linear_algebra.clifford_algebra.grading

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

34020e53

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

fdc286cc

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -194,7 +194,7 @@ of vectors. -/
 theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
     (hr :
       ∀ (v) (h : v ∈ (ι Q).range ^ n.val),
-        P v (Submodule.mem_iSup_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
+        P v (Submodule.mem_iSup_of_mem ⟨n.val, n.natCast_zmod_val⟩ h))
     (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
     (hιι_mul :
       ∀ (m₁ m₂) {x hx},

fdc286cc

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
 import LinearAlgebra.CliffordAlgebra.Basic
-import Data.Zmod.Basic
+import Data.ZMod.Basic
 import RingTheory.GradedAlgebra.Basic
 
 #align_import linear_algebra.clifford_algebra.grading from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"

fdc286cc

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -127,7 +127,7 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
   dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
   refine' Submodule.iSup_induction' _ (fun i x hx => _) _ (fun x y hx hy ihx ihy => _) hx'
   · obtain ⟨i, rfl⟩ := i
-    dsimp only [Subtype.coe_mk] at hx 
+    dsimp only [Subtype.coe_mk] at hx
     refine'
       Submodule.pow_induction_on_left' _ (fun r => _) (fun x y i hx hy ihx ihy => _)
         (fun m hm i x hx ih => _) hx

fdc286cc

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ 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.LinearAlgebra.CliffordAlgebra.Basic
-import Mathbin.Data.Zmod.Basic
-import Mathbin.RingTheory.GradedAlgebra.Basic
+import LinearAlgebra.CliffordAlgebra.Basic
+import Data.Zmod.Basic
+import RingTheory.GradedAlgebra.Basic
 
 #align_import linear_algebra.clifford_algebra.grading from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"

fdc286cc

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -90,7 +90,7 @@ theorem evenOdd_mul_le (i j : ZMod 2) : evenOdd Q i * evenOdd Q j ≤ evenOdd Q
 instance evenOdd.gradedMonoid : SetLike.GradedMonoid (evenOdd Q)
     where
   one_mem := Submodule.one_le.mp (one_le_evenOdd_zero Q)
-  mul_mem i j p q hp hq := Submodule.mul_le.mp (evenOdd_mul_le Q _ _) _ hp _ hq
+  hMul_mem i j p q hp hq := Submodule.mul_le.mp (evenOdd_mul_le Q _ _) _ hp _ hq
 #align clifford_algebra.even_odd.graded_monoid CliffordAlgebra.evenOdd.gradedMonoid
 -/

fdc286cc

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 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 linear_algebra.clifford_algebra.grading
-! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.CliffordAlgebra.Basic
 import Mathbin.Data.Zmod.Basic
 import Mathbin.RingTheory.GradedAlgebra.Basic
 
+#align_import linear_algebra.clifford_algebra.grading from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
+
 /-!
 # Results about the grading structure of the clifford algebra

fdc286cc

bump to nightly-2023-06-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

097db3c1

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 linear_algebra.clifford_algebra.grading
-! leanprover-community/mathlib commit 34020e531ebc4e8aac6d449d9eecbcd1508ea8d0
+! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.GradedAlgebra.Basic
 /-!
 # Results about the grading structure of the clifford algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main result is `clifford_algebra.graded_algebra`, which says that the clifford algebra is a
 ℤ₂-graded algebra (or "superalgebra").
 -/

34020e53

bump to nightly-2023-06-23-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

70450a3c

Diff

@@ -30,28 +30,37 @@ open scoped DirectSum
 
 variable (Q)
 
+#print CliffordAlgebra.evenOdd /-
 /-- The even or odd submodule, defined as the supremum of the even or odd powers of
 `(ι Q).range`. `even_odd 0` is the even submodule, and `even_odd 1` is the odd submodule. -/
 def evenOdd (i : ZMod 2) : Submodule R (CliffordAlgebra Q) :=
   ⨆ j : { n : ℕ // ↑n = i }, (ι Q).range ^ (j : ℕ)
 #align clifford_algebra.even_odd CliffordAlgebra.evenOdd
+-/
 
+#print CliffordAlgebra.one_le_evenOdd_zero /-
 theorem one_le_evenOdd_zero : 1 ≤ evenOdd Q 0 :=
   by
   refine' le_trans _ (le_iSup _ ⟨0, Nat.cast_zero⟩)
   exact (pow_zero _).ge
 #align clifford_algebra.one_le_even_odd_zero CliffordAlgebra.one_le_evenOdd_zero
+-/
 
+#print CliffordAlgebra.range_ι_le_evenOdd_one /-
 theorem range_ι_le_evenOdd_one : (ι Q).range ≤ evenOdd Q 1 :=
   by
   refine' le_trans _ (le_iSup _ ⟨1, Nat.cast_one⟩)
   exact (pow_one _).ge
 #align clifford_algebra.range_ι_le_even_odd_one CliffordAlgebra.range_ι_le_evenOdd_one
+-/
 
+#print CliffordAlgebra.ι_mem_evenOdd_one /-
 theorem ι_mem_evenOdd_one (m : M) : ι Q m ∈ evenOdd Q 1 :=
   range_ι_le_evenOdd_one Q <| LinearMap.mem_range_self _ m
 #align clifford_algebra.ι_mem_even_odd_one CliffordAlgebra.ι_mem_evenOdd_one
+-/
 
+#print CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero /-
 theorem ι_mul_ι_mem_evenOdd_zero (m₁ m₂ : M) : ι Q m₁ * ι Q m₂ ∈ evenOdd Q 0 :=
   Submodule.mem_iSup_of_mem ⟨2, rfl⟩
     (by
@@ -60,7 +69,9 @@ theorem ι_mul_ι_mem_evenOdd_zero (m₁ m₂ : M) : ι Q m₁ * ι Q m₂ ∈ e
         Submodule.mul_mem_mul (LinearMap.mem_range_self (ι Q) m₁)
           (LinearMap.mem_range_self (ι Q) m₂))
 #align clifford_algebra.ι_mul_ι_mem_even_odd_zero CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero
+-/
 
+#print CliffordAlgebra.evenOdd_mul_le /-
 theorem evenOdd_mul_le (i j : ZMod 2) : evenOdd Q i * evenOdd Q j ≤ evenOdd Q (i + j) :=
   by
   simp_rw [even_odd, Submodule.iSup_eq_span, Submodule.span_mul_span]
@@ -73,31 +84,41 @@ theorem evenOdd_mul_le (i j : ZMod 2) : evenOdd Q i * evenOdd Q j ≤ evenOdd Q
   simp only [Subtype.coe_mk, Nat.cast_add, pow_add]
   exact Submodule.mul_mem_mul hx' hy'
 #align clifford_algebra.even_odd_mul_le CliffordAlgebra.evenOdd_mul_le
+-/
 
+#print CliffordAlgebra.evenOdd.gradedMonoid /-
 instance evenOdd.gradedMonoid : SetLike.GradedMonoid (evenOdd Q)
     where
   one_mem := Submodule.one_le.mp (one_le_evenOdd_zero Q)
   mul_mem i j p q hp hq := Submodule.mul_le.mp (evenOdd_mul_le Q _ _) _ hp _ hq
 #align clifford_algebra.even_odd.graded_monoid CliffordAlgebra.evenOdd.gradedMonoid
+-/
 
+#print CliffordAlgebra.GradedAlgebra.ι /-
 /-- A version of `clifford_algebra.ι` that maps directly into the graded structure. This is
 primarily an auxiliary construction used to provide `clifford_algebra.graded_algebra`. -/
 def GradedAlgebra.ι : M →ₗ[R] ⨁ i : ZMod 2, evenOdd Q i :=
   DirectSum.lof R (ZMod 2) (fun i => ↥(evenOdd Q i)) 1 ∘ₗ (ι Q).codRestrict _ (ι_mem_evenOdd_one Q)
 #align clifford_algebra.graded_algebra.ι CliffordAlgebra.GradedAlgebra.ι
+-/
 
+#print CliffordAlgebra.GradedAlgebra.ι_apply /-
 theorem GradedAlgebra.ι_apply (m : M) :
     GradedAlgebra.ι Q m = DirectSum.of (fun i => ↥(evenOdd Q i)) 1 ⟨ι Q m, ι_mem_evenOdd_one Q m⟩ :=
   rfl
 #align clifford_algebra.graded_algebra.ι_apply CliffordAlgebra.GradedAlgebra.ι_apply
+-/
 
+#print CliffordAlgebra.GradedAlgebra.ι_sq_scalar /-
 theorem GradedAlgebra.ι_sq_scalar (m : M) :
     GradedAlgebra.ι Q m * GradedAlgebra.ι Q m = algebraMap R _ (Q m) :=
   by
   rw [graded_algebra.ι_apply Q, DirectSum.of_mul_of, DirectSum.algebraMap_apply]
   refine' DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext rfl <| ι_sq_scalar _ _)
 #align clifford_algebra.graded_algebra.ι_sq_scalar CliffordAlgebra.GradedAlgebra.ι_sq_scalar
+-/
 
+#print CliffordAlgebra.GradedAlgebra.lift_ι_eq /-
 theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
     lift Q ⟨by apply graded_algebra.ι Q, GradedAlgebra.ι_sq_scalar Q⟩ x' =
       DirectSum.of (fun i => evenOdd Q i) i' x' :=
@@ -123,7 +144,9 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
     apply dfinsupp.single_eq_zero.mpr; rfl
   · rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
 #align clifford_algebra.graded_algebra.lift_ι_eq CliffordAlgebra.GradedAlgebra.lift_ι_eq
+-/
 
+#print CliffordAlgebra.gradedAlgebra /-
 /-- The clifford algebra is graded by the even and odd parts. -/
 instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
   GradedAlgebra.ofAlgHom (evenOdd Q)
@@ -139,7 +162,9 @@ instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
       rw [lift_ι_apply, graded_algebra.ι_apply Q, DirectSum.coeAlgHom_of, Subtype.coe_mk])
     (by apply graded_algebra.lift_ι_eq Q)
 #align clifford_algebra.graded_algebra CliffordAlgebra.gradedAlgebra
+-/
 
+#print CliffordAlgebra.iSup_ι_range_eq_top /-
 theorem iSup_ι_range_eq_top : (⨆ i : ℕ, (ι Q).range ^ i) = ⊤ :=
   by
   rw [← (DirectSum.Decomposition.isInternal (even_odd Q)).submodule_iSup_eq_top, eq_comm]
@@ -150,14 +175,18 @@ theorem iSup_ι_range_eq_top : (⨆ i : ℕ, (ι Q).range ^ i) = ⊤ :=
     _ = ⨆ i : ℕ, (ι Q).range ^ i :=
       Function.Surjective.iSup_congr (fun i => i.2) (fun i => ⟨⟨_, i, rfl⟩, rfl⟩) fun _ => rfl
 #align clifford_algebra.supr_ι_range_eq_top CliffordAlgebra.iSup_ι_range_eq_top
+-/
 
+#print CliffordAlgebra.evenOdd_isCompl /-
 theorem evenOdd_isCompl : IsCompl (evenOdd Q 0) (evenOdd Q 1) :=
   (DirectSum.Decomposition.isInternal (evenOdd Q)).IsCompl zero_ne_one <|
     by
     have : (Finset.univ : Finset (ZMod 2)) = {0, 1} := rfl
     simpa using congr_arg (coe : Finset (ZMod 2) → Set (ZMod 2)) this
 #align clifford_algebra.even_odd_is_compl CliffordAlgebra.evenOdd_isCompl
+-/
 
+#print CliffordAlgebra.evenOdd_induction /-
 /-- To show a property is true on the even or odd part, it suffices to show it is true on the
 scalars or vectors (respectively), closed under addition, and under left-multiplication by a pair
 of vectors. -/
@@ -202,7 +231,9 @@ theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
   · intro x y hx hy
     apply hadd
 #align clifford_algebra.even_odd_induction CliffordAlgebra.evenOdd_induction
+-/
 
+#print CliffordAlgebra.even_induction /-
 /-- To show a property is true on the even parts, it suffices to show it is true on the
 scalars, closed under addition, and under left-multiplication by a pair of vectors. -/
 @[elab_as_elim]
@@ -221,7 +252,9 @@ theorem even_induction {P : ∀ x, x ∈ evenOdd Q 0 → Prop}
   rintro ⟨r, rfl⟩
   exact hr r
 #align clifford_algebra.even_induction CliffordAlgebra.even_induction
+-/
 
+#print CliffordAlgebra.odd_induction /-
 /-- To show a property is true on the odd parts, it suffices to show it is true on the
 vectors, closed under addition, and under left-multiplication by a pair of vectors. -/
 @[elab_as_elim]
@@ -240,6 +273,7 @@ theorem odd_induction {P : ∀ x, x ∈ evenOdd Q 1 → Prop}
   rintro ⟨v, rfl⟩
   exact hι v
 #align clifford_algebra.odd_induction CliffordAlgebra.odd_induction
+-/
 
 end CliffordAlgebra

34020e53

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -149,7 +149,6 @@ theorem iSup_ι_range_eq_top : (⨆ i : ℕ, (ι Q).range ^ i) = ⊤ :=
       by rw [iSup_sigma]
     _ = ⨆ i : ℕ, (ι Q).range ^ i :=
       Function.Surjective.iSup_congr (fun i => i.2) (fun i => ⟨⟨_, i, rfl⟩, rfl⟩) fun _ => rfl
-    
 #align clifford_algebra.supr_ι_range_eq_top CliffordAlgebra.iSup_ι_range_eq_top
 
 theorem evenOdd_isCompl : IsCompl (evenOdd Q 0) (evenOdd Q 1) :=

34020e53

bump to nightly-2023-06-05-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

43f0fba3

Diff

@@ -163,7 +163,7 @@ theorem evenOdd_isCompl : IsCompl (evenOdd Q 0) (evenOdd Q 1) :=
 scalars or vectors (respectively), closed under addition, and under left-multiplication by a pair
 of vectors. -/
 @[elab_as_elim]
-theorem evenOddInduction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
+theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
     (hr :
       ∀ (v) (h : v ∈ (ι Q).range ^ n.val),
         P v (Submodule.mem_iSup_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
@@ -202,12 +202,12 @@ theorem evenOddInduction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
         apply hadd ihx ihy
   · intro x y hx hy
     apply hadd
-#align clifford_algebra.even_odd_induction CliffordAlgebra.evenOddInduction
+#align clifford_algebra.even_odd_induction CliffordAlgebra.evenOdd_induction
 
 /-- To show a property is true on the even parts, it suffices to show it is true on the
 scalars, closed under addition, and under left-multiplication by a pair of vectors. -/
 @[elab_as_elim]
-theorem evenInduction {P : ∀ x, x ∈ evenOdd Q 0 → Prop}
+theorem even_induction {P : ∀ x, x ∈ evenOdd Q 0 → Prop}
     (hr : ∀ r : R, P (algebraMap _ _ r) (SetLike.algebraMap_mem_graded _ _))
     (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
     (hιι_mul :
@@ -221,12 +221,13 @@ theorem evenInduction {P : ∀ x, x ∈ evenOdd Q 0 → Prop}
   simp_rw [ZMod.val_zero, pow_zero]
   rintro ⟨r, rfl⟩
   exact hr r
-#align clifford_algebra.even_induction CliffordAlgebra.evenInduction
+#align clifford_algebra.even_induction CliffordAlgebra.even_induction
 
 /-- To show a property is true on the odd parts, it suffices to show it is true on the
 vectors, closed under addition, and under left-multiplication by a pair of vectors. -/
 @[elab_as_elim]
-theorem oddInduction {P : ∀ x, x ∈ evenOdd Q 1 → Prop} (hι : ∀ v, P (ι Q v) (ι_mem_evenOdd_one _ _))
+theorem odd_induction {P : ∀ x, x ∈ evenOdd Q 1 → Prop}
+    (hι : ∀ v, P (ι Q v) (ι_mem_evenOdd_one _ _))
     (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
     (hιι_mul :
       ∀ (m₁ m₂) {x hx},
@@ -239,7 +240,7 @@ theorem oddInduction {P : ∀ x, x ∈ evenOdd Q 1 → Prop} (hι : ∀ v, P (ι
   simp_rw [ZMod.val_one, pow_one]
   rintro ⟨v, rfl⟩
   exact hι v
-#align clifford_algebra.odd_induction CliffordAlgebra.oddInduction
+#align clifford_algebra.odd_induction CliffordAlgebra.odd_induction
 
 end CliffordAlgebra

34020e53

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -106,7 +106,7 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
   dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
   refine' Submodule.iSup_induction' _ (fun i x hx => _) _ (fun x y hx hy ihx ihy => _) hx'
   · obtain ⟨i, rfl⟩ := i
-    dsimp only [Subtype.coe_mk] at hx
+    dsimp only [Subtype.coe_mk] at hx 
     refine'
       Submodule.pow_induction_on_left' _ (fun r => _) (fun x y i hx hy ihx ihy => _)
         (fun m hm i x hx ih => _) hx
@@ -145,7 +145,7 @@ theorem iSup_ι_range_eq_top : (⨆ i : ℕ, (ι Q).range ^ i) = ⊤ :=
   rw [← (DirectSum.Decomposition.isInternal (even_odd Q)).submodule_iSup_eq_top, eq_comm]
   calc
     (⨆ (i : ZMod 2) (j : { n // ↑n = i }), (ι Q).range ^ ↑j) =
-        ⨆ i : Σi : ZMod 2, { n : ℕ // ↑n = i }, (ι Q).range ^ (i.2 : ℕ) :=
+        ⨆ i : Σ i : ZMod 2, { n : ℕ // ↑n = i }, (ι Q).range ^ (i.2 : ℕ) :=
       by rw [iSup_sigma]
     _ = ⨆ i : ℕ, (ι Q).range ^ i :=
       Function.Surjective.iSup_congr (fun i => i.2) (fun i => ⟨⟨_, i, rfl⟩, rfl⟩) fun _ => rfl

34020e53

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ variable {R M : Type _} [CommRing R] [AddCommGroup M] [Module R M]
 
 variable {Q : QuadraticForm R M}
 
-open DirectSum
+open scoped DirectSum
 
 variable (Q)

34020e53

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -110,10 +110,8 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
     refine'
       Submodule.pow_induction_on_left' _ (fun r => _) (fun x y i hx hy ihx ihy => _)
         (fun m hm i x hx ih => _) hx
-    · rw [AlgHom.commutes, DirectSum.algebraMap_apply]
-      rfl
-    · rw [AlgHom.map_add, ihx, ihy, ← map_add]
-      rfl
+    · rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
+    · rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
     · obtain ⟨_, rfl⟩ := hm
       rw [AlgHom.map_mul, ih, lift_ι_apply, graded_algebra.ι_apply Q, DirectSum.of_mul_of]
       refine' DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext _ _) <;>
@@ -122,10 +120,8 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
       rfl
   · rw [AlgHom.map_zero]
     apply Eq.symm
-    apply dfinsupp.single_eq_zero.mpr
-    rfl
-  · rw [AlgHom.map_add, ihx, ihy, ← map_add]
-    rfl
+    apply dfinsupp.single_eq_zero.mpr; rfl
+  · rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
 #align clifford_algebra.graded_algebra.lift_ι_eq CliffordAlgebra.GradedAlgebra.lift_ι_eq
 
 /-- The clifford algebra is graded by the even and odd parts. -/

34020e53

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -38,13 +38,13 @@ def evenOdd (i : ZMod 2) : Submodule R (CliffordAlgebra Q) :=
 
 theorem one_le_evenOdd_zero : 1 ≤ evenOdd Q 0 :=
   by
-  refine' le_trans _ (le_supᵢ _ ⟨0, Nat.cast_zero⟩)
+  refine' le_trans _ (le_iSup _ ⟨0, Nat.cast_zero⟩)
   exact (pow_zero _).ge
 #align clifford_algebra.one_le_even_odd_zero CliffordAlgebra.one_le_evenOdd_zero
 
 theorem range_ι_le_evenOdd_one : (ι Q).range ≤ evenOdd Q 1 :=
   by
-  refine' le_trans _ (le_supᵢ _ ⟨1, Nat.cast_one⟩)
+  refine' le_trans _ (le_iSup _ ⟨1, Nat.cast_one⟩)
   exact (pow_one _).ge
 #align clifford_algebra.range_ι_le_even_odd_one CliffordAlgebra.range_ι_le_evenOdd_one
 
@@ -53,7 +53,7 @@ theorem ι_mem_evenOdd_one (m : M) : ι Q m ∈ evenOdd Q 1 :=
 #align clifford_algebra.ι_mem_even_odd_one CliffordAlgebra.ι_mem_evenOdd_one
 
 theorem ι_mul_ι_mem_evenOdd_zero (m₁ m₂ : M) : ι Q m₁ * ι Q m₂ ∈ evenOdd Q 0 :=
-  Submodule.mem_supᵢ_of_mem ⟨2, rfl⟩
+  Submodule.mem_iSup_of_mem ⟨2, rfl⟩
     (by
       rw [Subtype.coe_mk, pow_two]
       exact
@@ -63,7 +63,7 @@ theorem ι_mul_ι_mem_evenOdd_zero (m₁ m₂ : M) : ι Q m₁ * ι Q m₂ ∈ e
 
 theorem evenOdd_mul_le (i j : ZMod 2) : evenOdd Q i * evenOdd Q j ≤ evenOdd Q (i + j) :=
   by
-  simp_rw [even_odd, Submodule.supᵢ_eq_span, Submodule.span_mul_span]
+  simp_rw [even_odd, Submodule.iSup_eq_span, Submodule.span_mul_span]
   apply Submodule.span_mono
   intro z hz
   obtain ⟨x, y, hx, hy, rfl⟩ := hz
@@ -104,7 +104,7 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
   by
   cases' x' with x' hx'
   dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
-  refine' Submodule.supᵢ_induction' _ (fun i x hx => _) _ (fun x y hx hy ihx ihy => _) hx'
+  refine' Submodule.iSup_induction' _ (fun i x hx => _) _ (fun x y hx hy ihx ihy => _) hx'
   · obtain ⟨i, rfl⟩ := i
     dsimp only [Subtype.coe_mk] at hx
     refine'
@@ -144,17 +144,17 @@ instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
     (by apply graded_algebra.lift_ι_eq Q)
 #align clifford_algebra.graded_algebra CliffordAlgebra.gradedAlgebra
 
-theorem supᵢ_ι_range_eq_top : (⨆ i : ℕ, (ι Q).range ^ i) = ⊤ :=
+theorem iSup_ι_range_eq_top : (⨆ i : ℕ, (ι Q).range ^ i) = ⊤ :=
   by
-  rw [← (DirectSum.Decomposition.isInternal (even_odd Q)).submodule_supᵢ_eq_top, eq_comm]
+  rw [← (DirectSum.Decomposition.isInternal (even_odd Q)).submodule_iSup_eq_top, eq_comm]
   calc
     (⨆ (i : ZMod 2) (j : { n // ↑n = i }), (ι Q).range ^ ↑j) =
         ⨆ i : Σi : ZMod 2, { n : ℕ // ↑n = i }, (ι Q).range ^ (i.2 : ℕ) :=
-      by rw [supᵢ_sigma]
+      by rw [iSup_sigma]
     _ = ⨆ i : ℕ, (ι Q).range ^ i :=
-      Function.Surjective.supᵢ_congr (fun i => i.2) (fun i => ⟨⟨_, i, rfl⟩, rfl⟩) fun _ => rfl
+      Function.Surjective.iSup_congr (fun i => i.2) (fun i => ⟨⟨_, i, rfl⟩, rfl⟩) fun _ => rfl
     
-#align clifford_algebra.supr_ι_range_eq_top CliffordAlgebra.supᵢ_ι_range_eq_top
+#align clifford_algebra.supr_ι_range_eq_top CliffordAlgebra.iSup_ι_range_eq_top
 
 theorem evenOdd_isCompl : IsCompl (evenOdd Q 0) (evenOdd Q 1) :=
   (DirectSum.Decomposition.isInternal (evenOdd Q)).IsCompl zero_ne_one <|
@@ -170,7 +170,7 @@ of vectors. -/
 theorem evenOddInduction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
     (hr :
       ∀ (v) (h : v ∈ (ι Q).range ^ n.val),
-        P v (Submodule.mem_supᵢ_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
+        P v (Submodule.mem_iSup_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
     (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
     (hιι_mul :
       ∀ (m₁ m₂) {x hx},
@@ -179,7 +179,7 @@ theorem evenOddInduction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
             (zero_add n ▸ SetLike.mul_mem_graded (ι_mul_ι_mem_evenOdd_zero Q m₁ m₂) hx))
     (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q n) : P x hx :=
   by
-  apply Submodule.supᵢ_induction' _ _ (hr 0 (Submodule.zero_mem _)) @hadd
+  apply Submodule.iSup_induction' _ _ (hr 0 (Submodule.zero_mem _)) @hadd
   refine' Subtype.rec _
   simp_rw [Subtype.coe_mk, ZMod.nat_coe_zmod_eq_iff, add_comm n.val]
   rintro n' ⟨k, rfl⟩ xv

34020e53

bump to nightly-2023-03-18-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

1c3193ff

Diff

@@ -170,7 +170,7 @@ of vectors. -/
 theorem evenOddInduction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
     (hr :
       ∀ (v) (h : v ∈ (ι Q).range ^ n.val),
-        P v (Submodule.mem_supᵢ_of_mem ⟨n.val, n.nat_cast_zMod_val⟩ h))
+        P v (Submodule.mem_supᵢ_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
     (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
     (hιι_mul :
       ∀ (m₁ m₂) {x hx},
@@ -181,7 +181,7 @@ theorem evenOddInduction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
   by
   apply Submodule.supᵢ_induction' _ _ (hr 0 (Submodule.zero_mem _)) @hadd
   refine' Subtype.rec _
-  simp_rw [Subtype.coe_mk, ZMod.nat_coe_zMod_eq_iff, add_comm n.val]
+  simp_rw [Subtype.coe_mk, ZMod.nat_coe_zmod_eq_iff, add_comm n.val]
   rintro n' ⟨k, rfl⟩ xv
   simp_rw [pow_add, pow_mul]
   refine' Submodule.mul_induction_on' _ _

34020e53

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

34020e53

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -161,7 +161,7 @@ of vectors. -/
 @[elab_as_elim]
 theorem evenOdd_induction (n : ZMod 2) {motive : ∀ x, x ∈ evenOdd Q n → Prop}
     (range_ι_pow : ∀ (v) (h : v ∈ LinearMap.range (ι Q) ^ n.val),
-        motive v (Submodule.mem_iSup_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
+        motive v (Submodule.mem_iSup_of_mem ⟨n.val, n.natCast_zmod_val⟩ h))
     (add : ∀ x y hx hy, motive x hx → motive y hy → motive (x + y) (Submodule.add_mem _ hx hy))
     (ι_mul_ι_mul :
       ∀ m₁ m₂ x hx,

34020e53

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

@@ -20,7 +20,6 @@ The main result is `CliffordAlgebra.gradedAlgebra`, which says that the clifford
 namespace CliffordAlgebra
 
 variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
-
 variable {Q : QuadraticForm R M}
 
 open scoped DirectSum

34020e53

style: homogenise porting notes (#11145)

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".

8be0b69c

Diff

@@ -73,7 +73,7 @@ instance evenOdd.gradedMonoid : SetLike.GradedMonoid (evenOdd Q) where
 
 /-- A version of `CliffordAlgebra.ι` that maps directly into the graded structure. This is
 primarily an auxiliary construction used to provide `CliffordAlgebra.gradedAlgebra`. -/
--- porting note: added `protected`
+-- Porting note: added `protected`
 protected def GradedAlgebra.ι : M →ₗ[R] ⨁ i : ZMod 2, evenOdd Q i :=
   DirectSum.lof R (ZMod 2) (fun i => ↥(evenOdd Q i)) 1 ∘ₗ (ι Q).codRestrict _ (ι_mem_evenOdd_one Q)
 #align clifford_algebra.graded_algebra.ι CliffordAlgebra.GradedAlgebra.ι
@@ -90,7 +90,7 @@ nonrec theorem GradedAlgebra.ι_sq_scalar (m : M) :
 #align clifford_algebra.graded_algebra.ι_sq_scalar CliffordAlgebra.GradedAlgebra.ι_sq_scalar
 
 theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
-    -- porting note: added a second `by apply`
+    -- Porting note: added a second `by apply`
     lift Q ⟨by apply GradedAlgebra.ι Q, by apply GradedAlgebra.ι_sq_scalar Q⟩ x' =
       DirectSum.of (fun i => evenOdd Q i) i' x' := by
   cases' x' with x' hx'
@@ -98,7 +98,7 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
   induction hx' using Submodule.iSup_induction' with
   | mem i x hx =>
     obtain ⟨i, rfl⟩ := i
-    -- porting note: `dsimp only [Subtype.coe_mk] at hx` doesn't work, use `change` instead
+    -- Porting note: `dsimp only [Subtype.coe_mk] at hx` doesn't work, use `change` instead
     change x ∈ LinearMap.range (ι Q) ^ i at hx
     induction hx using Submodule.pow_induction_on_left' with
     | algebraMap r =>
@@ -141,7 +141,7 @@ instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
 theorem iSup_ι_range_eq_top : ⨆ i : ℕ, LinearMap.range (ι Q) ^ i = ⊤ := by
   rw [← (DirectSum.Decomposition.isInternal (evenOdd Q)).submodule_iSup_eq_top, eq_comm]
   calc
-    -- porting note: needs extra annotations, no longer unifies against the goal in the face of
+    -- Porting note: needs extra annotations, no longer unifies against the goal in the face of
     -- ambiguity
     ⨆ (i : ZMod 2) (j : { n : ℕ // ↑n = i }), LinearMap.range (ι Q) ^ (j : ℕ) =
         ⨆ i : Σ i : ZMod 2, { n : ℕ // ↑n = i }, LinearMap.range (ι Q) ^ (i.2 : ℕ) :=
@@ -232,7 +232,7 @@ theorem odd_induction {P : ∀ x, x ∈ evenOdd Q 1 → Prop}
             (zero_add (1 : ZMod 2) ▸ SetLike.mul_mem_graded (ι_mul_ι_mem_evenOdd_zero Q m₁ m₂) hx))
     (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q 1) : P x hx := by
   refine' evenOdd_induction Q 1 (fun ιv => _) (@add) ι_mul_ι_mul x hx
-  -- porting note: was `simp_rw [ZMod.val_one, pow_one]`, lean4#1926
+  -- Porting note: was `simp_rw [ZMod.val_one, pow_one]`, lean4#1926
   intro h; rw [ZMod.val_one, pow_one] at h; revert h
   rintro ⟨v, rfl⟩
   exact ι v

34020e53

chore: rename induction principle arguments around CliffordAlgebra (#10908)

In order to improve the ergonomics of the induction tactic, this renames the arguments of:

ExteriorAlgebra.induction
TensorAlgebra.induction
CliffordAlgebra.induction
CliffordAlgebra.left_induction
CliffordAlgebra.right_induction
CliffordAlgebra.even_induction
CliffordAlgebra.odd_induction
Submodule.iSup_induction'
Submodule.pow_induction_on_left'
Submodule.pow_induction_on_right'

This is slightly awkward for name-resolution within these induction principles, as the argument names end up clashing with the function they are about. Thankfully, this pain is not transferred to the caller using induction _ using _.

0257770c

Diff

@@ -96,30 +96,30 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
   cases' x' with x' hx'
   dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
   induction hx' using Submodule.iSup_induction' with
-  | hp i x hx =>
+  | mem i x hx =>
     obtain ⟨i, rfl⟩ := i
     -- porting note: `dsimp only [Subtype.coe_mk] at hx` doesn't work, use `change` instead
     change x ∈ LinearMap.range (ι Q) ^ i at hx
     induction hx using Submodule.pow_induction_on_left' with
-    | hr r =>
+    | algebraMap r =>
       rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
-    | hadd x y i hx hy ihx ihy =>
+    | add x y i hx hy ihx ihy =>
       -- Note: in #8386 `map_add` had to be specialized to avoid a timeout
       -- (the definition was already very slow)
       rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]
       rfl
-    | hmul m hm i x hx ih =>
+    | mem_mul m hm i x hx ih =>
       obtain ⟨_, rfl⟩ := hm
       rw [AlgHom.map_mul, ih, lift_ι_apply, GradedAlgebra.ι_apply Q, DirectSum.of_mul_of]
       refine' DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext _ _) <;>
         dsimp only [GradedMonoid.mk, Subtype.coe_mk]
       · rw [Nat.succ_eq_add_one, add_comm, Nat.cast_add, Nat.cast_one]
       rfl
-  | h0 =>
+  | zero =>
     rw [AlgHom.map_zero]
     apply Eq.symm
     apply DFinsupp.single_eq_zero.mpr; rfl
-  | hadd x y hx hy ihx ihy =>
+  | add x y hx hy ihx ihy =>
     rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]; rfl
 #align clifford_algebra.graded_algebra.lift_ι_eq CliffordAlgebra.GradedAlgebra.lift_ι_eq
 
@@ -160,83 +160,82 @@ theorem evenOdd_isCompl : IsCompl (evenOdd Q 0) (evenOdd Q 1) :=
 scalars or vectors (respectively), closed under addition, and under left-multiplication by a pair
 of vectors. -/
 @[elab_as_elim]
-theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
-    (hr :
-      ∀ (v) (h : v ∈ LinearMap.range (ι Q) ^ n.val),
-        P v (Submodule.mem_iSup_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
-    (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
-    (hιι_mul :
-      ∀ (m₁ m₂) {x hx},
-        P x hx →
-          P (ι Q m₁ * ι Q m₂ * x)
+theorem evenOdd_induction (n : ZMod 2) {motive : ∀ x, x ∈ evenOdd Q n → Prop}
+    (range_ι_pow : ∀ (v) (h : v ∈ LinearMap.range (ι Q) ^ n.val),
+        motive v (Submodule.mem_iSup_of_mem ⟨n.val, n.nat_cast_zmod_val⟩ h))
+    (add : ∀ x y hx hy, motive x hx → motive y hy → motive (x + y) (Submodule.add_mem _ hx hy))
+    (ι_mul_ι_mul :
+      ∀ m₁ m₂ x hx,
+        motive x hx →
+          motive (ι Q m₁ * ι Q m₂ * x)
             (zero_add n ▸ SetLike.mul_mem_graded (ι_mul_ι_mem_evenOdd_zero Q m₁ m₂) hx))
-    (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q n) : P x hx := by
-  apply Submodule.iSup_induction' (C := P) _ (hr 0 (Submodule.zero_mem _)) @hadd
+    (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q n) : motive x hx := by
+  apply Submodule.iSup_induction' (C := motive) _ (range_ι_pow 0 (Submodule.zero_mem _)) add
   refine' Subtype.rec _
   simp_rw [ZMod.nat_coe_zmod_eq_iff, add_comm n.val]
   rintro n' ⟨k, rfl⟩ xv
   simp_rw [pow_add, pow_mul]
   intro hxv
   induction hxv using Submodule.mul_induction_on' with
-  | hm a ha b hb =>
+  | mem_mul_mem a ha b hb =>
     induction ha using Submodule.pow_induction_on_left' with
-    | hr r =>
+    | algebraMap r =>
       simp_rw [← Algebra.smul_def]
-      exact hr _ (Submodule.smul_mem _ _ hb)
-    | hadd x y n hx hy ihx ihy =>
+      exact range_ι_pow _ (Submodule.smul_mem _ _ hb)
+    | add x y n hx hy ihx ihy =>
       simp_rw [add_mul]
-      apply hadd ihx ihy
-    | hmul x hx n'' y hy ihy =>
+      apply add _ _ _ _ ihx ihy
+    | mem_mul x hx n'' y hy ihy =>
       revert hx
       simp_rw [pow_two]
       intro hx2
       induction hx2 using Submodule.mul_induction_on' with
-      | hm m hm n hn =>
+      | mem_mul_mem m hm n hn =>
         simp_rw [LinearMap.mem_range] at hm hn
         obtain ⟨m₁, rfl⟩ := hm; obtain ⟨m₂, rfl⟩ := hn
         simp_rw [mul_assoc _ y b]
-        exact hιι_mul _ _ ihy
-      | ha x hx y hy ihx ihy =>
+        exact ι_mul_ι_mul _ _ _ _ ihy
+      | add x hx y hy ihx ihy =>
         simp_rw [add_mul]
-        apply hadd ihx ihy
-  | ha x y hx hy ihx ihy =>
-    apply hadd ihx ihy
+        apply add _ _ _ _ ihx ihy
+  | add x y hx hy ihx ihy =>
+    apply add _ _ _ _ ihx ihy
 #align clifford_algebra.even_odd_induction CliffordAlgebra.evenOdd_induction
 
 /-- To show a property is true on the even parts, it suffices to show it is true on the
 scalars, closed under addition, and under left-multiplication by a pair of vectors. -/
 @[elab_as_elim]
-theorem even_induction {P : ∀ x, x ∈ evenOdd Q 0 → Prop}
-    (hr : ∀ r : R, P (algebraMap _ _ r) (SetLike.algebraMap_mem_graded _ _))
-    (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
-    (hιι_mul :
-      ∀ (m₁ m₂) {x hx},
-        P x hx →
-          P (ι Q m₁ * ι Q m₂ * x)
+theorem even_induction {motive : ∀ x, x ∈ evenOdd Q 0 → Prop}
+    (algebraMap : ∀ r : R, motive (algebraMap _ _ r) (SetLike.algebraMap_mem_graded _ _))
+    (add : ∀ x y hx hy, motive x hx → motive y hy → motive (x + y) (Submodule.add_mem _ hx hy))
+    (ι_mul_ι_mul :
+      ∀ m₁ m₂ x hx,
+        motive x hx →
+          motive (ι Q m₁ * ι Q m₂ * x)
             (zero_add (0 : ZMod 2) ▸ SetLike.mul_mem_graded (ι_mul_ι_mem_evenOdd_zero Q m₁ m₂) hx))
-    (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q 0) : P x hx := by
-  refine' evenOdd_induction Q 0 (fun rx => _) (@hadd) hιι_mul x hx
+    (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q 0) : motive x hx := by
+  refine' evenOdd_induction Q 0 (fun rx => _) (@add) ι_mul_ι_mul x hx
   rintro ⟨r, rfl⟩
-  exact hr r
+  exact algebraMap r
 #align clifford_algebra.even_induction CliffordAlgebra.even_induction
 
 /-- To show a property is true on the odd parts, it suffices to show it is true on the
 vectors, closed under addition, and under left-multiplication by a pair of vectors. -/
 @[elab_as_elim]
 theorem odd_induction {P : ∀ x, x ∈ evenOdd Q 1 → Prop}
-    (hι : ∀ v, P (ι Q v) (ι_mem_evenOdd_one _ _))
-    (hadd : ∀ {x y hx hy}, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
-    (hιι_mul :
-      ∀ (m₁ m₂) {x hx},
+    (ι : ∀ v, P (ι Q v) (ι_mem_evenOdd_one _ _))
+    (add : ∀ x y hx hy, P x hx → P y hy → P (x + y) (Submodule.add_mem _ hx hy))
+    (ι_mul_ι_mul :
+      ∀ m₁ m₂ x hx,
         P x hx →
-          P (ι Q m₁ * ι Q m₂ * x)
+          P (CliffordAlgebra.ι Q m₁ * CliffordAlgebra.ι Q m₂ * x)
             (zero_add (1 : ZMod 2) ▸ SetLike.mul_mem_graded (ι_mul_ι_mem_evenOdd_zero Q m₁ m₂) hx))
     (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q 1) : P x hx := by
-  refine' evenOdd_induction Q 1 (fun ιv => _) (@hadd) hιι_mul x hx
+  refine' evenOdd_induction Q 1 (fun ιv => _) (@add) ι_mul_ι_mul x hx
   -- porting note: was `simp_rw [ZMod.val_one, pow_one]`, lean4#1926
   intro h; rw [ZMod.val_one, pow_one] at h; revert h
   rintro ⟨v, rfl⟩
-  exact hι v
+  exact ι v
 #align clifford_algebra.odd_induction CliffordAlgebra.odd_induction
 
 end CliffordAlgebra

34020e53

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -86,7 +86,7 @@ theorem GradedAlgebra.ι_apply (m : M) :
 nonrec theorem GradedAlgebra.ι_sq_scalar (m : M) :
     GradedAlgebra.ι Q m * GradedAlgebra.ι Q m = algebraMap R _ (Q m) := by
   rw [GradedAlgebra.ι_apply Q, DirectSum.of_mul_of, DirectSum.algebraMap_apply]
-  refine' DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext rfl <| ι_sq_scalar _ _)
+  exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext rfl <| ι_sq_scalar _ _)
 #align clifford_algebra.graded_algebra.ι_sq_scalar CliffordAlgebra.GradedAlgebra.ι_sq_scalar
 
 theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
@@ -195,7 +195,7 @@ theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
         simp_rw [LinearMap.mem_range] at hm hn
         obtain ⟨m₁, rfl⟩ := hm; obtain ⟨m₂, rfl⟩ := hn
         simp_rw [mul_assoc _ y b]
-        refine' hιι_mul _ _ ihy
+        exact hιι_mul _ _ ihy
       | ha x hx y hy ihx ihy =>
         simp_rw [add_mul]
         apply hadd ihx ihy

34020e53

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

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

Zulip thread

Important changes

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

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

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

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

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

Similarly, MyEquivClass should take EquivLike as a parameter.

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

Remaining issues

Slower (failing) search

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

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

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

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

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

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

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

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

`simp` not firing sometimes

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

Missing instances due to unification failing

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

Workaround for issues

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

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

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

c6a73d4f

Diff

@@ -104,7 +104,9 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
     | hr r =>
       rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
     | hadd x y i hx hy ihx ihy =>
-      rw [AlgHom.map_add, ihx, ihy, ← map_add]
+      -- Note: in #8386 `map_add` had to be specialized to avoid a timeout
+      -- (the definition was already very slow)
+      rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]
       rfl
     | hmul m hm i x hx ih =>
       obtain ⟨_, rfl⟩ := hm
@@ -118,7 +120,7 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
     apply Eq.symm
     apply DFinsupp.single_eq_zero.mpr; rfl
   | hadd x y hx hy ihx ihy =>
-    rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
+    rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]; rfl
 #align clifford_algebra.graded_algebra.lift_ι_eq CliffordAlgebra.GradedAlgebra.lift_ι_eq
 
 /-- The clifford algebra is graded by the even and odd parts. -/

34020e53

chore(*): use rintro to golf some proofs (#9204)

983cf222

Diff

@@ -59,13 +59,11 @@ theorem ι_mul_ι_mem_evenOdd_zero (m₁ m₂ : M) : ι Q m₁ * ι Q m₂ ∈ e
 theorem evenOdd_mul_le (i j : ZMod 2) : evenOdd Q i * evenOdd Q j ≤ evenOdd Q (i + j) := by
   simp_rw [evenOdd, Submodule.iSup_eq_span, Submodule.span_mul_span]
   apply Submodule.span_mono
-  intro z hz
-  obtain ⟨x, y, hx, hy, rfl⟩ := hz
-  obtain ⟨xi, hx'⟩ := Set.mem_iUnion.mp hx
-  obtain ⟨yi, hy'⟩ := Set.mem_iUnion.mp hy
-  refine' Set.mem_iUnion.mpr ⟨⟨xi + yi, by simp only [Nat.cast_add, xi.prop, yi.prop]⟩, _⟩
+  simp_rw [Set.iUnion_mul, Set.mul_iUnion, Set.iUnion_subset_iff, Set.mul_subset_iff]
+  rintro ⟨xi, rfl⟩ ⟨yi, rfl⟩ x hx y hy
+  refine Set.mem_iUnion.mpr ⟨⟨xi + yi, Nat.cast_add _ _⟩, ?_⟩
   simp only [Subtype.coe_mk, Nat.cast_add, pow_add]
-  exact Submodule.mul_mem_mul hx' hy'
+  exact Submodule.mul_mem_mul hx hy
 #align clifford_algebra.even_odd_mul_le CliffordAlgebra.evenOdd_mul_le
 
 instance evenOdd.gradedMonoid : SetLike.GradedMonoid (evenOdd Q) where

34020e53

chore: bump toolchain to v4.3.0-rc1 (#8051)

This incorporates changes from

#7845
#7847
#7853
#7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

1ff3bf34

Diff

@@ -173,26 +173,9 @@ theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
     (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q n) : P x hx := by
   apply Submodule.iSup_induction' (C := P) _ (hr 0 (Submodule.zero_mem _)) @hadd
   refine' Subtype.rec _
-  -- porting note: was `simp_rw [Subtype.coe_mk, ZMod.nat_coe_zmod_eq_iff, add_comm n.val]`
-  -- leanprover/lean4#1926 is to blame.
-  dsimp only [Subtype.coe_mk]
-  let hlean1926 : ∀ val : ℕ, ↑val = n ↔ ∃ k, val = 2 * k + ZMod.val n := by
-    intro val
-    simp_rw [ZMod.nat_coe_zmod_eq_iff, add_comm n.val]
-  have := fun val : ℕ => forall_prop_congr'
-    (q := fun property => ∀ x (hx : x ∈ LinearMap.range (ι Q) ^ val),
-      P x (Submodule.mem_iSup_of_mem { val := val, property := property } hx))
-    (hq := fun property => Iff.rfl) (hp := hlean1926 val)
-  simp_rw [this]; clear this
-  -- end porting note
+  simp_rw [ZMod.nat_coe_zmod_eq_iff, add_comm n.val]
   rintro n' ⟨k, rfl⟩ xv
-  -- porting note: was `simp_rw [pow_add, pow_mul]`
-  -- leanprover/lean4#1926 is to blame.
-  refine (forall_prop_congr' (hq := fun property => Iff.rfl) (
-    show xv ∈ LinearMap.range (ι Q) ^ (2 * k + ZMod.val n)
-        ↔ xv ∈ (LinearMap.range (ι Q) ^ 2) ^ k * LinearMap.range (ι Q) ^ ZMod.val n by
-      simp_rw [pow_add, pow_mul])).mpr ?_
-  -- end porting note
+  simp_rw [pow_add, pow_mul]
   intro hxv
   induction hxv using Submodule.mul_induction_on' with
   | hm a ha b hb =>
@@ -205,13 +188,7 @@ theorem evenOdd_induction (n : ZMod 2) {P : ∀ x, x ∈ evenOdd Q n → Prop}
       apply hadd ihx ihy
     | hmul x hx n'' y hy ihy =>
       revert hx
-      -- porting note: was `simp_rw [pow_two]`
-      -- leanprover/lean4#1926 is to blame.
-      let hlean1926'' : x ∈ LinearMap.range (ι Q) ^ 2
-          ↔ x ∈ LinearMap.range (ι Q) * LinearMap.range (ι Q) := by
-        rw [pow_two]
-      refine (forall_prop_congr' (hq := fun property => Iff.rfl) hlean1926'').mpr ?_
-      -- end porting note
+      simp_rw [pow_two]
       intro hx2
       induction hx2 using Submodule.mul_induction_on' with
       | hm m hm n hn =>

34020e53

chore: update/remove heart beat bumps (#6860)

We clean up heart beat bumps after #6474.

c95f05bd

Diff

@@ -123,7 +123,6 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
     rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
 #align clifford_algebra.graded_algebra.lift_ι_eq CliffordAlgebra.GradedAlgebra.lift_ι_eq
 
-set_option maxHeartbeats 300000 in
 /-- The clifford algebra is graded by the even and odd parts. -/
 instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
   GradedAlgebra.ofAlgHom (evenOdd Q)
@@ -139,7 +138,6 @@ instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
     (by apply GradedAlgebra.lift_ι_eq Q)
 #align clifford_algebra.graded_algebra CliffordAlgebra.gradedAlgebra
 
-set_option maxHeartbeats 300000 in
 theorem iSup_ι_range_eq_top : ⨆ i : ℕ, LinearMap.range (ι Q) ^ i = ⊤ := by
   rw [← (DirectSum.Decomposition.isInternal (evenOdd Q)).submodule_iSup_eq_top, eq_comm]
   calc

34020e53

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -241,7 +241,6 @@ theorem even_induction {P : ∀ x, x ∈ evenOdd Q 0 → Prop}
             (zero_add (0 : ZMod 2) ▸ SetLike.mul_mem_graded (ι_mul_ι_mem_evenOdd_zero Q m₁ m₂) hx))
     (x : CliffordAlgebra Q) (hx : x ∈ evenOdd Q 0) : P x hx := by
   refine' evenOdd_induction Q 0 (fun rx => _) (@hadd) hιι_mul x hx
-  simp_rw [ZMod.val_zero, pow_zero]
   rintro ⟨r, rfl⟩
   exact hr r
 #align clifford_algebra.even_induction CliffordAlgebra.even_induction

34020e53

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

@@ -19,7 +19,7 @@ The main result is `CliffordAlgebra.gradedAlgebra`, which says that the clifford
 
 namespace CliffordAlgebra
 
-variable {R M : Type _} [CommRing R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
 
 variable {Q : QuadraticForm R M}

34020e53

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

@@ -2,16 +2,13 @@
 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 linear_algebra.clifford_algebra.grading
-! leanprover-community/mathlib commit 34020e531ebc4e8aac6d449d9eecbcd1508ea8d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.CliffordAlgebra.Basic
 import Mathlib.Data.ZMod.Basic
 import Mathlib.RingTheory.GradedAlgebra.Basic
 
+#align_import linear_algebra.clifford_algebra.grading from "leanprover-community/mathlib"@"34020e531ebc4e8aac6d449d9eecbcd1508ea8d0"
+
 /-!
 # Results about the grading structure of the clifford algebra

34020e53

chore: rename Dfinsupp to DFinsupp (#5822)

See #4354

268b7d43

Diff

@@ -121,7 +121,7 @@ theorem GradedAlgebra.lift_ι_eq (i' : ZMod 2) (x' : evenOdd Q i') :
   | h0 =>
     rw [AlgHom.map_zero]
     apply Eq.symm
-    apply Dfinsupp.single_eq_zero.mpr; rfl
+    apply DFinsupp.single_eq_zero.mpr; rfl
   | hadd x y hx hy ihx ihy =>
     rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
 #align clifford_algebra.graded_algebra.lift_ι_eq CliffordAlgebra.GradedAlgebra.lift_ι_eq

34020e53

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -143,12 +143,12 @@ instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
 #align clifford_algebra.graded_algebra CliffordAlgebra.gradedAlgebra
 
 set_option maxHeartbeats 300000 in
-theorem iSup_ι_range_eq_top : (⨆ i : ℕ, LinearMap.range (ι Q) ^ i) = ⊤ := by
+theorem iSup_ι_range_eq_top : ⨆ i : ℕ, LinearMap.range (ι Q) ^ i = ⊤ := by
   rw [← (DirectSum.Decomposition.isInternal (evenOdd Q)).submodule_iSup_eq_top, eq_comm]
   calc
     -- porting note: needs extra annotations, no longer unifies against the goal in the face of
     -- ambiguity
-    (⨆ (i : ZMod 2) (j : { n : ℕ // ↑n = i }), LinearMap.range (ι Q) ^ (j : ℕ)) =
+    ⨆ (i : ZMod 2) (j : { n : ℕ // ↑n = i }), LinearMap.range (ι Q) ^ (j : ℕ) =
         ⨆ i : Σ i : ZMod 2, { n : ℕ // ↑n = i }, LinearMap.range (ι Q) ^ (i.2 : ℕ) :=
       by rw [iSup_sigma]
     _ = ⨆ i : ℕ, LinearMap.range (ι Q) ^ i :=

34020e53

chore: tidy various files (#5449)

ff656fa9

Diff

@@ -31,7 +31,7 @@ open scoped DirectSum
 variable (Q)
 
 /-- The even or odd submodule, defined as the supremum of the even or odd powers of
-`(ι Q).range`. `even_odd 0` is the even submodule, and `even_odd 1` is the odd submodule. -/
+`(ι Q).range`. `evenOdd 0` is the even submodule, and `evenOdd 1` is the odd submodule. -/
 def evenOdd (i : ZMod 2) : Submodule R (CliffordAlgebra Q) :=
   ⨆ j : { n : ℕ // ↑n = i }, LinearMap.range (ι Q) ^ (j : ℕ)
 #align clifford_algebra.even_odd CliffordAlgebra.evenOdd
@@ -133,7 +133,7 @@ instance gradedAlgebra : GradedAlgebra (evenOdd Q) :=
     -- while not necessary, the `by apply` makes this elaborate faster
     (lift Q ⟨by apply GradedAlgebra.ι Q, by apply GradedAlgebra.ι_sq_scalar Q⟩)
     -- the proof from here onward is mostly similar to the `TensorAlgebra` case, with some extra
-    -- handling for the `iSup` in `even_odd`.
+    -- handling for the `iSup` in `evenOdd`.
     (by
       ext m
       dsimp only [LinearMap.comp_apply, AlgHom.toLinearMap_apply, AlgHom.comp_apply,

34020e53

feat: port LinearAlgebra.CliffordAlgebra.Grading (#5349)

This runs into some annoying problems with https://github.com/leanprover/lean4/issues/1926 which makes working with the dependent types much worse than it was in Lean 3.

4a17605f

`linear_algebra.clifford_algebra.grading` ⟷ `Mathlib.LinearAlgebra.CliffordAlgebra.Grading`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 639

linear_algebra.clifford_algebra.grading ⟷ Mathlib.LinearAlgebra.CliffordAlgebra.Grading

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 639

`linear_algebra.clifford_algebra.grading` ⟷ `Mathlib.LinearAlgebra.CliffordAlgebra.Grading`

`simp` not firing sometimes