous_im /-
 @[continuity]
 theorem continuous_im : Continuous fun q : ℍ => q.im := by
   simpa only [← sub_self_re] using continuous_id.sub (continuous_coe.comp continuous_re)
 #align quaternion.continuous_im Quaternion.continuous_im
+-/
 
 instance : CompleteSpace ℍ :=
   haveI : UniformEmbedding linear_isometry_equiv_tuple.to_linear_equiv.to_equiv.symm :=
@@ -247,19 +298,24 @@ section infinite_sum
 
 variable {α : Type _}
 
+#print Quaternion.hasSum_coe /-
 @[simp, norm_cast]
 theorem hasSum_coe {f : α → ℝ} {r : ℝ} : HasSum (fun a => (f a : ℍ)) (↑r : ℍ) ↔ HasSum f r :=
   ⟨fun h => by simpa only using h.map (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reₗ _ _) continuous_re,
     fun h => by simpa only using h.map (algebraMap ℝ ℍ) (continuous_algebraMap _ _)⟩
 #align quaternion.has_sum_coe Quaternion.hasSum_coe
+-/
 
+#print Quaternion.summable_coe /-
 @[simp, norm_cast]
 theorem summable_coe {f : α → ℝ} : (Summable fun a => (f a : ℍ)) ↔ Summable f := by
   simpa only using
     Summable.map_iff_of_leftInverse (algebraMap ℝ ℍ) (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reₗ _ _)
       (continuous_algebraMap _ _) continuous_re coe_re
 #align quaternion.summable_coe Quaternion.summable_coe
+-/
 
+#print Quaternion.tsum_coe /-
 @[norm_cast]
 theorem tsum_coe (f : α → ℝ) : ∑' a, (f a : ℍ) = ↑(∑' a, f a) :=
   by
@@ -267,6 +323,7 @@ theorem tsum_coe (f : α → ℝ) : ∑' a, (f a : ℍ) = ↑(∑' a, f a) :=
   · exact (has_sum_coe.mpr hf.has_sum).tsum_eq
   · simp [tsum_eq_zero_of_not_summable hf, tsum_eq_zero_of_not_summable (summable_coe.not.mpr hf)]
 #align quaternion.tsum_coe Quaternion.tsum_coe
+-/
 
 end infinite_sum
 

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

@@ -261,7 +261,7 @@ theorem summable_coe {f : α → ℝ} : (Summable fun a => (f a : ℍ)) ↔ Summ
 #align quaternion.summable_coe Quaternion.summable_coe
 
 @[norm_cast]
-theorem tsum_coe (f : α → ℝ) : (∑' a, (f a : ℍ)) = ↑(∑' a, f a) :=
+theorem tsum_coe (f : α → ℝ) : ∑' a, (f a : ℍ) = ↑(∑' a, f a) :=
   by
   by_cases hf : Summable f
   · exact (has_sum_coe.mpr hf.has_sum).tsum_eq

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit 07992a1d1f7a4176c6d3f160209608be4e198566
+! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.Algebra
 /-!
 # Quaternions as a normed algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the following structures on the space `ℍ := ℍ[ℝ]` of quaternions:
 
 * inner product space;

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

@@ -66,9 +66,9 @@ noncomputable instance : NormedAddCommGroup ℍ :=
 noncomputable instance : InnerProductSpace ℝ ℍ :=
   InnerProductSpace.ofCore _
 
-theorem normSq_eq_normSq (a : ℍ) : normSq a = ‖a‖ * ‖a‖ := by
+theorem normSq_eq_norm_mul_self (a : ℍ) : normSq a = ‖a‖ * ‖a‖ := by
   rw [← inner_self, real_inner_self_eq_norm_mul_norm]
-#align quaternion.norm_sq_eq_norm_sq Quaternion.normSq_eq_normSq
+#align quaternion.norm_sq_eq_norm_sq Quaternion.normSq_eq_norm_mul_self
 
 instance : NormOneClass ℍ :=
   ⟨by rw [norm_eq_sqrt_real_inner, inner_self, norm_sq.map_one, Real.sqrt_one]⟩
@@ -111,60 +111,64 @@ instance : CstarRing ℍ
 instance : Coe ℂ ℍ :=
   ⟨fun z => ⟨z.re, z.im, 0, 0⟩⟩
 
+#print Quaternion.coeComplex_re /-
 @[simp, norm_cast]
-theorem coe_complex_re (z : ℂ) : (z : ℍ).re = z.re :=
+theorem coeComplex_re (z : ℂ) : (z : ℍ).re = z.re :=
   rfl
-#align quaternion.coe_complex_re Quaternion.coe_complex_re
+#align quaternion.coe_complex_re Quaternion.coeComplex_re
+-/
 
+#print Quaternion.coeComplex_imI /-
 @[simp, norm_cast]
-theorem coe_complex_imI (z : ℂ) : (z : ℍ).imI = z.im :=
+theorem coeComplex_imI (z : ℂ) : (z : ℍ).imI = z.im :=
   rfl
-#align quaternion.coe_complex_im_i Quaternion.coe_complex_imI
+#align quaternion.coe_complex_im_i Quaternion.coeComplex_imI
+-/
 
 @[simp, norm_cast]
-theorem coe_complex_imJ (z : ℂ) : (z : ℍ).imJ = 0 :=
+theorem coeComplex_imJ (z : ℂ) : (z : ℍ).imJ = 0 :=
   rfl
-#align quaternion.coe_complex_im_j Quaternion.coe_complex_imJ
+#align quaternion.coe_complex_im_j Quaternion.coeComplex_imJ
 
 @[simp, norm_cast]
-theorem coe_complex_imK (z : ℂ) : (z : ℍ).imK = 0 :=
+theorem coeComplex_imK (z : ℂ) : (z : ℍ).imK = 0 :=
   rfl
-#align quaternion.coe_complex_im_k Quaternion.coe_complex_imK
+#align quaternion.coe_complex_im_k Quaternion.coeComplex_imK
 
 @[simp, norm_cast]
-theorem coe_complex_add (z w : ℂ) : ↑(z + w) = (z + w : ℍ) := by ext <;> simp
-#align quaternion.coe_complex_add Quaternion.coe_complex_add
+theorem coeComplex_add (z w : ℂ) : ↑(z + w) = (z + w : ℍ) := by ext <;> simp
+#align quaternion.coe_complex_add Quaternion.coeComplex_add
 
 @[simp, norm_cast]
-theorem coe_complex_mul (z w : ℂ) : ↑(z * w) = (z * w : ℍ) := by ext <;> simp
-#align quaternion.coe_complex_mul Quaternion.coe_complex_mul
+theorem coeComplex_mul (z w : ℂ) : ↑(z * w) = (z * w : ℍ) := by ext <;> simp
+#align quaternion.coe_complex_mul Quaternion.coeComplex_mul
 
 @[simp, norm_cast]
-theorem coe_complex_zero : ((0 : ℂ) : ℍ) = 0 :=
+theorem coeComplex_zero : ((0 : ℂ) : ℍ) = 0 :=
   rfl
-#align quaternion.coe_complex_zero Quaternion.coe_complex_zero
+#align quaternion.coe_complex_zero Quaternion.coeComplex_zero
 
 @[simp, norm_cast]
-theorem coe_complex_one : ((1 : ℂ) : ℍ) = 1 :=
+theorem coeComplex_one : ((1 : ℂ) : ℍ) = 1 :=
   rfl
-#align quaternion.coe_complex_one Quaternion.coe_complex_one
+#align quaternion.coe_complex_one Quaternion.coeComplex_one
 
 @[simp, norm_cast]
 theorem coe_real_complex_mul (r : ℝ) (z : ℂ) : (r • z : ℍ) = ↑r * ↑z := by ext <;> simp
 #align quaternion.coe_real_complex_mul Quaternion.coe_real_complex_mul
 
 @[simp, norm_cast]
-theorem coe_complex_coe (r : ℝ) : ((r : ℂ) : ℍ) = r :=
+theorem coeComplex_coe (r : ℝ) : ((r : ℂ) : ℍ) = r :=
   rfl
-#align quaternion.coe_complex_coe Quaternion.coe_complex_coe
+#align quaternion.coe_complex_coe Quaternion.coeComplex_coe
 
 /-- Coercion `ℂ →ₐ[ℝ] ℍ` as an algebra homomorphism. -/
 def ofComplex : ℂ →ₐ[ℝ] ℍ where
   toFun := coe
   map_one' := rfl
   map_zero' := rfl
-  map_add' := coe_complex_add
-  map_mul' := coe_complex_mul
+  map_add' := coeComplex_add
+  map_mul' := coeComplex_mul
   commutes' x := rfl
 #align quaternion.of_complex Quaternion.ofComplex
 

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

@@ -39,7 +39,7 @@ quaternion, normed ring, normed space, normed algebra
 -- mathport name: quaternion.real
 scoped[Quaternion] notation "ℍ" => Quaternion ℝ
 
-open RealInnerProductSpace
+open scoped RealInnerProductSpace
 
 namespace Quaternion
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -43,7 +43,7 @@ open RealInnerProductSpace
 
 namespace Quaternion
 
-instance : HasInner ℝ ℍ :=
+instance : Inner ℝ ℍ :=
   ⟨fun a b => (a * star b).re⟩
 
 theorem inner_self (a : ℍ) : ⟪a, a⟫ = normSq a :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

@@ -242,17 +242,15 @@ variable {α : Type _}
 
 @[simp, norm_cast]
 theorem hasSum_coe {f : α → ℝ} {r : ℝ} : HasSum (fun a => (f a : ℍ)) (↑r : ℍ) ↔ HasSum f r :=
-  ⟨fun h => by
-    simpa only using h.map (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reLm _ _) continuous_re, fun h =>
-    by simpa only using h.map (algebraMap ℝ ℍ) (continuous_algebraMap _ _)⟩
+  ⟨fun h => by simpa only using h.map (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reₗ _ _) continuous_re,
+    fun h => by simpa only using h.map (algebraMap ℝ ℍ) (continuous_algebraMap _ _)⟩
 #align quaternion.has_sum_coe Quaternion.hasSum_coe
 
 @[simp, norm_cast]
 theorem summable_coe {f : α → ℝ} : (Summable fun a => (f a : ℍ)) ↔ Summable f := by
   simpa only using
-    Summable.map_iff_of_leftInverse (algebraMap ℝ ℍ)
-      (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reLm _ _) (continuous_algebraMap _ _) continuous_re
-      coe_re
+    Summable.map_iff_of_leftInverse (algebraMap ℝ ℍ) (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reₗ _ _)
+      (continuous_algebraMap _ _) continuous_re coe_re
 #align quaternion.summable_coe Quaternion.summable_coe
 
 @[norm_cast]

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
+! leanprover-community/mathlib commit 07992a1d1f7a4176c6d3f160209608be4e198566
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -55,8 +55,8 @@ theorem inner_def (a b : ℍ) : ⟪a, b⟫ = (a * star b).re :=
 #align quaternion.inner_def Quaternion.inner_def
 
 noncomputable instance : NormedAddCommGroup ℍ :=
-  @InnerProductSpace.OfCore.toNormedAddCommGroup ℝ ℍ _ _ _
-    { inner := HasInner.inner
+  @InnerProductSpace.Core.toNormedAddCommGroup ℝ ℍ _ _ _
+    { toHasInner := inferInstance
       conj_symm := fun x y => by simp [inner_def, mul_comm]
       nonneg_re := fun x => normSq_nonneg
       definite := fun x => normSq_eq_zero.1

mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
+! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -44,13 +44,13 @@ open RealInnerProductSpace
 namespace Quaternion
 
 instance : HasInner ℝ ℍ :=
-  ⟨fun a b => (a * b.conj).re⟩
+  ⟨fun a b => (a * star b).re⟩
 
 theorem inner_self (a : ℍ) : ⟪a, a⟫ = normSq a :=
   rfl
 #align quaternion.inner_self Quaternion.inner_self
 
-theorem inner_def (a b : ℍ) : ⟪a, b⟫ = (a * b.conj).re :=
+theorem inner_def (a b : ℍ) : ⟪a, b⟫ = (a * star b).re :=
   rfl
 #align quaternion.inner_def Quaternion.inner_def
 
@@ -84,14 +84,14 @@ theorem nnnorm_coe (a : ℝ) : ‖(a : ℍ)‖₊ = ‖a‖₊ :=
 #align quaternion.nnnorm_coe Quaternion.nnnorm_coe
 
 @[simp]
-theorem norm_conj (a : ℍ) : ‖conj a‖ = ‖a‖ := by
-  simp_rw [norm_eq_sqrt_real_inner, inner_self, norm_sq_conj]
-#align quaternion.norm_conj Quaternion.norm_conj
+theorem norm_star (a : ℍ) : ‖star a‖ = ‖a‖ := by
+  simp_rw [norm_eq_sqrt_real_inner, inner_self, norm_sq_star]
+#align quaternion.norm_star Quaternion.norm_star
 
 @[simp]
-theorem nnnorm_conj (a : ℍ) : ‖conj a‖₊ = ‖a‖₊ :=
-  Subtype.ext <| norm_conj a
-#align quaternion.nnnorm_conj Quaternion.nnnorm_conj
+theorem nnnorm_star (a : ℍ) : ‖star a‖₊ = ‖a‖₊ :=
+  Subtype.ext <| norm_star a
+#align quaternion.nnnorm_star Quaternion.nnnorm_star
 
 noncomputable instance : NormedDivisionRing ℍ
     where
@@ -106,7 +106,7 @@ instance : NormedAlgebra ℝ ℍ where
   toAlgebra := (Quaternion.algebra : Algebra ℝ ℍ)
 
 instance : CstarRing ℍ
-    where norm_star_mul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) (norm_conj x)
+    where norm_star_mul_self x := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) (norm_star x)
 
 instance : Coe ℂ ℍ :=
   ⟨fun z => ⟨z.re, z.im, 0, 0⟩⟩
@@ -195,11 +195,6 @@ noncomputable def linearIsometryEquivTuple : ℍ ≃ₗᵢ[ℝ] EuclideanSpace 
     norm_map' := norm_piLp_equiv_symm_equivTuple }
 #align quaternion.linear_isometry_equiv_tuple Quaternion.linearIsometryEquivTuple
 
-@[continuity]
-theorem continuous_conj : Continuous (conj : ℍ → ℍ) :=
-  continuous_star
-#align quaternion.continuous_conj Quaternion.continuous_conj
-
 @[continuity]
 theorem continuous_coe : Continuous (coe : ℝ → ℍ) :=
   continuous_algebraMap ℝ ℍ

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: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit da3fc4a33ff6bc75f077f691dc94c217b8d41559
+! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -54,8 +54,8 @@ theorem inner_def (a b : ℍ) : ⟪a, b⟫ = (a * b.conj).re :=
   rfl
 #align quaternion.inner_def Quaternion.inner_def
 
-noncomputable instance : InnerProductSpace ℝ ℍ :=
-  InnerProductSpace.ofCore
+noncomputable instance : NormedAddCommGroup ℍ :=
+  @InnerProductSpace.OfCore.toNormedAddCommGroup ℝ ℍ _ _ _
     { inner := HasInner.inner
       conj_symm := fun x y => by simp [inner_def, mul_comm]
       nonneg_re := fun x => normSq_nonneg
@@ -63,6 +63,9 @@ noncomputable instance : InnerProductSpace ℝ ℍ :=
       add_left := fun x y z => by simp only [inner_def, add_mul, add_re]
       smul_left := fun x y r => by simp [inner_def] }
 
+noncomputable instance : InnerProductSpace ℝ ℍ :=
+  InnerProductSpace.ofCore _
+
 theorem normSq_eq_normSq (a : ℍ) : normSq a = ‖a‖ * ‖a‖ := by
   rw [← inner_self, real_inner_self_eq_norm_mul_norm]
 #align quaternion.norm_sq_eq_norm_sq Quaternion.normSq_eq_normSq
@@ -98,9 +101,8 @@ noncomputable instance : NormedDivisionRing ℍ
     simp only [norm_eq_sqrt_real_inner, inner_self, norm_sq.map_mul]
     exact Real.sqrt_mul norm_sq_nonneg _
 
-instance : NormedAlgebra ℝ ℍ
-    where
-  norm_smul_le a x := (norm_smul a x).le
+instance : NormedAlgebra ℝ ℍ where
+  norm_smul_le := norm_smul_le
   toAlgebra := (Quaternion.algebra : Algebra ℝ ℍ)
 
 instance : CstarRing ℍ

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
+! leanprover-community/mathlib commit da3fc4a33ff6bc75f077f691dc94c217b8d41559
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -239,5 +239,34 @@ instance : CompleteSpace ℍ :=
     linear_isometry_equiv_tuple.to_continuous_linear_equiv.symm.uniform_embedding
   (completeSpace_congr this).1 (by infer_instance)
 
+section infinite_sum
+
+variable {α : Type _}
+
+@[simp, norm_cast]
+theorem hasSum_coe {f : α → ℝ} {r : ℝ} : HasSum (fun a => (f a : ℍ)) (↑r : ℍ) ↔ HasSum f r :=
+  ⟨fun h => by
+    simpa only using h.map (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reLm _ _) continuous_re, fun h =>
+    by simpa only using h.map (algebraMap ℝ ℍ) (continuous_algebraMap _ _)⟩
+#align quaternion.has_sum_coe Quaternion.hasSum_coe
+
+@[simp, norm_cast]
+theorem summable_coe {f : α → ℝ} : (Summable fun a => (f a : ℍ)) ↔ Summable f := by
+  simpa only using
+    Summable.map_iff_of_leftInverse (algebraMap ℝ ℍ)
+      (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reLm _ _) (continuous_algebraMap _ _) continuous_re
+      coe_re
+#align quaternion.summable_coe Quaternion.summable_coe
+
+@[norm_cast]
+theorem tsum_coe (f : α → ℝ) : (∑' a, (f a : ℍ)) = ↑(∑' a, f a) :=
+  by
+  by_cases hf : Summable f
+  · exact (has_sum_coe.mpr hf.has_sum).tsum_eq
+  · simp [tsum_eq_zero_of_not_summable hf, tsum_eq_zero_of_not_summable (summable_coe.not.mpr hf)]
+#align quaternion.tsum_coe Quaternion.tsum_coe
+
+end infinite_sum
+
 end Quaternion
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit d90149e913bf65828b011379540c3379e01105fd
+! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -57,7 +57,7 @@ theorem inner_def (a b : ℍ) : ⟪a, b⟫ = (a * b.conj).re :=
 noncomputable instance : InnerProductSpace ℝ ℍ :=
   InnerProductSpace.ofCore
     { inner := HasInner.inner
-      conj_sym := fun x y => by simp [inner_def, mul_comm]
+      conj_symm := fun x y => by simp [inner_def, mul_comm]
       nonneg_re := fun x => normSq_nonneg
       definite := fun x => normSq_eq_zero.1
       add_left := fun x y z => by simp only [inner_def, add_mul, add_re]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit 48085f140e684306f9e7da907cd5932056d1aded
+! leanprover-community/mathlib commit d90149e913bf65828b011379540c3379e01105fd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -229,6 +229,11 @@ theorem continuous_imK : Continuous fun q : ℍ => q.imK :=
   (continuous_apply 3).comp linearIsometryEquivTuple.Continuous
 #align quaternion.continuous_im_k Quaternion.continuous_imK
 
+@[continuity]
+theorem continuous_im : Continuous fun q : ℍ => q.im := by
+  simpa only [← sub_self_re] using continuous_id.sub (continuous_coe.comp continuous_re)
+#align quaternion.continuous_im Quaternion.continuous_im
+
 instance : CompleteSpace ℍ :=
   haveI : UniformEmbedding linear_isometry_equiv_tuple.to_linear_equiv.to_equiv.symm :=
     linear_isometry_equiv_tuple.to_continuous_linear_equiv.symm.uniform_embedding

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

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

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

@@ -33,7 +33,6 @@ quaternion, normed ring, normed space, normed algebra
 -/
 
 
--- mathport name: quaternion.real
 @[inherit_doc] scoped[Quaternion] notation "ℍ" => Quaternion ℝ
 
 open scoped RealInnerProductSpace

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.

@@ -175,7 +175,7 @@ theorem norm_piLp_equiv_symm_equivTuple (x : ℍ) :
     ‖(WithLp.equiv 2 (Fin 4 → _)).symm (equivTuple ℝ x)‖ = ‖x‖ := by
   rw [norm_eq_sqrt_real_inner, norm_eq_sqrt_real_inner, inner_self, normSq_def', PiLp.inner_apply,
     Fin.sum_univ_four]
-  simp_rw [IsROrC.inner_apply, starRingEnd_apply, star_trivial, ← sq]
+  simp_rw [RCLike.inner_apply, starRingEnd_apply, star_trivial, ← sq]
   rfl
 set_option linter.uppercaseLean3 false in
 #align quaternion.norm_pi_Lp_equiv_symm_equiv_tuple Quaternion.norm_piLp_equiv_symm_equivTuple

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -96,7 +96,7 @@ noncomputable instance : NormedDivisionRing ℍ where
     simp only [norm_eq_sqrt_real_inner, inner_self, normSq.map_mul]
     exact Real.sqrt_mul normSq_nonneg _
 
--- porting note: added `noncomputable`
+-- Porting note: added `noncomputable`
 noncomputable instance : NormedAlgebra ℝ ℍ where
   norm_smul_le := norm_smul_le
   toAlgebra := Quaternion.algebra

Classifies by adding issue number #10959 porting notes claiming anything semantically equivalent to:

• "simp cannot prove this"
• "simp used to be able to close this goal"
• "simp can't handle this"
• "simp used to work here"

@@ -80,12 +80,12 @@ theorem nnnorm_coe (a : ℝ) : ‖(a : ℍ)‖₊ = ‖a‖₊ :=
   Subtype.ext <| norm_coe a
 #align quaternion.nnnorm_coe Quaternion.nnnorm_coe
 
-@[simp, nolint simpNF] -- Porting note: simp cannot prove this
+@[simp, nolint simpNF] -- Porting note (#10959): simp cannot prove this
 theorem norm_star (a : ℍ) : ‖star a‖ = ‖a‖ := by
   simp_rw [norm_eq_sqrt_real_inner, inner_self, normSq_star]
 #align quaternion.norm_star Quaternion.norm_star
 
-@[simp, nolint simpNF] -- Porting note: simp cannot prove this
+@[simp, nolint simpNF] -- Porting note (#10959): simp cannot prove this
 theorem nnnorm_star (a : ℍ) : ‖star a‖₊ = ‖a‖₊ :=
   Subtype.ext <| norm_star a
 #align quaternion.nnnorm_star Quaternion.nnnorm_star
@@ -147,7 +147,7 @@ theorem coeComplex_one : ((1 : ℂ) : ℍ) = 1 :=
   rfl
 #align quaternion.coe_complex_one Quaternion.coeComplex_one
 
-@[simp, norm_cast, nolint simpNF] -- Porting note: simp cannot prove this
+@[simp, norm_cast, nolint simpNF] -- Porting note (#10959): simp cannot prove this
 theorem coe_real_complex_mul (r : ℝ) (z : ℂ) : (r • z : ℍ) = ↑r * ↑z := by ext <;> simp
 #align quaternion.coe_real_complex_mul Quaternion.coe_real_complex_mul
 

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

@@ -34,7 +34,7 @@ quaternion, normed ring, normed space, normed algebra
 
 
 -- mathport name: quaternion.real
-scoped[Quaternion] notation "ℍ" => Quaternion ℝ
+@[inherit_doc] scoped[Quaternion] notation "ℍ" => Quaternion ℝ
 
 open scoped RealInnerProductSpace
 

This removes the (PiLp.equiv 2 fun i => α i) abbreviation, replacing it with its implementation (WithLp.equiv 2 (∀ i, α i)). The same thing is done for PiLp.linearEquiv.

@@ -172,7 +172,7 @@ theorem coe_ofComplex : ⇑ofComplex = coeComplex := rfl
 
 /-- The norm of the components as a euclidean vector equals the norm of the quaternion. -/
 theorem norm_piLp_equiv_symm_equivTuple (x : ℍ) :
-    ‖(PiLp.equiv 2 fun _ : Fin 4 => _).symm (equivTuple ℝ x)‖ = ‖x‖ := by
+    ‖(WithLp.equiv 2 (Fin 4 → _)).symm (equivTuple ℝ x)‖ = ‖x‖ := by
   rw [norm_eq_sqrt_real_inner, norm_eq_sqrt_real_inner, inner_self, normSq_def', PiLp.inner_apply,
     Fin.sum_univ_four]
   simp_rw [IsROrC.inner_apply, starRingEnd_apply, star_trivial, ← sq]
@@ -184,8 +184,8 @@ set_option linter.uppercaseLean3 false in
 @[simps apply symm_apply]
 noncomputable def linearIsometryEquivTuple : ℍ ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin 4) :=
   { (QuaternionAlgebra.linearEquivTuple (-1 : ℝ) (-1 : ℝ)).trans
-      (PiLp.linearEquiv 2 ℝ fun _ : Fin 4 => ℝ).symm with
-    toFun := fun a => (PiLp.equiv _ fun _ : Fin 4 => _).symm ![a.1, a.2, a.3, a.4]
+      (WithLp.linearEquiv 2 ℝ (Fin 4 → ℝ)).symm with
+    toFun := fun a => (WithLp.equiv _ (Fin 4 → _)).symm ![a.1, a.2, a.3, a.4]
     invFun := fun a => ⟨a 0, a 1, a 2, a 3⟩
     norm_map' := norm_piLp_equiv_symm_equivTuple }
 #align quaternion.linear_isometry_equiv_tuple Quaternion.linearIsometryEquivTuple

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

This has nice performance benefits.

@@ -233,7 +233,7 @@ instance : CompleteSpace ℍ :=
 
 section infinite_sum
 
-variable {α : Type _}
+variable {α : Type*}
 
 @[simp, norm_cast]
 theorem hasSum_coe {f : α → ℝ} {r : ℝ} : HasSum (fun a => (f a : ℍ)) (↑r : ℍ) ↔ HasSum f r :=

• 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) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.quaternion
-! leanprover-community/mathlib commit 07992a1d1f7a4176c6d3f160209608be4e198566
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Quaternion
 import Mathlib.Analysis.InnerProductSpace.Basic
 import Mathlib.Analysis.InnerProductSpace.PiL2
 import Mathlib.Topology.Algebra.Algebra
 
+#align_import analysis.quaternion from "leanprover-community/mathlib"@"07992a1d1f7a4176c6d3f160209608be4e198566"
+
 /-!
 # Quaternions as a normed algebra
 

These are all doc fixes

@@ -107,7 +107,7 @@ noncomputable instance : NormedAlgebra ℝ ℍ where
 instance : CstarRing ℍ where
   norm_star_mul_self {x} := (norm_mul _ _).trans <| congr_arg (· * ‖x‖) (norm_star x)
 
-/-- Coerction from `ℂ` to `ℍ`. -/
+/-- Coercion from `ℂ` to `ℍ`. -/
 @[coe] def coeComplex (z : ℂ) : ℍ := ⟨z.re, z.im, 0, 0⟩
 
 instance : Coe ℂ ℍ := ⟨coeComplex⟩

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