algebra.quaternion_basis | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

3aa5b8a9

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

38df578a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Algebra.Quaternion
-import Mathbin.Tactic.Ring
+import Algebra.Quaternion
+import Tactic.Ring
 
 #align_import algebra.quaternion_basis from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"

38df578a

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -40,10 +40,10 @@ Note that for definitional convenience, `k` is provided as a field even though `
 determines it. -/
 structure Basis {R : Type _} (A : Type _) [CommRing R] [Ring A] [Algebra R A] (c₁ c₂ : R) where
   (i j k : A)
-  i_mul_i : i * i = c₁ • 1
-  j_mul_j : j * j = c₂ • 1
-  i_mul_j : i * j = k
-  j_mul_i : j * i = -k
+  i_hMul_i : i * i = c₁ • 1
+  j_hMul_j : j * j = c₂ • 1
+  i_hMul_j : i * j = k
+  j_hMul_i : j * i = -k
 #align quaternion_algebra.basis QuaternionAlgebra.Basis
 -/
 
@@ -74,12 +74,12 @@ variable (R)
 protected def self : Basis ℍ[R,c₁,c₂] c₁ c₂
     where
   i := ⟨0, 1, 0, 0⟩
-  i_mul_i := by ext <;> simp
+  i_hMul_i := by ext <;> simp
   j := ⟨0, 0, 1, 0⟩
-  j_mul_j := by ext <;> simp
+  j_hMul_j := by ext <;> simp
   k := ⟨0, 0, 0, 1⟩
-  i_mul_j := by ext <;> simp
-  j_mul_i := by ext <;> simp
+  i_hMul_j := by ext <;> simp
+  j_hMul_i := by ext <;> simp
 #align quaternion_algebra.basis.self QuaternionAlgebra.Basis.self
 -/
 
@@ -194,12 +194,12 @@ def liftHom : ℍ[R,c₁,c₂] →ₐ[R] A :=
 def compHom (F : A →ₐ[R] B) : Basis B c₁ c₂
     where
   i := F q.i
-  i_mul_i := by rw [← F.map_mul, q.i_mul_i, F.map_smul, F.map_one]
+  i_hMul_i := by rw [← F.map_mul, q.i_mul_i, F.map_smul, F.map_one]
   j := F q.j
-  j_mul_j := by rw [← F.map_mul, q.j_mul_j, F.map_smul, F.map_one]
+  j_hMul_j := by rw [← F.map_mul, q.j_mul_j, F.map_smul, F.map_one]
   k := F q.k
-  i_mul_j := by rw [← F.map_mul, q.i_mul_j]
-  j_mul_i := by rw [← F.map_mul, q.j_mul_i, F.map_neg]
+  i_hMul_j := by rw [← F.map_mul, q.i_mul_j]
+  j_hMul_i := by rw [← F.map_mul, q.j_mul_i, F.map_neg]
 #align quaternion_algebra.basis.comp_hom QuaternionAlgebra.Basis.compHom
 -/

38df578a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 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 algebra.quaternion_basis
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Quaternion
 import Mathbin.Tactic.Ring
 
+#align_import algebra.quaternion_basis from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Basis on a quaternion-like algebra

38df578a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -56,6 +56,7 @@ variable {c₁ c₂ : R}
 
 namespace Basis
 
+#print QuaternionAlgebra.Basis.ext /-
 /-- Since `k` is redundant, it is not necessary to show `q₁.k = q₂.k` when showing `q₁ = q₂`. -/
 @[ext]
 protected theorem ext ⦃q₁ q₂ : Basis A c₁ c₂⦄ (hi : q₁.i = q₂.i) (hj : q₁.j = q₂.j) : q₁ = q₂ :=
@@ -66,9 +67,11 @@ protected theorem ext ⦃q₁ q₂ : Basis A c₁ c₂⦄ (hi : q₁.i = q₂.i)
   rw [← q₁_i_mul_j, ← q₂_i_mul_j]
   congr
 #align quaternion_algebra.basis.ext QuaternionAlgebra.Basis.ext
+-/
 
 variable (R)
 
+#print QuaternionAlgebra.Basis.self /-
 /-- There is a natural quaternionic basis for the `quaternion_algebra`. -/
 @[simps i j k]
 protected def self : Basis ℍ[R,c₁,c₂] c₁ c₂
@@ -81,6 +84,7 @@ protected def self : Basis ℍ[R,c₁,c₂] c₁ c₂
   i_mul_j := by ext <;> simp
   j_mul_i := by ext <;> simp
 #align quaternion_algebra.basis.self QuaternionAlgebra.Basis.self
+-/
 
 variable {R}
 
@@ -89,35 +93,43 @@ instance : Inhabited (Basis ℍ[R,c₁,c₂] c₁ c₂) :=
 
 variable (q : Basis A c₁ c₂)
 
-include q
-
 attribute [simp] i_mul_i j_mul_j i_mul_j j_mul_i
 
+#print QuaternionAlgebra.Basis.i_mul_k /-
 @[simp]
 theorem i_mul_k : q.i * q.k = c₁ • q.j := by
   rw [← i_mul_j, ← mul_assoc, i_mul_i, smul_mul_assoc, one_mul]
 #align quaternion_algebra.basis.i_mul_k QuaternionAlgebra.Basis.i_mul_k
+-/
 
+#print QuaternionAlgebra.Basis.k_mul_i /-
 @[simp]
 theorem k_mul_i : q.k * q.i = -c₁ • q.j := by
   rw [← i_mul_j, mul_assoc, j_mul_i, mul_neg, i_mul_k, neg_smul]
 #align quaternion_algebra.basis.k_mul_i QuaternionAlgebra.Basis.k_mul_i
+-/
 
+#print QuaternionAlgebra.Basis.k_mul_j /-
 @[simp]
 theorem k_mul_j : q.k * q.j = c₂ • q.i := by
   rw [← i_mul_j, mul_assoc, j_mul_j, mul_smul_comm, mul_one]
 #align quaternion_algebra.basis.k_mul_j QuaternionAlgebra.Basis.k_mul_j
+-/
 
+#print QuaternionAlgebra.Basis.j_mul_k /-
 @[simp]
 theorem j_mul_k : q.j * q.k = -c₂ • q.i := by
   rw [← i_mul_j, ← mul_assoc, j_mul_i, neg_mul, k_mul_j, neg_smul]
 #align quaternion_algebra.basis.j_mul_k QuaternionAlgebra.Basis.j_mul_k
+-/
 
+#print QuaternionAlgebra.Basis.k_mul_k /-
 @[simp]
 theorem k_mul_k : q.k * q.k = -((c₁ * c₂) • 1) := by
   rw [← i_mul_j, mul_assoc, ← mul_assoc q.j _ _, j_mul_i, ← i_mul_j, ← mul_assoc, mul_neg, ←
     mul_assoc, i_mul_i, smul_mul_assoc, one_mul, neg_mul, smul_mul_assoc, j_mul_j, smul_smul]
 #align quaternion_algebra.basis.k_mul_k QuaternionAlgebra.Basis.k_mul_k
+-/
 
 #print QuaternionAlgebra.Basis.lift /-
 /-- Intermediate result used to define `quaternion_algebra.basis.lift_hom`. -/
@@ -126,16 +138,23 @@ def lift (x : ℍ[R,c₁,c₂]) : A :=
 #align quaternion_algebra.basis.lift QuaternionAlgebra.Basis.lift
 -/
 
+#print QuaternionAlgebra.Basis.lift_zero /-
 theorem lift_zero : q.lift (0 : ℍ[R,c₁,c₂]) = 0 := by simp [lift]
 #align quaternion_algebra.basis.lift_zero QuaternionAlgebra.Basis.lift_zero
+-/
 
+#print QuaternionAlgebra.Basis.lift_one /-
 theorem lift_one : q.lift (1 : ℍ[R,c₁,c₂]) = 1 := by simp [lift]
 #align quaternion_algebra.basis.lift_one QuaternionAlgebra.Basis.lift_one
+-/
 
+#print QuaternionAlgebra.Basis.lift_add /-
 theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y := by
   simp [lift, add_smul]; abel
 #align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_add
+-/
 
+#print QuaternionAlgebra.Basis.lift_mul /-
 theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y :=
   by
   simp only [lift, Algebra.algebraMap_eq_smul_one]
@@ -151,11 +170,15 @@ theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y
   simp [sub_eq_add_neg, add_smul, ← add_assoc]
   abel
 #align quaternion_algebra.basis.lift_mul QuaternionAlgebra.Basis.lift_mul
+-/
 
+#print QuaternionAlgebra.Basis.lift_smul /-
 theorem lift_smul (r : R) (x : ℍ[R,c₁,c₂]) : q.lift (r • x) = r • q.lift x := by
   simp [lift, mul_smul, ← Algebra.smul_def]
 #align quaternion_algebra.basis.lift_smul QuaternionAlgebra.Basis.lift_smul
+-/
 
+#print QuaternionAlgebra.Basis.liftHom /-
 /-- A `quaternion_algebra.basis` implies an `alg_hom` from the quaternions. -/
 @[simps]
 def liftHom : ℍ[R,c₁,c₂] →ₐ[R] A :=
@@ -166,6 +189,7 @@ def liftHom : ℍ[R,c₁,c₂] →ₐ[R] A :=
       map_add' := q.lift_add
       map_mul' := q.lift_mul } q.lift_smul
 #align quaternion_algebra.basis.lift_hom QuaternionAlgebra.Basis.liftHom
+-/
 
 #print QuaternionAlgebra.Basis.compHom /-
 /-- Transform a `quaternion_algebra.basis` through an `alg_hom`. -/
@@ -184,6 +208,7 @@ def compHom (F : A →ₐ[R] B) : Basis B c₁ c₂
 
 end Basis
 
+#print QuaternionAlgebra.lift /-
 /-- A quaternionic basis on `A` is equivalent to a map from the quaternion algebra to `A`. -/
 @[simps]
 def lift : Basis A c₁ c₂ ≃ (ℍ[R,c₁,c₂] →ₐ[R] A)
@@ -200,6 +225,7 @@ def lift : Basis A c₁ c₂ ≃ (ℍ[R,c₁,c₂] →ₐ[R] A)
     congr
     simp
 #align quaternion_algebra.lift QuaternionAlgebra.lift
+-/
 
 end QuaternionAlgebra

38df578a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -30,7 +30,7 @@ import Mathbin.Tactic.Ring
 -/
 
 
-open Quaternion
+open scoped Quaternion
 
 namespace QuaternionAlgebra

38df578a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -56,12 +56,6 @@ variable {c₁ c₂ : R}
 
 namespace Basis
 
-/- warning: quaternion_algebra.basis.ext -> QuaternionAlgebra.Basis.ext is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} {{q₁ : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂}} {{q₂ : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂}}, (Eq.{succ u2} A (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u2} A (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u2} (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) q₁ q₂)
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2)] {c₁ : R} {c₂ : R} {{q₁ : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂}} {{q₂ : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂}}, (Eq.{succ u1} A (QuaternionAlgebra.Basis.i.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.i.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u1} A (QuaternionAlgebra.Basis.j.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.j.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u1} (QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂) q₁ q₂)
-Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.ext QuaternionAlgebra.Basis.extₓ'. -/
 /-- Since `k` is redundant, it is not necessary to show `q₁.k = q₂.k` when showing `q₁ = q₂`. -/
 @[ext]
 protected theorem ext ⦃q₁ q₂ : Basis A c₁ c₂⦄ (hi : q₁.i = q₂.i) (hj : q₁.j = q₂.j) : q₁ = q₂ :=
@@ -75,12 +69,6 @@ protected theorem ext ⦃q₁ q₂ : Basis A c₁ c₂⦄ (hi : q₁.i = q₂.i)
 
 variable (R)
 
-/- warning: quaternion_algebra.basis.self -> QuaternionAlgebra.Basis.self is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, QuaternionAlgebra.Basis.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) _inst_1 (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) c₁ c₂
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, QuaternionAlgebra.Basis.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) _inst_1 (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) c₁ c₂
-Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.self QuaternionAlgebra.Basis.selfₓ'. -/
 /-- There is a natural quaternionic basis for the `quaternion_algebra`. -/
 @[simps i j k]
 protected def self : Basis ℍ[R,c₁,c₂] c₁ c₂
@@ -105,56 +93,26 @@ include q
 
 attribute [simp] i_mul_i j_mul_j i_mul_j j_mul_i
 
-/- warning: quaternion_algebra.basis.i_mul_k -> QuaternionAlgebra.Basis.i_mul_k is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂), Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_2))) (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q) (QuaternionAlgebra.Basis.k.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_4))))) c₁ (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q))
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-Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.i_mul_k QuaternionAlgebra.Basis.i_mul_kₓ'. -/
 @[simp]
 theorem i_mul_k : q.i * q.k = c₁ • q.j := by
   rw [← i_mul_j, ← mul_assoc, i_mul_i, smul_mul_assoc, one_mul]
 #align quaternion_algebra.basis.i_mul_k QuaternionAlgebra.Basis.i_mul_k
 
-/- warning: quaternion_algebra.basis.k_mul_i -> QuaternionAlgebra.Basis.k_mul_i is a dubious translation:
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 @[simp]
 theorem k_mul_i : q.k * q.i = -c₁ • q.j := by
   rw [← i_mul_j, mul_assoc, j_mul_i, mul_neg, i_mul_k, neg_smul]
 #align quaternion_algebra.basis.k_mul_i QuaternionAlgebra.Basis.k_mul_i
 
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 @[simp]
 theorem k_mul_j : q.k * q.j = c₂ • q.i := by
   rw [← i_mul_j, mul_assoc, j_mul_j, mul_smul_comm, mul_one]
 #align quaternion_algebra.basis.k_mul_j QuaternionAlgebra.Basis.k_mul_j
 
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 @[simp]
 theorem j_mul_k : q.j * q.k = -c₂ • q.i := by
   rw [← i_mul_j, ← mul_assoc, j_mul_i, neg_mul, k_mul_j, neg_smul]
 #align quaternion_algebra.basis.j_mul_k QuaternionAlgebra.Basis.j_mul_k
 
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 @[simp]
 theorem k_mul_k : q.k * q.k = -((c₁ * c₂) • 1) := by
   rw [← i_mul_j, mul_assoc, ← mul_assoc q.j _ _, j_mul_i, ← i_mul_j, ← mul_assoc, mul_neg, ←
@@ -168,40 +126,16 @@ def lift (x : ℍ[R,c₁,c₂]) : A :=
 #align quaternion_algebra.basis.lift QuaternionAlgebra.Basis.lift
 -/
 
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 theorem lift_zero : q.lift (0 : ℍ[R,c₁,c₂]) = 0 := by simp [lift]
 #align quaternion_algebra.basis.lift_zero QuaternionAlgebra.Basis.lift_zero
 
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 theorem lift_one : q.lift (1 : ℍ[R,c₁,c₂]) = 1 := by simp [lift]
 #align quaternion_algebra.basis.lift_one QuaternionAlgebra.Basis.lift_one
 
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 theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y := by
   simp [lift, add_smul]; abel
 #align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_add
 
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 theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y :=
   by
   simp only [lift, Algebra.algebraMap_eq_smul_one]
@@ -218,22 +152,10 @@ theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y
   abel
 #align quaternion_algebra.basis.lift_mul QuaternionAlgebra.Basis.lift_mul
 
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 theorem lift_smul (r : R) (x : ℍ[R,c₁,c₂]) : q.lift (r • x) = r • q.lift x := by
   simp [lift, mul_smul, ← Algebra.smul_def]
 #align quaternion_algebra.basis.lift_smul QuaternionAlgebra.Basis.lift_smul
 
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 /-- A `quaternion_algebra.basis` implies an `alg_hom` from the quaternions. -/
 @[simps]
 def liftHom : ℍ[R,c₁,c₂] →ₐ[R] A :=
@@ -262,12 +184,6 @@ def compHom (F : A →ₐ[R] B) : Basis B c₁ c₂
 
 end Basis
 
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-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R}, Equiv.{succ u2, max (succ u2) (succ u1)} (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (AlgHom.{u1, u1, u2} R (QuaternionAlgebra.{u1} R c₁ c₂) A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (Ring.toSemiring.{u2} A _inst_2) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_4)
-Case conversion may be inaccurate. Consider using '#align quaternion_algebra.lift QuaternionAlgebra.liftₓ'. -/
 /-- A quaternionic basis on `A` is equivalent to a map from the quaternion algebra to `A`. -/
 @[simps]
 def lift : Basis A c₁ c₂ ≃ (ℍ[R,c₁,c₂] →ₐ[R] A)

38df578a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -192,10 +192,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (x : QuaternionAlgebra.{u2} R c₁ c₂) (y : QuaternionAlgebra.{u2} R c₁ c₂), Eq.{succ u1} A (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (HAdd.hAdd.{u2, u2, u2} (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (instHAdd.{u2} (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.instAddQuaternionAlgebra.{u2} R _inst_1 c₁ c₂)) x y)) (HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (Distrib.toAdd.{u1} A (NonUnitalNonAssocSemiring.toDistrib.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A _inst_2)))))) (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x) (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q y))
 Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_addₓ'. -/
-theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y :=
-  by
-  simp [lift, add_smul]
-  abel
+theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y := by
+  simp [lift, add_smul]; abel
 #align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_add
 
 /- warning: quaternion_algebra.basis.lift_mul -> QuaternionAlgebra.Basis.lift_mul is a dubious translation:

38df578a

bump to nightly-2023-05-24-03

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

2c55cf2c

Diff

@@ -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 algebra.quaternion_basis
-! leanprover-community/mathlib commit 3aa5b8a9ed7a7cabd36e6e1d022c9858ab8a8c2d
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Tactic.Ring
 /-!
 # Basis on a quaternion-like algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `quaternion_algebra.basis A c₁ c₂`: a basis for a subspace of an `R`-algebra `A` that has the

3aa5b8a9

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -31,6 +31,7 @@ open Quaternion
 
 namespace QuaternionAlgebra
 
+#print QuaternionAlgebra.Basis /-
 /-- A quaternion basis contains the information both sufficient and necessary to construct an
 `R`-algebra homomorphism from `ℍ[R,c₁,c₂]` to `A`; or equivalently, a surjective
 `R`-algebra homomorphism from `ℍ[R,c₁,c₂]` to an `R`-subalgebra of `A`.
@@ -44,6 +45,7 @@ structure Basis {R : Type _} (A : Type _) [CommRing R] [Ring A] [Algebra R A] (c
   i_mul_j : i * j = k
   j_mul_i : j * i = -k
 #align quaternion_algebra.basis QuaternionAlgebra.Basis
+-/
 
 variable {R : Type _} {A B : Type _} [CommRing R] [Ring A] [Ring B] [Algebra R A] [Algebra R B]
 
@@ -51,6 +53,12 @@ variable {c₁ c₂ : R}
 
 namespace Basis
 
+/- warning: quaternion_algebra.basis.ext -> QuaternionAlgebra.Basis.ext is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} {{q₁ : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂}} {{q₂ : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂}}, (Eq.{succ u2} A (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u2} A (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u2} (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) q₁ q₂)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2)] {c₁ : R} {c₂ : R} {{q₁ : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂}} {{q₂ : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂}}, (Eq.{succ u1} A (QuaternionAlgebra.Basis.i.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.i.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u1} A (QuaternionAlgebra.Basis.j.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₁) (QuaternionAlgebra.Basis.j.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q₂)) -> (Eq.{succ u1} (QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂) q₁ q₂)
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.ext QuaternionAlgebra.Basis.extₓ'. -/
 /-- Since `k` is redundant, it is not necessary to show `q₁.k = q₂.k` when showing `q₁ = q₂`. -/
 @[ext]
 protected theorem ext ⦃q₁ q₂ : Basis A c₁ c₂⦄ (hi : q₁.i = q₂.i) (hj : q₁.j = q₂.j) : q₁ = q₂ :=
@@ -64,6 +72,12 @@ protected theorem ext ⦃q₁ q₂ : Basis A c₁ c₂⦄ (hi : q₁.i = q₂.i)
 
 variable (R)
 
+/- warning: quaternion_algebra.basis.self -> QuaternionAlgebra.Basis.self is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, QuaternionAlgebra.Basis.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) _inst_1 (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) c₁ c₂
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {c₁ : R} {c₂ : R}, QuaternionAlgebra.Basis.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) _inst_1 (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) c₁ c₂
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.self QuaternionAlgebra.Basis.selfₓ'. -/
 /-- There is a natural quaternionic basis for the `quaternion_algebra`. -/
 @[simps i j k]
 protected def self : Basis ℍ[R,c₁,c₂] c₁ c₂
@@ -88,49 +102,105 @@ include q
 
 attribute [simp] i_mul_i j_mul_j i_mul_j j_mul_i
 
+/- warning: quaternion_algebra.basis.i_mul_k -> QuaternionAlgebra.Basis.i_mul_k is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂), Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_2)))) (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q) (QuaternionAlgebra.Basis.k.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q)) (HSMul.hSMul.{u1, u2, u2} R A A (instHSMul.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_4)) c₁ (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.i_mul_k QuaternionAlgebra.Basis.i_mul_kₓ'. -/
 @[simp]
 theorem i_mul_k : q.i * q.k = c₁ • q.j := by
   rw [← i_mul_j, ← mul_assoc, i_mul_i, smul_mul_assoc, one_mul]
 #align quaternion_algebra.basis.i_mul_k QuaternionAlgebra.Basis.i_mul_k
 
+/- warning: quaternion_algebra.basis.k_mul_i -> QuaternionAlgebra.Basis.k_mul_i is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂), Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_2))) (QuaternionAlgebra.Basis.k.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q) (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_4))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) c₁) (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂), Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_2)))) (QuaternionAlgebra.Basis.k.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q) (QuaternionAlgebra.Basis.i.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q)) (HSMul.hSMul.{u1, u2, u2} R A A (instHSMul.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_4)) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) c₁) (QuaternionAlgebra.Basis.j.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.k_mul_i QuaternionAlgebra.Basis.k_mul_iₓ'. -/
 @[simp]
 theorem k_mul_i : q.k * q.i = -c₁ • q.j := by
   rw [← i_mul_j, mul_assoc, j_mul_i, mul_neg, i_mul_k, neg_smul]
 #align quaternion_algebra.basis.k_mul_i QuaternionAlgebra.Basis.k_mul_i
 
+/- warning: quaternion_algebra.basis.k_mul_j -> QuaternionAlgebra.Basis.k_mul_j is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.k_mul_j QuaternionAlgebra.Basis.k_mul_jₓ'. -/
 @[simp]
 theorem k_mul_j : q.k * q.j = c₂ • q.i := by
   rw [← i_mul_j, mul_assoc, j_mul_j, mul_smul_comm, mul_one]
 #align quaternion_algebra.basis.k_mul_j QuaternionAlgebra.Basis.k_mul_j
 
+/- warning: quaternion_algebra.basis.j_mul_k -> QuaternionAlgebra.Basis.j_mul_k is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.j_mul_k QuaternionAlgebra.Basis.j_mul_kₓ'. -/
 @[simp]
 theorem j_mul_k : q.j * q.k = -c₂ • q.i := by
   rw [← i_mul_j, ← mul_assoc, j_mul_i, neg_mul, k_mul_j, neg_smul]
 #align quaternion_algebra.basis.j_mul_k QuaternionAlgebra.Basis.j_mul_k
 
+/- warning: quaternion_algebra.basis.k_mul_k -> QuaternionAlgebra.Basis.k_mul_k is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.k_mul_k QuaternionAlgebra.Basis.k_mul_kₓ'. -/
 @[simp]
 theorem k_mul_k : q.k * q.k = -((c₁ * c₂) • 1) := by
   rw [← i_mul_j, mul_assoc, ← mul_assoc q.j _ _, j_mul_i, ← i_mul_j, ← mul_assoc, mul_neg, ←
     mul_assoc, i_mul_i, smul_mul_assoc, one_mul, neg_mul, smul_mul_assoc, j_mul_j, smul_smul]
 #align quaternion_algebra.basis.k_mul_k QuaternionAlgebra.Basis.k_mul_k
 
+#print QuaternionAlgebra.Basis.lift /-
 /-- Intermediate result used to define `quaternion_algebra.basis.lift_hom`. -/
 def lift (x : ℍ[R,c₁,c₂]) : A :=
   algebraMap R _ x.re + x.imI • q.i + x.imJ • q.j + x.imK • q.k
 #align quaternion_algebra.basis.lift QuaternionAlgebra.Basis.lift
+-/
 
+/- warning: quaternion_algebra.basis.lift_zero -> QuaternionAlgebra.Basis.lift_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_zero QuaternionAlgebra.Basis.lift_zeroₓ'. -/
 theorem lift_zero : q.lift (0 : ℍ[R,c₁,c₂]) = 0 := by simp [lift]
 #align quaternion_algebra.basis.lift_zero QuaternionAlgebra.Basis.lift_zero
 
+/- warning: quaternion_algebra.basis.lift_one -> QuaternionAlgebra.Basis.lift_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_one QuaternionAlgebra.Basis.lift_oneₓ'. -/
 theorem lift_one : q.lift (1 : ℍ[R,c₁,c₂]) = 1 := by simp [lift]
 #align quaternion_algebra.basis.lift_one QuaternionAlgebra.Basis.lift_one
 
+/- warning: quaternion_algebra.basis.lift_add -> QuaternionAlgebra.Basis.lift_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (x : QuaternionAlgebra.{u1} R c₁ c₂) (y : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u2} A (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (HAdd.hAdd.{u1, u1, u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (instHAdd.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.hasAdd.{u1} R _inst_1 c₁ c₂)) x y)) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (Ring.toDistrib.{u2} A _inst_2))) (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x) (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q y))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (x : QuaternionAlgebra.{u2} R c₁ c₂) (y : QuaternionAlgebra.{u2} R c₁ c₂), Eq.{succ u1} A (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (HAdd.hAdd.{u2, u2, u2} (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (instHAdd.{u2} (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.instAddQuaternionAlgebra.{u2} R _inst_1 c₁ c₂)) x y)) (HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (Distrib.toAdd.{u1} A (NonUnitalNonAssocSemiring.toDistrib.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A _inst_2)))))) (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x) (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q y))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_addₓ'. -/
 theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y :=
   by
   simp [lift, add_smul]
   abel
 #align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_add
 
+/- warning: quaternion_algebra.basis.lift_mul -> QuaternionAlgebra.Basis.lift_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (x : QuaternionAlgebra.{u1} R c₁ c₂) (y : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u2} A (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (HMul.hMul.{u1, u1, u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.{u1} R c₁ c₂) (instHMul.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.hasMul.{u1} R _inst_1 c₁ c₂)) x y)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_2))) (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x) (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q y))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (x : QuaternionAlgebra.{u2} R c₁ c₂) (y : QuaternionAlgebra.{u2} R c₁ c₂), Eq.{succ u1} A (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (HMul.hMul.{u2, u2, u2} (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (instHMul.{u2} (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.instMulQuaternionAlgebra.{u2} R _inst_1 c₁ c₂)) x y)) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A _inst_2)))) (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x) (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q y))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_mul QuaternionAlgebra.Basis.lift_mulₓ'. -/
 theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y :=
   by
   simp only [lift, Algebra.algebraMap_eq_smul_one]
@@ -147,10 +217,22 @@ theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y
   abel
 #align quaternion_algebra.basis.lift_mul QuaternionAlgebra.Basis.lift_mul
 
+/- warning: quaternion_algebra.basis.lift_smul -> QuaternionAlgebra.Basis.lift_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (r : R) (x : QuaternionAlgebra.{u1} R c₁ c₂), Eq.{succ u2} A (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (SMul.smul.{u1, u1} R (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.hasSmul.{u1, u1} R R _inst_1 c₁ c₂ (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))))) r x)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_4))))) r (QuaternionAlgebra.Basis.lift.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2)] {c₁ : R} {c₂ : R} (q : QuaternionAlgebra.Basis.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (r : R) (x : QuaternionAlgebra.{u2} R c₁ c₂), Eq.{succ u1} A (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q (HSMul.hSMul.{u2, u2, u2} R (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.{u2} R c₁ c₂) (instHSMul.{u2, u2} R (QuaternionAlgebra.{u2} R c₁ c₂) (QuaternionAlgebra.instSMulQuaternionAlgebra.{u2, u2} R R c₁ c₂ (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) r x)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_2) _inst_4)) r (QuaternionAlgebra.Basis.lift.{u2, u1} R A _inst_1 _inst_2 _inst_4 c₁ c₂ q x))
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_smul QuaternionAlgebra.Basis.lift_smulₓ'. -/
 theorem lift_smul (r : R) (x : ℍ[R,c₁,c₂]) : q.lift (r • x) = r • q.lift x := by
   simp [lift, mul_smul, ← Algebra.smul_def]
 #align quaternion_algebra.basis.lift_smul QuaternionAlgebra.Basis.lift_smul
 
+/- warning: quaternion_algebra.basis.lift_hom -> QuaternionAlgebra.Basis.liftHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R}, (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) -> (AlgHom.{u1, u1, u2} R (QuaternionAlgebra.{u1} R c₁ c₂) A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (Ring.toSemiring.{u2} A _inst_2) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_4)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R}, (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) -> (AlgHom.{u1, u1, u2} R (QuaternionAlgebra.{u1} R c₁ c₂) A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (Ring.toSemiring.{u2} A _inst_2) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_4)
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.basis.lift_hom QuaternionAlgebra.Basis.liftHomₓ'. -/
 /-- A `quaternion_algebra.basis` implies an `alg_hom` from the quaternions. -/
 @[simps]
 def liftHom : ℍ[R,c₁,c₂] →ₐ[R] A :=
@@ -162,6 +244,7 @@ def liftHom : ℍ[R,c₁,c₂] →ₐ[R] A :=
       map_mul' := q.lift_mul } q.lift_smul
 #align quaternion_algebra.basis.lift_hom QuaternionAlgebra.Basis.liftHom
 
+#print QuaternionAlgebra.Basis.compHom /-
 /-- Transform a `quaternion_algebra.basis` through an `alg_hom`. -/
 @[simps i j k]
 def compHom (F : A →ₐ[R] B) : Basis B c₁ c₂
@@ -174,9 +257,16 @@ def compHom (F : A →ₐ[R] B) : Basis B c₁ c₂
   i_mul_j := by rw [← F.map_mul, q.i_mul_j]
   j_mul_i := by rw [← F.map_mul, q.j_mul_i, F.map_neg]
 #align quaternion_algebra.basis.comp_hom QuaternionAlgebra.Basis.compHom
+-/
 
 end Basis
 
+/- warning: quaternion_algebra.lift -> QuaternionAlgebra.lift is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R}, Equiv.{succ u2, max (succ u1) (succ u2)} (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (AlgHom.{u1, u1, u2} R (QuaternionAlgebra.{u1} R c₁ c₂) A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.ring.{u1} R _inst_1 c₁ c₂)) (Ring.toSemiring.{u2} A _inst_2) (QuaternionAlgebra.algebra.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_4)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] {c₁ : R} {c₂ : R}, Equiv.{succ u2, max (succ u2) (succ u1)} (QuaternionAlgebra.Basis.{u1, u2} R A _inst_1 _inst_2 _inst_4 c₁ c₂) (AlgHom.{u1, u1, u2} R (QuaternionAlgebra.{u1} R c₁ c₂) A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (QuaternionAlgebra.{u1} R c₁ c₂) (QuaternionAlgebra.instRing.{u1} R _inst_1 c₁ c₂)) (Ring.toSemiring.{u2} A _inst_2) (QuaternionAlgebra.instAlgebraQuaternionAlgebraToSemiringInstRing.{u1, u1} R R _inst_1 c₁ c₂ (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_4)
+Case conversion may be inaccurate. Consider using '#align quaternion_algebra.lift QuaternionAlgebra.liftₓ'. -/
 /-- A quaternionic basis on `A` is equivalent to a map from the quaternion algebra to `A`. -/
 @[simps]
 def lift : Basis A c₁ c₂ ≃ (ℍ[R,c₁,c₂] →ₐ[R] A)

3aa5b8a9

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

3aa5b8a9

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -43,7 +43,6 @@ structure Basis {R : Type*} (A : Type*) [CommRing R] [Ring A] [Algebra R A] (c
 #align quaternion_algebra.basis QuaternionAlgebra.Basis
 
 variable {R : Type*} {A B : Type*} [CommRing R] [Ring A] [Ring B] [Algebra R A] [Algebra R B]
-
 variable {c₁ c₂ : R}
 
 namespace Basis

3aa5b8a9

feat(Algebra/QuaternionBasis): extensionality for algebra morphisms from quaternions (#9441)

This result was basically already here, this just registers it with ext.

0c2c47a2

Diff

@@ -180,4 +180,25 @@ def lift : Basis A c₁ c₂ ≃ (ℍ[R,c₁,c₂] →ₐ[R] A) where
     congr <;> simp
 #align quaternion_algebra.lift QuaternionAlgebra.lift
 
+/-- Two `R`-algebra morphisms from a quaternion algebra are equal if they agree on `i` and `j`. -/
+@[ext]
+theorem hom_ext ⦃f g : ℍ[R,c₁,c₂] →ₐ[R] A⦄
+    (hi : f (Basis.self R).i = g (Basis.self R).i) (hj : f (Basis.self R).j = g (Basis.self R).j) :
+    f = g :=
+  lift.symm.injective <| Basis.ext hi hj
+
 end QuaternionAlgebra
+
+namespace Quaternion
+variable {R A : Type*} [CommRing R] [Ring A] [Algebra R A]
+
+open QuaternionAlgebra (Basis)
+
+/-- Two `R`-algebra morphisms from the quaternions are equal if they agree on `i` and `j`. -/
+@[ext]
+theorem hom_ext ⦃f g : ℍ[R] →ₐ[R] A⦄
+    (hi : f (Basis.self R).i = g (Basis.self R).i) (hj : f (Basis.self R).j = g (Basis.self R).j) :
+    f = g :=
+  QuaternionAlgebra.hom_ext hi hj
+
+end Quaternion

3aa5b8a9

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -119,7 +119,7 @@ theorem lift_one : q.lift (1 : ℍ[R,c₁,c₂]) = 1 := by simp [lift]
 #align quaternion_algebra.basis.lift_one QuaternionAlgebra.Basis.lift_one
 
 theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y := by
-  simp [lift, add_smul]
+  simp only [lift, add_re, map_add, add_imI, add_smul, add_imJ, add_imK]
   abel
 #align quaternion_algebra.basis.lift_add QuaternionAlgebra.Basis.lift_add
 
@@ -132,7 +132,7 @@ theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y
   simp only [mul_comm _ c₁, mul_right_comm _ _ c₁]
   simp only [mul_comm _ c₂, mul_right_comm _ _ c₂]
   simp only [← mul_comm c₁ c₂, ← mul_assoc]
-  simp [sub_eq_add_neg, add_smul, ← add_assoc]
+  simp only [mul_re, sub_eq_add_neg, add_smul, neg_smul, mul_imI, ← add_assoc, mul_imJ, mul_imK]
   abel
 #align quaternion_algebra.basis.lift_mul QuaternionAlgebra.Basis.lift_mul

3aa5b8a9

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -125,9 +125,7 @@ theorem lift_add (x y : ℍ[R,c₁,c₂]) : q.lift (x + y) = q.lift x + q.lift y
 
 theorem lift_mul (x y : ℍ[R,c₁,c₂]) : q.lift (x * y) = q.lift x * q.lift y := by
   simp only [lift, Algebra.algebraMap_eq_smul_one]
-  simp only [add_mul]
-  simp_rw [add_mul, mul_add, smul_mul_assoc, mul_smul_comm, one_mul, mul_one, ← Algebra.smul_def,
-    smul_add, smul_smul]
+  simp_rw [add_mul, mul_add, smul_mul_assoc, mul_smul_comm, one_mul, mul_one, smul_smul]
   simp only [i_mul_i, j_mul_j, i_mul_j, j_mul_i, i_mul_k, k_mul_i, k_mul_j, j_mul_k, k_mul_k]
   simp only [smul_smul, smul_neg, sub_eq_add_neg, add_smul, ← add_assoc, mul_neg, neg_smul]
   simp only [mul_right_comm _ _ (c₁ * c₂), mul_comm _ (c₁ * c₂)]

3aa5b8a9

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -34,7 +34,7 @@ namespace QuaternionAlgebra
 
 Note that for definitional convenience, `k` is provided as a field even though `i_mul_j` fully
 determines it. -/
-structure Basis {R : Type _} (A : Type _) [CommRing R] [Ring A] [Algebra R A] (c₁ c₂ : R) where
+structure Basis {R : Type*} (A : Type*) [CommRing R] [Ring A] [Algebra R A] (c₁ c₂ : R) where
   (i j k : A)
   i_mul_i : i * i = c₁ • (1 : A)
   j_mul_j : j * j = c₂ • (1 : A)
@@ -42,7 +42,7 @@ structure Basis {R : Type _} (A : Type _) [CommRing R] [Ring A] [Algebra R A] (c
   j_mul_i : j * i = -k
 #align quaternion_algebra.basis QuaternionAlgebra.Basis
 
-variable {R : Type _} {A B : Type _} [CommRing R] [Ring A] [Ring B] [Algebra R A] [Algebra R B]
+variable {R : Type*} {A B : Type*} [CommRing R] [Ring A] [Ring B] [Algebra R A] [Algebra R B]
 
 variable {c₁ c₂ : R}

3aa5b8a9

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 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 algebra.quaternion_basis
-! leanprover-community/mathlib commit 3aa5b8a9ed7a7cabd36e6e1d022c9858ab8a8c2d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Quaternion
 import Mathlib.Tactic.Ring
 
+#align_import algebra.quaternion_basis from "leanprover-community/mathlib"@"3aa5b8a9ed7a7cabd36e6e1d022c9858ab8a8c2d"
+
 /-!
 # Basis on a quaternion-like algebra

3aa5b8a9

feat: port Algebra.QuaternionBasis (#4199)

75a6e216

`algebra.quaternion_basis` ⟷ `Mathlib.Algebra.QuaternionBasis`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 512

algebra.quaternion_basis ⟷ Mathlib.Algebra.QuaternionBasis

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 512

`algebra.quaternion_basis` ⟷ `Mathlib.Algebra.QuaternionBasis`