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

@@ -81,7 +81,7 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
     ext n : 1
     let k : ℝ := ↑(2 * n + 1)!
     calc
-      k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-norm_sq q) ^ n * q) := by rw [pow_succ', pow_mul, hq2]
+      k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-norm_sq q) ^ n * q) := by rw [pow_succ, pow_mul, hq2]
       _ = k⁻¹ • ((-1) ^ n * ‖q‖ ^ (2 * n)) • q := _
       _ = ((-1) ^ n * ‖q‖ ^ (2 * n + 1) / k / ‖q‖) • q := _
     · congr 1
@@ -89,7 +89,7 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
       push_cast
     · rw [smul_smul]
       congr 1
-      simp_rw [pow_succ', mul_div_assoc, div_div_cancel_left' hqn]
+      simp_rw [pow_succ, mul_div_assoc, div_div_cancel_left' hqn]
       ring
 #align quaternion.has_sum_exp_series_of_imaginary Quaternion.hasSum_expSeries_of_imaginary
 -/
@@ -149,7 +149,7 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (NormedSpace.exp ℝ q) = NormedSpace
       · simp [hv]
       rw [norm_sq_add, norm_sq_smul, star_smul, coe_mul_eq_smul, smul_re, smul_re, star_re, im_re,
         smul_zero, smul_zero, MulZeroClass.mul_zero, add_zero, div_pow, norm_sq_coe,
-        norm_sq_eq_norm_sq, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
+        norm_sq_eq_norm_sq, ← sq, div_mul_cancel₀ _ (pow_ne_zero _ hv)]
     _ = NormedSpace.exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
 #align quaternion.norm_sq_exp Quaternion.normSq_exp
 -/

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

@@ -51,7 +51,7 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
   replace hs := (hs.div_const ‖q‖).smul_const q
   obtain rfl | hq0 := eq_or_ne q 0
   · simp_rw [NormedSpace.expSeries_apply_zero, norm_zero, div_zero, zero_smul, add_zero]
-    simp_rw [norm_zero] at hc 
+    simp_rw [norm_zero] at hc
     convert hc
     ext (_ | n) : 1
     ·

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

@@ -34,8 +34,8 @@ namespace Quaternion
 
 #print Quaternion.exp_coe /-
 @[simp, norm_cast]
-theorem exp_coe (r : ℝ) : exp ℝ (r : ℍ[ℝ]) = ↑(exp ℝ r) :=
-  (map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
+theorem exp_coe (r : ℝ) : NormedSpace.exp ℝ (r : ℍ[ℝ]) = ↑(NormedSpace.exp ℝ r) :=
+  (NormedSpace.map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
 #align quaternion.exp_coe Quaternion.exp_coe
 -/
 
@@ -45,12 +45,12 @@ at `‖q‖` tend to `c` and `s`, then the exponential series tends to `c + (s /
 theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s : ℝ}
     (hc : HasSum (fun n => (-1) ^ n * ‖q‖ ^ (2 * n) / (2 * n)!) c)
     (hs : HasSum (fun n => (-1) ^ n * ‖q‖ ^ (2 * n + 1) / (2 * n + 1)!) s) :
-    HasSum (fun n => expSeries ℝ _ n fun _ => q) (↑c + (s / ‖q‖) • q) :=
+    HasSum (fun n => NormedSpace.expSeries ℝ _ n fun _ => q) (↑c + (s / ‖q‖) • q) :=
   by
   replace hc := has_sum_coe.mpr hc
   replace hs := (hs.div_const ‖q‖).smul_const q
   obtain rfl | hq0 := eq_or_ne q 0
-  · simp_rw [expSeries_apply_zero, norm_zero, div_zero, zero_smul, add_zero]
+  · simp_rw [NormedSpace.expSeries_apply_zero, norm_zero, div_zero, zero_smul, add_zero]
     simp_rw [norm_zero] at hc 
     convert hc
     ext (_ | n) : 1
@@ -60,7 +60,7 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
     ·
       rw [zero_pow (mul_pos two_pos (Nat.succ_pos _)), MulZeroClass.mul_zero, zero_div,
         Pi.single_eq_of_ne n.succ_ne_zero, coe_zero]
-  simp_rw [expSeries_apply_eq]
+  simp_rw [NormedSpace.expSeries_apply_eq]
   have hq2 : q ^ 2 = -norm_sq q := sq_eq_neg_norm_sq.mpr hq
   have hqn := norm_ne_zero_iff.mpr hq0
   refine' HasSum.even_add_odd _ _
@@ -97,11 +97,11 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
 #print Quaternion.exp_of_re_eq_zero /-
 /-- The closed form for the quaternion exponential on imaginary quaternions. -/
 theorem exp_of_re_eq_zero (q : Quaternion ℝ) (hq : q.re = 0) :
-    exp ℝ q = ↑(Real.cos ‖q‖) + (Real.sin ‖q‖ / ‖q‖) • q :=
+    NormedSpace.exp ℝ q = ↑(Real.cos ‖q‖) + (Real.sin ‖q‖ / ‖q‖) • q :=
   by
-  rw [exp_eq_tsum]
+  rw [NormedSpace.exp_eq_tsum]
   refine' HasSum.tsum_eq _
-  simp_rw [← expSeries_apply_eq]
+  simp_rw [← NormedSpace.expSeries_apply_eq]
   exact has_sum_exp_series_of_imaginary hq (Real.hasSum_cos _) (Real.hasSum_sin _)
 #align quaternion.exp_of_re_eq_zero Quaternion.exp_of_re_eq_zero
 -/
@@ -109,34 +109,40 @@ theorem exp_of_re_eq_zero (q : Quaternion ℝ) (hq : q.re = 0) :
 #print Quaternion.exp_eq /-
 /-- The closed form for the quaternion exponential on arbitrary quaternions. -/
 theorem exp_eq (q : Quaternion ℝ) :
-    exp ℝ q = exp ℝ q.re • (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im) :=
+    NormedSpace.exp ℝ q =
+      NormedSpace.exp ℝ q.re • (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im) :=
   by
-  rw [← exp_of_re_eq_zero q.im q.im_re, ← coe_mul_eq_smul, ← exp_coe, ← exp_add_of_commute,
-    re_add_im]
+  rw [← exp_of_re_eq_zero q.im q.im_re, ← coe_mul_eq_smul, ← exp_coe, ←
+    NormedSpace.exp_add_of_commute, re_add_im]
   exact Algebra.commutes q.re (_ : ℍ[ℝ])
 #align quaternion.exp_eq Quaternion.exp_eq
 -/
 
 #print Quaternion.re_exp /-
-theorem re_exp (q : ℍ[ℝ]) : (exp ℝ q).re = exp ℝ q.re * Real.cos ‖q - q.re‖ := by simp [exp_eq]
+theorem re_exp (q : ℍ[ℝ]) :
+    (NormedSpace.exp ℝ q).re = NormedSpace.exp ℝ q.re * Real.cos ‖q - q.re‖ := by simp [exp_eq]
 #align quaternion.re_exp Quaternion.re_exp
 -/
 
 #print Quaternion.im_exp /-
-theorem im_exp (q : ℍ[ℝ]) : (exp ℝ q).im = (exp ℝ q.re * (Real.sin ‖q.im‖ / ‖q.im‖)) • q.im := by
+theorem im_exp (q : ℍ[ℝ]) :
+    (NormedSpace.exp ℝ q).im = (NormedSpace.exp ℝ q.re * (Real.sin ‖q.im‖ / ‖q.im‖)) • q.im := by
   simp [exp_eq, smul_smul]
 #align quaternion.im_exp Quaternion.im_exp
 -/
 
 #print Quaternion.normSq_exp /-
-theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
+theorem normSq_exp (q : ℍ[ℝ]) : normSq (NormedSpace.exp ℝ q) = NormedSpace.exp ℝ q.re ^ 2 :=
   calc
-    normSq (exp ℝ q) =
-        normSq (exp ℝ q.re • (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im)) :=
+    normSq (NormedSpace.exp ℝ q) =
+        normSq
+          (NormedSpace.exp ℝ q.re • (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im)) :=
       by rw [exp_eq]
-    _ = exp ℝ q.re ^ 2 * normSq (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im) := by
-      rw [norm_sq_smul]
-    _ = exp ℝ q.re ^ 2 * (Real.cos ‖q.im‖ ^ 2 + Real.sin ‖q.im‖ ^ 2) :=
+    _ =
+        NormedSpace.exp ℝ q.re ^ 2 *
+          normSq (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im) :=
+      by rw [norm_sq_smul]
+    _ = NormedSpace.exp ℝ q.re ^ 2 * (Real.cos ‖q.im‖ ^ 2 + Real.sin ‖q.im‖ ^ 2) :=
       by
       congr 1
       obtain hv | hv := eq_or_ne ‖q.im‖ 0
@@ -144,7 +150,7 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
       rw [norm_sq_add, norm_sq_smul, star_smul, coe_mul_eq_smul, smul_re, smul_re, star_re, im_re,
         smul_zero, smul_zero, MulZeroClass.mul_zero, add_zero, div_pow, norm_sq_coe,
         norm_sq_eq_norm_sq, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
-    _ = exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
+    _ = NormedSpace.exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
 #align quaternion.norm_sq_exp Quaternion.normSq_exp
 -/
 
@@ -152,8 +158,8 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
 /-- Note that this implies that exponentials of pure imaginary quaternions are unit quaternions
 since in that case the RHS is `1` via `exp_zero` and `norm_one`. -/
 @[simp]
-theorem norm_exp (q : ℍ[ℝ]) : ‖exp ℝ q‖ = ‖exp ℝ q.re‖ := by
-  rw [norm_eq_sqrt_real_inner (exp ℝ q), inner_self, norm_sq_exp, Real.sqrt_sq_eq_abs,
+theorem norm_exp (q : ℍ[ℝ]) : ‖NormedSpace.exp ℝ q‖ = ‖NormedSpace.exp ℝ q.re‖ := by
+  rw [norm_eq_sqrt_real_inner (NormedSpace.exp ℝ q), inner_self, norm_sq_exp, Real.sqrt_sq_eq_abs,
     Real.norm_eq_abs]
 #align quaternion.norm_exp Quaternion.norm_exp
 -/

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

@@ -3,9 +3,9 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Analysis.Quaternion
-import Mathbin.Analysis.NormedSpace.Exponential
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Series
+import Analysis.Quaternion
+import Analysis.NormedSpace.Exponential
+import Analysis.SpecialFunctions.Trigonometric.Series
 
 #align_import analysis.normed_space.quaternion_exponential from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.normed_space.quaternion_exponential
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Quaternion
 import Mathbin.Analysis.NormedSpace.Exponential
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.Series
 
+#align_import analysis.normed_space.quaternion_exponential from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Lemmas about `exp` on `quaternion`s
 

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

@@ -35,11 +35,14 @@ open scoped Quaternion Nat
 
 namespace Quaternion
 
+#print Quaternion.exp_coe /-
 @[simp, norm_cast]
 theorem exp_coe (r : ℝ) : exp ℝ (r : ℍ[ℝ]) = ↑(exp ℝ r) :=
   (map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
 #align quaternion.exp_coe Quaternion.exp_coe
+-/
 
+#print Quaternion.hasSum_expSeries_of_imaginary /-
 /-- Auxiliary result; if the power series corresponding to `real.cos` and `real.sin` evaluated
 at `‖q‖` tend to `c` and `s`, then the exponential series tends to `c + (s / ‖q‖)`. -/
 theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s : ℝ}
@@ -92,7 +95,9 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
       simp_rw [pow_succ', mul_div_assoc, div_div_cancel_left' hqn]
       ring
 #align quaternion.has_sum_exp_series_of_imaginary Quaternion.hasSum_expSeries_of_imaginary
+-/
 
+#print Quaternion.exp_of_re_eq_zero /-
 /-- The closed form for the quaternion exponential on imaginary quaternions. -/
 theorem exp_of_re_eq_zero (q : Quaternion ℝ) (hq : q.re = 0) :
     exp ℝ q = ↑(Real.cos ‖q‖) + (Real.sin ‖q‖ / ‖q‖) • q :=
@@ -102,7 +107,9 @@ theorem exp_of_re_eq_zero (q : Quaternion ℝ) (hq : q.re = 0) :
   simp_rw [← expSeries_apply_eq]
   exact has_sum_exp_series_of_imaginary hq (Real.hasSum_cos _) (Real.hasSum_sin _)
 #align quaternion.exp_of_re_eq_zero Quaternion.exp_of_re_eq_zero
+-/
 
+#print Quaternion.exp_eq /-
 /-- The closed form for the quaternion exponential on arbitrary quaternions. -/
 theorem exp_eq (q : Quaternion ℝ) :
     exp ℝ q = exp ℝ q.re • (↑(Real.cos ‖q.im‖) + (Real.sin ‖q.im‖ / ‖q.im‖) • q.im) :=
@@ -111,14 +118,20 @@ theorem exp_eq (q : Quaternion ℝ) :
     re_add_im]
   exact Algebra.commutes q.re (_ : ℍ[ℝ])
 #align quaternion.exp_eq Quaternion.exp_eq
+-/
 
+#print Quaternion.re_exp /-
 theorem re_exp (q : ℍ[ℝ]) : (exp ℝ q).re = exp ℝ q.re * Real.cos ‖q - q.re‖ := by simp [exp_eq]
 #align quaternion.re_exp Quaternion.re_exp
+-/
 
+#print Quaternion.im_exp /-
 theorem im_exp (q : ℍ[ℝ]) : (exp ℝ q).im = (exp ℝ q.re * (Real.sin ‖q.im‖ / ‖q.im‖)) • q.im := by
   simp [exp_eq, smul_smul]
 #align quaternion.im_exp Quaternion.im_exp
+-/
 
+#print Quaternion.normSq_exp /-
 theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
   calc
     normSq (exp ℝ q) =
@@ -136,7 +149,9 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
         norm_sq_eq_norm_sq, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
     _ = exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
 #align quaternion.norm_sq_exp Quaternion.normSq_exp
+-/
 
+#print Quaternion.norm_exp /-
 /-- Note that this implies that exponentials of pure imaginary quaternions are unit quaternions
 since in that case the RHS is `1` via `exp_zero` and `norm_one`. -/
 @[simp]
@@ -144,6 +159,7 @@ theorem norm_exp (q : ℍ[ℝ]) : ‖exp ℝ q‖ = ‖exp ℝ q.re‖ := by
   rw [norm_eq_sqrt_real_inner (exp ℝ q), inner_self, norm_sq_exp, Real.sqrt_sq_eq_abs,
     Real.norm_eq_abs]
 #align quaternion.norm_exp Quaternion.norm_exp
+-/
 
 end Quaternion
 

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

@@ -71,7 +71,6 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
       k⁻¹ • q ^ (2 * n) = k⁻¹ • (-norm_sq q) ^ n := by rw [pow_mul, hq2]
       _ = k⁻¹ • ↑((-1) ^ n * ‖q‖ ^ (2 * n)) := _
       _ = ↑((-1) ^ n * ‖q‖ ^ (2 * n) / k) := _
-      
     · congr 1
       rw [neg_pow, norm_sq_eq_norm_sq, pow_mul, sq]
       push_cast
@@ -85,7 +84,6 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
       k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-norm_sq q) ^ n * q) := by rw [pow_succ', pow_mul, hq2]
       _ = k⁻¹ • ((-1) ^ n * ‖q‖ ^ (2 * n)) • q := _
       _ = ((-1) ^ n * ‖q‖ ^ (2 * n + 1) / k / ‖q‖) • q := _
-      
     · congr 1
       rw [neg_pow, norm_sq_eq_norm_sq, pow_mul, sq, ← coe_mul_eq_smul]
       push_cast
@@ -137,7 +135,6 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
         smul_zero, smul_zero, MulZeroClass.mul_zero, add_zero, div_pow, norm_sq_coe,
         norm_sq_eq_norm_sq, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
     _ = exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
-    
 #align quaternion.norm_sq_exp Quaternion.normSq_exp
 
 /-- Note that this implies that exponentials of pure imaginary quaternions are unit quaternions

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed_space.quaternion_exponential
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.SpecialFunctions.Trigonometric.Series
 /-!
 # Lemmas about `exp` on `quaternion`s
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains results about `exp` on `quaternion ℝ`.
 
 ## Main results

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

@@ -48,7 +48,7 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
   replace hs := (hs.div_const ‖q‖).smul_const q
   obtain rfl | hq0 := eq_or_ne q 0
   · simp_rw [expSeries_apply_zero, norm_zero, div_zero, zero_smul, add_zero]
-    simp_rw [norm_zero] at hc
+    simp_rw [norm_zero] at hc 
     convert hc
     ext (_ | n) : 1
     ·

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

@@ -28,7 +28,7 @@ This file contains results about `exp` on `quaternion ℝ`.
 -/
 
 
-open Quaternion Nat
+open scoped Quaternion Nat
 
 namespace Quaternion
 

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

@@ -4,13 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed_space.quaternion_exponential
-! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Quaternion
 import Mathbin.Analysis.NormedSpace.Exponential
-import Mathbin.Analysis.InnerProductSpace.PiL2
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.Series
 
 /-!

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: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed_space.quaternion_exponential
-! leanprover-community/mathlib commit da3fc4a33ff6bc75f077f691dc94c217b8d41559
+! leanprover-community/mathlib commit cf7a7252c1989efe5800e0b3cdfeb4228ac6b40e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -33,10 +33,6 @@ open Quaternion Nat
 
 namespace Quaternion
 
-theorem conj_exp (q : ℍ[ℝ]) : conj (exp ℝ q) = exp ℝ (conj q) :=
-  star_exp q
-#align quaternion.conj_exp Quaternion.conj_exp
-
 @[simp, norm_cast]
 theorem exp_coe (r : ℝ) : exp ℝ (r : ℍ[ℝ]) = ↑(exp ℝ r) :=
   (map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
@@ -135,7 +131,7 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
       congr 1
       obtain hv | hv := eq_or_ne ‖q.im‖ 0
       · simp [hv]
-      rw [norm_sq_add, norm_sq_smul, conj_smul, coe_mul_eq_smul, smul_re, smul_re, conj_re, im_re,
+      rw [norm_sq_add, norm_sq_smul, star_smul, coe_mul_eq_smul, smul_re, smul_re, star_re, im_re,
         smul_zero, smul_zero, MulZeroClass.mul_zero, add_zero, div_pow, norm_sq_coe,
         norm_sq_eq_norm_sq, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
     _ = exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]

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

@@ -10,9 +10,9 @@ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Series
 #align_import analysis.normed_space.quaternion_exponential from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
 
 /-!
-# Lemmas about `exp` on `Quaternion`s
+# Lemmas about `NormedSpace.exp` on `Quaternion`s
 
-This file contains results about `exp` on `Quaternion ℝ`.
+This file contains results about `NormedSpace.exp` on `Quaternion ℝ`.
 
 ## Main results
 
@@ -137,7 +137,7 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
 #align quaternion.norm_sq_exp Quaternion.normSq_exp
 
 /-- Note that this implies that exponentials of pure imaginary quaternions are unit quaternions
-since in that case the RHS is `1` via `exp_zero` and `norm_one`. -/
+since in that case the RHS is `1` via `NormedSpace.exp_zero` and `norm_one`. -/
 @[simp]
 theorem norm_exp (q : ℍ[ℝ]) : ‖exp ℝ q‖ = ‖exp ℝ q.re‖ := by
   rw [norm_eq_sqrt_real_inner (exp ℝ q), inner_self, normSq_exp, Real.sqrt_sq_eq_abs,

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -66,7 +66,7 @@ theorem expSeries_odd_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) (n : ℕ
   have hqn := norm_ne_zero_iff.mpr hq0
   let k : ℝ := ↑(2 * n + 1)!
   calc
-    k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-normSq q) ^ n * q) := by rw [pow_succ', pow_mul, hq2]
+    k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-normSq q) ^ n * q) := by rw [pow_succ, pow_mul, hq2]
     _ = k⁻¹ • ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) • q := ?_
     _ = ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n + 1) / k / ‖q‖) • q := ?_
   · congr 1
@@ -74,7 +74,7 @@ theorem expSeries_odd_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) (n : ℕ
     norm_cast
   · rw [smul_smul]
     congr 1
-    simp_rw [pow_succ', mul_div_assoc, div_div_cancel_left' hqn]
+    simp_rw [pow_succ, mul_div_assoc, div_div_cancel_left' hqn]
     ring
 
 /-- Auxiliary result; if the power series corresponding to `Real.cos` and `Real.sin` evaluated

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

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

| Statement | New name | Old name | |

@@ -131,7 +131,7 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
       · simp [hv]
       rw [normSq_add, normSq_smul, star_smul, coe_mul_eq_smul, smul_re, smul_re, star_re, im_re,
         smul_zero, smul_zero, mul_zero, add_zero, div_pow, normSq_coe,
-        normSq_eq_norm_mul_self, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
+        normSq_eq_norm_mul_self, ← sq, div_mul_cancel₀ _ (pow_ne_zero _ hv)]
     _ = exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
 
 #align quaternion.norm_sq_exp Quaternion.normSq_exp

Besides being split in three, this proof is largely untouched.

@@ -35,6 +35,48 @@ theorem exp_coe (r : ℝ) : exp ℝ (r : ℍ[ℝ]) = ↑(exp ℝ r) :=
   (map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
 #align quaternion.exp_coe Quaternion.exp_coe
 
+/-- The even terms of `expSeries` are real, and correspond to the series for $\cos ‖q‖$. -/
+theorem expSeries_even_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) (n : ℕ) :
+    expSeries ℝ (Quaternion ℝ) (2 * n) (fun _ => q) =
+      ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n) / (2 * n)!) := by
+  rw [expSeries_apply_eq]
+  have hq2 : q ^ 2 = -normSq q := sq_eq_neg_normSq.mpr hq
+  letI k : ℝ := ↑(2 * n)!
+  calc
+    k⁻¹ • q ^ (2 * n) = k⁻¹ • (-normSq q) ^ n := by rw [pow_mul, hq2]
+    _ = k⁻¹ • ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) := ?_
+    _ = ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n) / k) := ?_
+  · congr 1
+    rw [neg_pow, normSq_eq_norm_mul_self, pow_mul, sq]
+    push_cast
+    rfl
+  · rw [← coe_mul_eq_smul, div_eq_mul_inv]
+    norm_cast
+    ring_nf
+
+/-- The odd terms of `expSeries` are real, and correspond to the series for
+$\frac{q}{‖q‖} \sin ‖q‖$. -/
+theorem expSeries_odd_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) (n : ℕ) :
+    expSeries ℝ (Quaternion ℝ) (2 * n + 1) (fun _ => q) =
+      (((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n + 1) / (2 * n + 1)!) / ‖q‖) • q := by
+  rw [expSeries_apply_eq]
+  obtain rfl | hq0 := eq_or_ne q 0
+  · simp
+  have hq2 : q ^ 2 = -normSq q := sq_eq_neg_normSq.mpr hq
+  have hqn := norm_ne_zero_iff.mpr hq0
+  let k : ℝ := ↑(2 * n + 1)!
+  calc
+    k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-normSq q) ^ n * q) := by rw [pow_succ', pow_mul, hq2]
+    _ = k⁻¹ • ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) • q := ?_
+    _ = ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n + 1) / k / ‖q‖) • q := ?_
+  · congr 1
+    rw [neg_pow, normSq_eq_norm_mul_self, pow_mul, sq, ← coe_mul_eq_smul]
+    norm_cast
+  · rw [smul_smul]
+    congr 1
+    simp_rw [pow_succ', mul_div_assoc, div_div_cancel_left' hqn]
+    ring
+
 /-- Auxiliary result; if the power series corresponding to `Real.cos` and `Real.sin` evaluated
 at `‖q‖` tend to `c` and `s`, then the exponential series tends to `c + (s / ‖q‖)`. -/
 theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s : ℝ}
@@ -43,48 +85,13 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
     HasSum (fun n => expSeries ℝ (Quaternion ℝ) n fun _ => q) (↑c + (s / ‖q‖) • q) := by
   replace hc := hasSum_coe.mpr hc
   replace hs := (hs.div_const ‖q‖).smul_const q
-  obtain rfl | hq0 := eq_or_ne q 0
-  · simp_rw [expSeries_apply_zero, norm_zero, div_zero, zero_smul, add_zero]
-    simp_rw [norm_zero] at hc
-    convert hc using 1
-    ext (_ | n) : 1
-    · rw [pow_zero, Nat.zero_eq, mul_zero, pow_zero, Nat.factorial_zero, Nat.cast_one,
-        div_one, one_mul, Pi.single_eq_same, coe_one]
-    · rw [zero_pow (mul_pos two_pos (Nat.succ_pos _)), mul_zero, zero_div,
-        Pi.single_eq_of_ne n.succ_ne_zero, coe_zero]
-  simp_rw [expSeries_apply_eq]
-  have hq2 : q ^ 2 = -normSq q := sq_eq_neg_normSq.mpr hq
-  have hqn := norm_ne_zero_iff.mpr hq0
-  refine' HasSum.even_add_odd _ _
+  refine HasSum.even_add_odd ?_ ?_
   · convert hc using 1
     ext n : 1
-    letI k : ℝ := ↑(2 * n)!
-    calc
-      k⁻¹ • q ^ (2 * n) = k⁻¹ • (-normSq q) ^ n := by rw [pow_mul, hq2]
-      _ = k⁻¹ • ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) := ?_
-      _ = ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n) / k) := ?_
-    · congr 1
-      rw [neg_pow, normSq_eq_norm_mul_self, pow_mul, sq]
-      push_cast
-      rfl
-    · rw [← coe_mul_eq_smul, div_eq_mul_inv]
-      norm_cast
-      ring_nf
+    rw [expSeries_even_of_imaginary hq]
   · convert hs using 1
     ext n : 1
-    let k : ℝ := ↑(2 * n + 1)!
-    calc
-      k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-normSq q) ^ n * q) := by
-        rw [pow_succ', pow_mul, hq2]
-      _ = k⁻¹ • ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) • q := ?_
-      _ = ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n + 1) / k / ‖q‖) • q := ?_
-    · congr 1
-      rw [neg_pow, normSq_eq_norm_mul_self, pow_mul, sq, ← coe_mul_eq_smul]
-      norm_cast
-    · rw [smul_smul]
-      congr 1
-      simp_rw [pow_succ', mul_div_assoc, div_div_cancel_left' hqn]
-      ring
+    rw [expSeries_odd_of_imaginary hq]
 #align quaternion.has_sum_exp_series_of_imaginary Quaternion.hasSum_expSeries_of_imaginary
 
 /-- The closed form for the quaternion exponential on imaginary quaternions. -/

Per discussion at zulip

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

@@ -24,9 +24,10 @@ This file contains results about `exp` on `Quaternion ℝ`.
 
 -/
 
-
 open scoped Quaternion Nat
 
+open NormedSpace
+
 namespace Quaternion
 
 @[simp, norm_cast]

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>

@@ -34,8 +34,6 @@ theorem exp_coe (r : ℝ) : exp ℝ (r : ℍ[ℝ]) = ↑(exp ℝ r) :=
   (map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
 #align quaternion.exp_coe Quaternion.exp_coe
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 /-- Auxiliary result; if the power series corresponding to `Real.cos` and `Real.sin` evaluated
 at `‖q‖` tend to `c` and `s`, then the exponential series tends to `c + (s / ‖q‖)`. -/
 theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s : ℝ}
@@ -61,7 +59,7 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
     ext n : 1
     letI k : ℝ := ↑(2 * n)!
     calc
-      k⁻¹ • q ^ (2 * n) = k⁻¹ • (-normSq q) ^ n := by rw [pow_mul, hq2]; norm_cast
+      k⁻¹ • q ^ (2 * n) = k⁻¹ • (-normSq q) ^ n := by rw [pow_mul, hq2]
       _ = k⁻¹ • ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) := ?_
       _ = ↑((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n) / k) := ?_
     · congr 1
@@ -77,11 +75,11 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
     calc
       k⁻¹ • q ^ (2 * n + 1) = k⁻¹ • ((-normSq q) ^ n * q) := by
         rw [pow_succ', pow_mul, hq2]
-        norm_cast
       _ = k⁻¹ • ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n)) • q := ?_
       _ = ((-1 : ℝ) ^ n * ‖q‖ ^ (2 * n + 1) / k / ‖q‖) • q := ?_
     · congr 1
       rw [neg_pow, normSq_eq_norm_mul_self, pow_mul, sq, ← coe_mul_eq_smul]
+      norm_cast
     · rw [smul_smul]
       congr 1
       simp_rw [pow_succ', mul_div_assoc, div_div_cancel_left' hqn]

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).

@@ -49,9 +49,9 @@ theorem hasSum_expSeries_of_imaginary {q : Quaternion ℝ} (hq : q.re = 0) {c s
     simp_rw [norm_zero] at hc
     convert hc using 1
     ext (_ | n) : 1
-    · rw [pow_zero, Nat.zero_eq, MulZeroClass.mul_zero, pow_zero, Nat.factorial_zero, Nat.cast_one,
+    · rw [pow_zero, Nat.zero_eq, mul_zero, pow_zero, Nat.factorial_zero, Nat.cast_one,
         div_one, one_mul, Pi.single_eq_same, coe_one]
-    · rw [zero_pow (mul_pos two_pos (Nat.succ_pos _)), MulZeroClass.mul_zero, zero_div,
+    · rw [zero_pow (mul_pos two_pos (Nat.succ_pos _)), mul_zero, zero_div,
         Pi.single_eq_of_ne n.succ_ne_zero, coe_zero]
   simp_rw [expSeries_apply_eq]
   have hq2 : q ^ 2 = -normSq q := sq_eq_neg_normSq.mpr hq
@@ -124,7 +124,7 @@ theorem normSq_exp (q : ℍ[ℝ]) : normSq (exp ℝ q) = exp ℝ q.re ^ 2 :=
       obtain hv | hv := eq_or_ne ‖q.im‖ 0
       · simp [hv]
       rw [normSq_add, normSq_smul, star_smul, coe_mul_eq_smul, smul_re, smul_re, star_re, im_re,
-        smul_zero, smul_zero, MulZeroClass.mul_zero, add_zero, div_pow, normSq_coe,
+        smul_zero, smul_zero, mul_zero, add_zero, div_pow, normSq_coe,
         normSq_eq_norm_mul_self, ← sq, div_mul_cancel _ (pow_ne_zero _ hv)]
     _ = exp ℝ q.re ^ 2 := by rw [Real.cos_sq_add_sin_sq, mul_one]
 

@@ -34,8 +34,7 @@ theorem exp_coe (r : ℝ) : exp ℝ (r : ℍ[ℝ]) = ↑(exp ℝ r) :=
   (map_exp ℝ (algebraMap ℝ ℍ[ℝ]) (continuous_algebraMap _ _) _).symm
 #align quaternion.exp_coe Quaternion.exp_coe
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y)
--- porting note: lean4#2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 /-- Auxiliary result; if the power series corresponding to `Real.cos` and `Real.sin` evaluated
 at `‖q‖` tend to `c` and `s`, then the exponential series tends to `c + (s / ‖q‖)`. -/

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.normed_space.quaternion_exponential
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Quaternion
 import Mathlib.Analysis.NormedSpace.Exponential
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.Series
 
+#align_import analysis.normed_space.quaternion_exponential from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Lemmas about `exp` on `Quaternion`s