algebra.monoid_algebra.division ⟷ Mathlib.Algebra.MonoidAlgebra.Division

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Algebra.MonoidAlgebra.Basic
-import Mathbin.Data.Finsupp.Order
+import Algebra.MonoidAlgebra.Basic
+import Data.Finsupp.Order
 
 #align_import algebra.monoid_algebra.division from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 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.monoid_algebra.division
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.MonoidAlgebra.Basic
 import Mathbin.Data.Finsupp.Order
 
+#align_import algebra.monoid_algebra.division from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Division of `add_monoid_algebra` by monomials
 

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

@@ -63,39 +63,51 @@ noncomputable def divOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k
 #align add_monoid_algebra.div_of AddMonoidAlgebra.divOf
 -/
 
--- mathport name: «expr /ᵒᶠ »
 local infixl:70 " /ᵒᶠ " => divOf
 
+#print AddMonoidAlgebra.divOf_apply /-
 @[simp]
 theorem divOf_apply (g : G) (x : AddMonoidAlgebra k G) (g' : G) : (x /ᵒᶠ g) g' = x (g + g') :=
   rfl
 #align add_monoid_algebra.div_of_apply AddMonoidAlgebra.divOf_apply
+-/
 
+#print AddMonoidAlgebra.support_divOf /-
 @[simp]
 theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :
     (x /ᵒᶠ g).support =
       x.support.Preimage ((· + ·) g) (Function.Injective.injOn (add_right_injective g) _) :=
   rfl
 #align add_monoid_algebra.support_div_of AddMonoidAlgebra.support_divOf
+-/
 
+#print AddMonoidAlgebra.zero_divOf /-
 @[simp]
 theorem zero_divOf (g : G) : (0 : AddMonoidAlgebra k G) /ᵒᶠ g = 0 :=
   map_zero _
 #align add_monoid_algebra.zero_div_of AddMonoidAlgebra.zero_divOf
+-/
 
+#print AddMonoidAlgebra.divOf_zero /-
 @[simp]
 theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x := by ext;
   simp only [AddMonoidAlgebra.divOf_apply, zero_add]
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
+-/
 
+#print AddMonoidAlgebra.add_divOf /-
 theorem add_divOf (x y : AddMonoidAlgebra k G) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /ᵒᶠ g :=
   map_add _ _ _
 #align add_monoid_algebra.add_div_of AddMonoidAlgebra.add_divOf
+-/
 
+#print AddMonoidAlgebra.divOf_add /-
 theorem divOf_add (x : AddMonoidAlgebra k G) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by ext;
   simp only [AddMonoidAlgebra.divOf_apply, add_assoc]
 #align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_add
+-/
 
+#print AddMonoidAlgebra.divOfHom /-
 /-- A bundled version of `add_monoid_algebra.div_of`. -/
 @[simps]
 noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgebra k G)
@@ -108,7 +120,9 @@ noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgeb
   map_mul' g₁ g₂ :=
     AddMonoidHom.ext fun x => (congr_arg _ (add_comm g₁.toAdd g₂.toAdd)).trans (divOf_add _ _ _)
 #align add_monoid_algebra.div_of_hom AddMonoidAlgebra.divOfHom
+-/
 
+#print AddMonoidAlgebra.of'_mul_divOf /-
 theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ a = x :=
   by
   ext b
@@ -116,7 +130,9 @@ theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ
   intro c
   exact add_right_inj _
 #align add_monoid_algebra.of'_mul_div_of AddMonoidAlgebra.of'_mul_divOf
+-/
 
+#print AddMonoidAlgebra.mul_of'_divOf /-
 theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ a = x :=
   by
   ext b
@@ -125,10 +141,13 @@ theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ
   rw [add_comm]
   exact add_right_inj _
 #align add_monoid_algebra.mul_of'_div_of AddMonoidAlgebra.mul_of'_divOf
+-/
 
+#print AddMonoidAlgebra.of'_divOf /-
 theorem of'_divOf (a : G) : of' k G a /ᵒᶠ a = 1 := by
   simpa only [one_mul] using mul_of'_div_of (1 : AddMonoidAlgebra k G) a
 #align add_monoid_algebra.of'_div_of AddMonoidAlgebra.of'_divOf
+-/
 
 #print AddMonoidAlgebra.modOf /-
 /-- The remainder upon division by `of' k G g`. -/
@@ -137,31 +156,39 @@ noncomputable def modOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k
 #align add_monoid_algebra.mod_of AddMonoidAlgebra.modOf
 -/
 
--- mathport name: «expr %ᵒᶠ »
 local infixl:70 " %ᵒᶠ " => modOf
 
+#print AddMonoidAlgebra.modOf_apply_of_not_exists_add /-
 @[simp]
 theorem modOf_apply_of_not_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
     (h : ¬∃ d, g' = g + d) : (x %ᵒᶠ g) g' = x g' :=
   Finsupp.filter_apply_pos _ _ h
 #align add_monoid_algebra.mod_of_apply_of_not_exists_add AddMonoidAlgebra.modOf_apply_of_not_exists_add
+-/
 
+#print AddMonoidAlgebra.modOf_apply_of_exists_add /-
 @[simp]
 theorem modOf_apply_of_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
     (h : ∃ d, g' = g + d) : (x %ᵒᶠ g) g' = 0 :=
   Finsupp.filter_apply_neg _ _ <| by rwa [Classical.not_not]
 #align add_monoid_algebra.mod_of_apply_of_exists_add AddMonoidAlgebra.modOf_apply_of_exists_add
+-/
 
+#print AddMonoidAlgebra.modOf_apply_add_self /-
 @[simp]
 theorem modOf_apply_add_self (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (d + g) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, add_comm _ _⟩
 #align add_monoid_algebra.mod_of_apply_add_self AddMonoidAlgebra.modOf_apply_add_self
+-/
 
+#print AddMonoidAlgebra.modOf_apply_self_add /-
 @[simp]
 theorem modOf_apply_self_add (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (g + d) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, rfl⟩
 #align add_monoid_algebra.mod_of_apply_self_add AddMonoidAlgebra.modOf_apply_self_add
+-/
 
+#print AddMonoidAlgebra.of'_mul_modOf /-
 theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ g = 0 :=
   by
   ext g'
@@ -170,7 +197,9 @@ theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ
   · rw [mod_of_apply_self_add]
   · rw [mod_of_apply_of_not_exists_add _ _ _ h, of'_apply, single_mul_apply_of_not_exists_add _ _ h]
 #align add_monoid_algebra.of'_mul_mod_of AddMonoidAlgebra.of'_mul_modOf
+-/
 
+#print AddMonoidAlgebra.mul_of'_modOf /-
 theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ g = 0 :=
   by
   ext g'
@@ -180,11 +209,15 @@ theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ
   · rw [mod_of_apply_of_not_exists_add _ _ _ h, of'_apply, mul_single_apply_of_not_exists_add]
     simpa only [add_comm] using h
 #align add_monoid_algebra.mul_of'_mod_of AddMonoidAlgebra.mul_of'_modOf
+-/
 
+#print AddMonoidAlgebra.of'_modOf /-
 theorem of'_modOf (g : G) : of' k G g %ᵒᶠ g = 0 := by
   simpa only [one_mul] using mul_of'_mod_of (1 : AddMonoidAlgebra k G) g
 #align add_monoid_algebra.of'_mod_of AddMonoidAlgebra.of'_modOf
+-/
 
+#print AddMonoidAlgebra.divOf_add_modOf /-
 theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) : of' k G g * (x /ᵒᶠ g) + x %ᵒᶠ g = x :=
   by
   ext g'
@@ -199,11 +232,15 @@ theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) : of' k G g * (x /ᵒ
     intro a
     exact add_right_inj _
 #align add_monoid_algebra.div_of_add_mod_of AddMonoidAlgebra.divOf_add_modOf
+-/
 
+#print AddMonoidAlgebra.modOf_add_divOf /-
 theorem modOf_add_divOf (x : AddMonoidAlgebra k G) (g : G) : x %ᵒᶠ g + of' k G g * (x /ᵒᶠ g) = x :=
   by rw [add_comm, div_of_add_mod_of]
 #align add_monoid_algebra.mod_of_add_div_of AddMonoidAlgebra.modOf_add_divOf
+-/
 
+#print AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero /-
 theorem of'_dvd_iff_modOf_eq_zero {x : AddMonoidAlgebra k G} {g : G} :
     of' k G g ∣ x ↔ x %ᵒᶠ g = 0 := by
   constructor
@@ -213,6 +250,7 @@ theorem of'_dvd_iff_modOf_eq_zero {x : AddMonoidAlgebra k G} {g : G} :
     rw [← div_of_add_mod_of x g, h, add_zero]
     exact dvd_mul_right _ _
 #align add_monoid_algebra.of'_dvd_iff_mod_of_eq_zero AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero
+-/
 
 end
 

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

@@ -66,23 +66,11 @@ noncomputable def divOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k
 -- mathport name: «expr /ᵒᶠ »
 local infixl:70 " /ᵒᶠ " => divOf
 
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 @[simp]
 theorem divOf_apply (g : G) (x : AddMonoidAlgebra k G) (g' : G) : (x /ᵒᶠ g) g' = x (g + g') :=
   rfl
 #align add_monoid_algebra.div_of_apply AddMonoidAlgebra.divOf_apply
 
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 @[simp]
 theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :
     (x /ᵒᶠ g).support =
@@ -90,54 +78,24 @@ theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :
   rfl
 #align add_monoid_algebra.support_div_of AddMonoidAlgebra.support_divOf
 
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 @[simp]
 theorem zero_divOf (g : G) : (0 : AddMonoidAlgebra k G) /ᵒᶠ g = 0 :=
   map_zero _
 #align add_monoid_algebra.zero_div_of AddMonoidAlgebra.zero_divOf
 
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 @[simp]
 theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x := by ext;
   simp only [AddMonoidAlgebra.divOf_apply, zero_add]
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
 
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 theorem add_divOf (x y : AddMonoidAlgebra k G) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /ᵒᶠ g :=
   map_add _ _ _
 #align add_monoid_algebra.add_div_of AddMonoidAlgebra.add_divOf
 
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 theorem divOf_add (x : AddMonoidAlgebra k G) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by ext;
   simp only [AddMonoidAlgebra.divOf_apply, add_assoc]
 #align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_add
 
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 /-- A bundled version of `add_monoid_algebra.div_of`. -/
 @[simps]
 noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgebra k G)
@@ -151,12 +109,6 @@ noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgeb
     AddMonoidHom.ext fun x => (congr_arg _ (add_comm g₁.toAdd g₂.toAdd)).trans (divOf_add _ _ _)
 #align add_monoid_algebra.div_of_hom AddMonoidAlgebra.divOfHom
 
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 theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ a = x :=
   by
   ext b
@@ -165,12 +117,6 @@ theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ
   exact add_right_inj _
 #align add_monoid_algebra.of'_mul_div_of AddMonoidAlgebra.of'_mul_divOf
 
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 theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ a = x :=
   by
   ext b
@@ -180,12 +126,6 @@ theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ
   exact add_right_inj _
 #align add_monoid_algebra.mul_of'_div_of AddMonoidAlgebra.mul_of'_divOf
 
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 theorem of'_divOf (a : G) : of' k G a /ᵒᶠ a = 1 := by
   simpa only [one_mul] using mul_of'_div_of (1 : AddMonoidAlgebra k G) a
 #align add_monoid_algebra.of'_div_of AddMonoidAlgebra.of'_divOf
@@ -200,58 +140,28 @@ noncomputable def modOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k
 -- mathport name: «expr %ᵒᶠ »
 local infixl:70 " %ᵒᶠ " => modOf
 
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 @[simp]
 theorem modOf_apply_of_not_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
     (h : ¬∃ d, g' = g + d) : (x %ᵒᶠ g) g' = x g' :=
   Finsupp.filter_apply_pos _ _ h
 #align add_monoid_algebra.mod_of_apply_of_not_exists_add AddMonoidAlgebra.modOf_apply_of_not_exists_add
 
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 @[simp]
 theorem modOf_apply_of_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
     (h : ∃ d, g' = g + d) : (x %ᵒᶠ g) g' = 0 :=
   Finsupp.filter_apply_neg _ _ <| by rwa [Classical.not_not]
 #align add_monoid_algebra.mod_of_apply_of_exists_add AddMonoidAlgebra.modOf_apply_of_exists_add
 
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 @[simp]
 theorem modOf_apply_add_self (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (d + g) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, add_comm _ _⟩
 #align add_monoid_algebra.mod_of_apply_add_self AddMonoidAlgebra.modOf_apply_add_self
 
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 @[simp]
 theorem modOf_apply_self_add (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (g + d) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, rfl⟩
 #align add_monoid_algebra.mod_of_apply_self_add AddMonoidAlgebra.modOf_apply_self_add
 
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 theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ g = 0 :=
   by
   ext g'
@@ -261,12 +171,6 @@ theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ
   · rw [mod_of_apply_of_not_exists_add _ _ _ h, of'_apply, single_mul_apply_of_not_exists_add _ _ h]
 #align add_monoid_algebra.of'_mul_mod_of AddMonoidAlgebra.of'_mul_modOf
 
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 theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ g = 0 :=
   by
   ext g'
@@ -277,22 +181,10 @@ theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ
     simpa only [add_comm] using h
 #align add_monoid_algebra.mul_of'_mod_of AddMonoidAlgebra.mul_of'_modOf
 
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 theorem of'_modOf (g : G) : of' k G g %ᵒᶠ g = 0 := by
   simpa only [one_mul] using mul_of'_mod_of (1 : AddMonoidAlgebra k G) g
 #align add_monoid_algebra.of'_mod_of AddMonoidAlgebra.of'_modOf
 
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 theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) : of' k G g * (x /ᵒᶠ g) + x %ᵒᶠ g = x :=
   by
   ext g'
@@ -308,22 +200,10 @@ theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) : of' k G g * (x /ᵒ
     exact add_right_inj _
 #align add_monoid_algebra.div_of_add_mod_of AddMonoidAlgebra.divOf_add_modOf
 
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-Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.mod_of_add_div_of AddMonoidAlgebra.modOf_add_divOfₓ'. -/
 theorem modOf_add_divOf (x : AddMonoidAlgebra k G) (g : G) : x %ᵒᶠ g + of' k G g * (x /ᵒᶠ g) = x :=
   by rw [add_comm, div_of_add_mod_of]
 #align add_monoid_algebra.mod_of_add_div_of AddMonoidAlgebra.modOf_add_divOf
 
-/- warning: add_monoid_algebra.of'_dvd_iff_mod_of_eq_zero -> AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.of'_dvd_iff_mod_of_eq_zero AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zeroₓ'. -/
 theorem of'_dvd_iff_modOf_eq_zero {x : AddMonoidAlgebra k G} {g : G} :
     of' k G g ∣ x ↔ x %ᵒᶠ g = 0 := by
   constructor

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

@@ -108,9 +108,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zeroₓ'. -/
 @[simp]
-theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x :=
-  by
-  ext
+theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x := by ext;
   simp only [AddMonoidAlgebra.divOf_apply, zero_add]
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
 
@@ -130,9 +128,7 @@ lean 3 declaration is
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_addₓ'. -/
-theorem divOf_add (x : AddMonoidAlgebra k G) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b :=
-  by
-  ext
+theorem divOf_add (x : AddMonoidAlgebra k G) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by ext;
   simp only [AddMonoidAlgebra.divOf_apply, add_assoc]
 #align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_add
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -81,7 +81,7 @@ theorem divOf_apply (g : G) (x : AddMonoidAlgebra k G) (g' : G) : (x /ᵒᶠ g)
 lean 3 declaration is
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 but is expected to have type
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+  forall {k : Type.{u2}} {G : Type.{u1}} [_inst_1 : Semiring.{u2} k] [_inst_2 : AddCancelCommMonoid.{u1} G] (g : G) (x : AddMonoidAlgebra.{u2, u1} k G _inst_1), Eq.{succ u1} (Finset.{u1} G) (Finsupp.support.{u1, u2} G k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k _inst_1)) (AddMonoidAlgebra.divOf.{u2, u1} k G _inst_1 _inst_2 x g)) (Finset.preimage.{u1, u1} G G (Finsupp.support.{u1, u2} G k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k _inst_1)) x) ((fun (x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.821 : G) (x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.823 : G) => HAdd.hAdd.{u1, u1, u1} G G G (instHAdd.{u1} G (AddZeroClass.toAdd.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2)))))) x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.821 x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.823) g) (Function.Injective.injOn.{u1, u1} G G ((fun (x._@.Mathlib.Algebra.Group.Defs._hyg.2631 : G) (x._@.Mathlib.Algebra.Group.Defs._hyg.2633 : G) => HAdd.hAdd.{u1, u1, u1} G G G (instHAdd.{u1} G (AddZeroClass.toAdd.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2)))))) x._@.Mathlib.Algebra.Group.Defs._hyg.2631 x._@.Mathlib.Algebra.Group.Defs._hyg.2633) g) (add_right_injective.{u1} G (AddZeroClass.toAdd.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2))))) (IsCancelAdd.toIsLeftCancelAdd.{u1} G (AddZeroClass.toAdd.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2))))) (AddCancelMonoid.toIsCancelAdd.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2))) g) (Set.preimage.{u1, u1} G G ((fun (x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.821 : G) (x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.823 : G) => HAdd.hAdd.{u1, u1, u1} G G G (instHAdd.{u1} G (AddZeroClass.toAdd.{u1} G (AddMonoid.toAddZeroClass.{u1} G (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2)))))) x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.821 x._@.Mathlib.Algebra.MonoidAlgebra.Division._hyg.823) g) (Finset.toSet.{u1} G (Finsupp.support.{u1, u2} G k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k _inst_1)) x)))))
 Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.support_div_of AddMonoidAlgebra.support_divOfₓ'. -/
 @[simp]
 theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -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.monoid_algebra.division
-! leanprover-community/mathlib commit 72c366d0475675f1309d3027d3d7d47ee4423951
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Finsupp.Order
 /-!
 # Division of `add_monoid_algebra` by monomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file is most important for when `G = ℕ` (polynomials) or `G = σ →₀ ℕ` (multivariate
 polynomials).
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -49,6 +49,7 @@ section
 
 variable [AddCancelCommMonoid G]
 
+#print AddMonoidAlgebra.divOf /-
 /-- Divide by `of' k G g`, discarding terms not divisible by this. -/
 noncomputable def divOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k G :=
   -- note: comapping by `+ g` has the effect of subtracting `g` from every element in the support, and
@@ -57,15 +58,28 @@ noncomputable def divOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k
     @Finsupp.comapDomain.addMonoidHom
     _ _ _ _ ((· + ·) g) (add_right_injective g) x
 #align add_monoid_algebra.div_of AddMonoidAlgebra.divOf
+-/
 
 -- mathport name: «expr /ᵒᶠ »
 local infixl:70 " /ᵒᶠ " => divOf
 
+/- warning: add_monoid_algebra.div_of_apply -> AddMonoidAlgebra.divOf_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.div_of_apply AddMonoidAlgebra.divOf_applyₓ'. -/
 @[simp]
 theorem divOf_apply (g : G) (x : AddMonoidAlgebra k G) (g' : G) : (x /ᵒᶠ g) g' = x (g + g') :=
   rfl
 #align add_monoid_algebra.div_of_apply AddMonoidAlgebra.divOf_apply
 
+/- warning: add_monoid_algebra.support_div_of -> AddMonoidAlgebra.support_divOf is a dubious translation:
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 @[simp]
 theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :
     (x /ᵒᶠ g).support =
@@ -73,11 +87,23 @@ theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :
   rfl
 #align add_monoid_algebra.support_div_of AddMonoidAlgebra.support_divOf
 
+/- warning: add_monoid_algebra.zero_div_of -> AddMonoidAlgebra.zero_divOf is a dubious translation:
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 @[simp]
 theorem zero_divOf (g : G) : (0 : AddMonoidAlgebra k G) /ᵒᶠ g = 0 :=
   map_zero _
 #align add_monoid_algebra.zero_div_of AddMonoidAlgebra.zero_divOf
 
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 @[simp]
 theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x :=
   by
@@ -85,16 +111,34 @@ theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x :=
   simp only [AddMonoidAlgebra.divOf_apply, zero_add]
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
 
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 theorem add_divOf (x y : AddMonoidAlgebra k G) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /ᵒᶠ g :=
   map_add _ _ _
 #align add_monoid_algebra.add_div_of AddMonoidAlgebra.add_divOf
 
+/- warning: add_monoid_algebra.div_of_add -> AddMonoidAlgebra.divOf_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_addₓ'. -/
 theorem divOf_add (x : AddMonoidAlgebra k G) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b :=
   by
   ext
   simp only [AddMonoidAlgebra.divOf_apply, add_assoc]
 #align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_add
 
+/- warning: add_monoid_algebra.div_of_hom -> AddMonoidAlgebra.divOfHom is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.div_of_hom AddMonoidAlgebra.divOfHomₓ'. -/
 /-- A bundled version of `add_monoid_algebra.div_of`. -/
 @[simps]
 noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgebra k G)
@@ -108,6 +152,12 @@ noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgeb
     AddMonoidHom.ext fun x => (congr_arg _ (add_comm g₁.toAdd g₂.toAdd)).trans (divOf_add _ _ _)
 #align add_monoid_algebra.div_of_hom AddMonoidAlgebra.divOfHom
 
+/- warning: add_monoid_algebra.of'_mul_div_of -> AddMonoidAlgebra.of'_mul_divOf is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.of'_mul_div_of AddMonoidAlgebra.of'_mul_divOfₓ'. -/
 theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ a = x :=
   by
   ext b
@@ -116,6 +166,12 @@ theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ
   exact add_right_inj _
 #align add_monoid_algebra.of'_mul_div_of AddMonoidAlgebra.of'_mul_divOf
 
+/- warning: add_monoid_algebra.mul_of'_div_of -> AddMonoidAlgebra.mul_of'_divOf is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.mul_of'_div_of AddMonoidAlgebra.mul_of'_divOfₓ'. -/
 theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ a = x :=
   by
   ext b
@@ -125,40 +181,78 @@ theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ
   exact add_right_inj _
 #align add_monoid_algebra.mul_of'_div_of AddMonoidAlgebra.mul_of'_divOf
 
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 theorem of'_divOf (a : G) : of' k G a /ᵒᶠ a = 1 := by
   simpa only [one_mul] using mul_of'_div_of (1 : AddMonoidAlgebra k G) a
 #align add_monoid_algebra.of'_div_of AddMonoidAlgebra.of'_divOf
 
+#print AddMonoidAlgebra.modOf /-
 /-- The remainder upon division by `of' k G g`. -/
 noncomputable def modOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k G :=
   x.filterₓ fun g₁ => ¬∃ g₂, g₁ = g + g₂
 #align add_monoid_algebra.mod_of AddMonoidAlgebra.modOf
+-/
 
 -- mathport name: «expr %ᵒᶠ »
 local infixl:70 " %ᵒᶠ " => modOf
 
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 @[simp]
 theorem modOf_apply_of_not_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
     (h : ¬∃ d, g' = g + d) : (x %ᵒᶠ g) g' = x g' :=
   Finsupp.filter_apply_pos _ _ h
 #align add_monoid_algebra.mod_of_apply_of_not_exists_add AddMonoidAlgebra.modOf_apply_of_not_exists_add
 
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 @[simp]
 theorem modOf_apply_of_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
     (h : ∃ d, g' = g + d) : (x %ᵒᶠ g) g' = 0 :=
   Finsupp.filter_apply_neg _ _ <| by rwa [Classical.not_not]
 #align add_monoid_algebra.mod_of_apply_of_exists_add AddMonoidAlgebra.modOf_apply_of_exists_add
 
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 @[simp]
 theorem modOf_apply_add_self (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (d + g) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, add_comm _ _⟩
 #align add_monoid_algebra.mod_of_apply_add_self AddMonoidAlgebra.modOf_apply_add_self
 
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 @[simp]
 theorem modOf_apply_self_add (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (g + d) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, rfl⟩
 #align add_monoid_algebra.mod_of_apply_self_add AddMonoidAlgebra.modOf_apply_self_add
 
+/- warning: add_monoid_algebra.of'_mul_mod_of -> AddMonoidAlgebra.of'_mul_modOf is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.of'_mul_mod_of AddMonoidAlgebra.of'_mul_modOfₓ'. -/
 theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ g = 0 :=
   by
   ext g'
@@ -168,6 +262,12 @@ theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ
   · rw [mod_of_apply_of_not_exists_add _ _ _ h, of'_apply, single_mul_apply_of_not_exists_add _ _ h]
 #align add_monoid_algebra.of'_mul_mod_of AddMonoidAlgebra.of'_mul_modOf
 
+/- warning: add_monoid_algebra.mul_of'_mod_of -> AddMonoidAlgebra.mul_of'_modOf is a dubious translation:
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 theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ g = 0 :=
   by
   ext g'
@@ -178,10 +278,22 @@ theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ
     simpa only [add_comm] using h
 #align add_monoid_algebra.mul_of'_mod_of AddMonoidAlgebra.mul_of'_modOf
 
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 theorem of'_modOf (g : G) : of' k G g %ᵒᶠ g = 0 := by
   simpa only [one_mul] using mul_of'_mod_of (1 : AddMonoidAlgebra k G) g
 #align add_monoid_algebra.of'_mod_of AddMonoidAlgebra.of'_modOf
 
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 theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) : of' k G g * (x /ᵒᶠ g) + x %ᵒᶠ g = x :=
   by
   ext g'
@@ -197,10 +309,22 @@ theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) : of' k G g * (x /ᵒ
     exact add_right_inj _
 #align add_monoid_algebra.div_of_add_mod_of AddMonoidAlgebra.divOf_add_modOf
 
+/- warning: add_monoid_algebra.mod_of_add_div_of -> AddMonoidAlgebra.modOf_add_divOf is a dubious translation:
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 theorem modOf_add_divOf (x : AddMonoidAlgebra k G) (g : G) : x %ᵒᶠ g + of' k G g * (x /ᵒᶠ g) = x :=
   by rw [add_comm, div_of_add_mod_of]
 #align add_monoid_algebra.mod_of_add_div_of AddMonoidAlgebra.modOf_add_divOf
 
+/- warning: add_monoid_algebra.of'_dvd_iff_mod_of_eq_zero -> AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {G : Type.{u2}} [_inst_1 : Semiring.{u1} k] [_inst_2 : AddCancelCommMonoid.{u2} G] {x : AddMonoidAlgebra.{u1, u2} k G _inst_1} {g : G}, Iff (Dvd.Dvd.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (semigroupDvd.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (SemigroupWithZero.toSemigroup.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u1, u2} k G _inst_1 (AddMonoid.toAddSemigroup.{u2} G (AddRightCancelMonoid.toAddMonoid.{u2} G (AddCancelMonoid.toAddRightCancelMonoid.{u2} G (AddCancelCommMonoid.toAddCancelMonoid.{u2} G _inst_2)))))))) (AddMonoidAlgebra.of'.{u1, u2} k G _inst_1 g) x) (Eq.{max (succ u2) (succ u1)} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (AddMonoidAlgebra.modOf.{u1, u2} k G _inst_1 _inst_2 x g) (OfNat.ofNat.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) 0 (OfNat.mk.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) 0 (Zero.zero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} k G _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} k G _inst_1 (AddZeroClass.toHasAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (AddRightCancelMonoid.toAddMonoid.{u2} G (AddCancelMonoid.toAddRightCancelMonoid.{u2} G (AddCancelCommMonoid.toAddCancelMonoid.{u2} G _inst_2))))))))))))
+but is expected to have type
+  forall {k : Type.{u2}} {G : Type.{u1}} [_inst_1 : Semiring.{u2} k] [_inst_2 : AddCancelCommMonoid.{u1} G] {x : AddMonoidAlgebra.{u2, u1} k G _inst_1} {g : G}, Iff (Dvd.dvd.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (semigroupDvd.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (SemigroupWithZero.toSemigroup.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} k G _inst_1 (AddMonoid.toAddSemigroup.{u1} G (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2)))))))) (AddMonoidAlgebra.of'.{u2, u1} k G _inst_1 g) x) (Eq.{max (succ u2) (succ u1)} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (AddMonoidAlgebra.modOf.{u2, u1} k G _inst_1 _inst_2 x g) (OfNat.ofNat.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) 0 (Zero.toOfNat0.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (MonoidWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} k G _inst_1) (AddMonoidAlgebra.semiring.{u2, u1} k G _inst_1 (AddRightCancelMonoid.toAddMonoid.{u1} G (AddCancelMonoid.toAddRightCancelMonoid.{u1} G (AddCancelCommMonoid.toAddCancelMonoid.{u1} G _inst_2)))))))))
+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.of'_dvd_iff_mod_of_eq_zero AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zeroₓ'. -/
 theorem of'_dvd_iff_modOf_eq_zero {x : AddMonoidAlgebra k G} {g : G} :
     of' k G g ∣ x ↔ x %ᵒᶠ g = 0 := by
   constructor

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -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.monoid_algebra.division
-! leanprover-community/mathlib commit 57e09a1296bfb4330ddf6624f1028ba186117d82
+! leanprover-community/mathlib commit 72c366d0475675f1309d3027d3d7d47ee4423951
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -201,6 +201,16 @@ theorem modOf_add_divOf (x : AddMonoidAlgebra k G) (g : G) : x %ᵒᶠ g + of' k
   by rw [add_comm, div_of_add_mod_of]
 #align add_monoid_algebra.mod_of_add_div_of AddMonoidAlgebra.modOf_add_divOf
 
+theorem of'_dvd_iff_modOf_eq_zero {x : AddMonoidAlgebra k G} {g : G} :
+    of' k G g ∣ x ↔ x %ᵒᶠ g = 0 := by
+  constructor
+  · rintro ⟨x, rfl⟩
+    rw [of'_mul_mod_of]
+  · intro h
+    rw [← div_of_add_mod_of x g, h, add_zero]
+    exact dvd_mul_right _ _
+#align add_monoid_algebra.of'_dvd_iff_mod_of_eq_zero AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero
+
 end
 
 end AddMonoidAlgebra

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

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".

@@ -75,7 +75,7 @@ theorem zero_divOf (g : G) : (0 : k[G]) /ᵒᶠ g = 0 :=
 
 @[simp]
 theorem divOf_zero (x : k[G]) : x /ᵒᶠ 0 = x := by
-  refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
+  refine Finsupp.ext fun _ => ?_  -- Porting note: `ext` doesn't work
   simp only [AddMonoidAlgebra.divOf_apply, zero_add]
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
 
@@ -84,7 +84,7 @@ theorem add_divOf (x y : k[G]) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /
 #align add_monoid_algebra.add_div_of AddMonoidAlgebra.add_divOf
 
 theorem divOf_add (x : k[G]) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by
-  refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
+  refine Finsupp.ext fun _ => ?_  -- Porting note: `ext` doesn't work
   simp only [AddMonoidAlgebra.divOf_apply, add_assoc]
 #align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_add
 
@@ -103,14 +103,14 @@ noncomputable def divOfHom : Multiplicative G →* AddMonoid.End k[G] where
 #align add_monoid_algebra.div_of_hom AddMonoidAlgebra.divOfHom
 
 theorem of'_mul_divOf (a : G) (x : k[G]) : of' k G a * x /ᵒᶠ a = x := by
-  refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
+  refine Finsupp.ext fun _ => ?_  -- Porting note: `ext` doesn't work
   rw [AddMonoidAlgebra.divOf_apply, of'_apply, single_mul_apply_aux, one_mul]
   intro c
   exact add_right_inj _
 #align add_monoid_algebra.of'_mul_div_of AddMonoidAlgebra.of'_mul_divOf
 
 theorem mul_of'_divOf (x : k[G]) (a : G) : x * of' k G a /ᵒᶠ a = x := by
-  refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
+  refine Finsupp.ext fun _ => ?_  -- Porting note: `ext` doesn't work
   rw [AddMonoidAlgebra.divOf_apply, of'_apply, mul_single_apply_aux, mul_one]
   intro c
   rw [add_comm]
@@ -152,7 +152,7 @@ theorem modOf_apply_self_add (x : k[G]) (g : G) (d : G) : (x %ᵒᶠ g) (g + d)
 #align add_monoid_algebra.mod_of_apply_self_add AddMonoidAlgebra.modOf_apply_self_add
 
 theorem of'_mul_modOf (g : G) (x : k[G]) : of' k G g * x %ᵒᶠ g = 0 := by
-  refine Finsupp.ext fun g' => ?_  -- porting note: `ext g'` doesn't work
+  refine Finsupp.ext fun g' => ?_  -- Porting note: `ext g'` doesn't work
   rw [Finsupp.zero_apply]
   obtain ⟨d, rfl⟩ | h := em (∃ d, g' = g + d)
   · rw [modOf_apply_self_add]
@@ -160,7 +160,7 @@ theorem of'_mul_modOf (g : G) (x : k[G]) : of' k G g * x %ᵒᶠ g = 0 := by
 #align add_monoid_algebra.of'_mul_mod_of AddMonoidAlgebra.of'_mul_modOf
 
 theorem mul_of'_modOf (x : k[G]) (g : G) : x * of' k G g %ᵒᶠ g = 0 := by
-  refine Finsupp.ext fun g' => ?_  -- porting note: `ext g'` doesn't work
+  refine Finsupp.ext fun g' => ?_  -- Porting note: `ext g'` doesn't work
   rw [Finsupp.zero_apply]
   obtain ⟨d, rfl⟩ | h := em (∃ d, g' = g + d)
   · rw [modOf_apply_self_add]
@@ -174,8 +174,8 @@ theorem of'_modOf (g : G) : of' k G g %ᵒᶠ g = 0 := by
 
 theorem divOf_add_modOf (x : k[G]) (g : G) :
     of' k G g * (x /ᵒᶠ g) + x %ᵒᶠ g = x := by
-  refine Finsupp.ext fun g' => ?_  -- porting note: `ext` doesn't work
-  rw [Finsupp.add_apply] -- porting note: changed from `simp_rw` which can't see through the type
+  refine Finsupp.ext fun g' => ?_  -- Porting note: `ext` doesn't work
+  rw [Finsupp.add_apply] -- Porting note: changed from `simp_rw` which can't see through the type
   obtain ⟨d, rfl⟩ | h := em (∃ d, g' = g + d)
   swap
   · rw [modOf_apply_of_not_exists_add x _ _ h, of'_apply, single_mul_apply_of_not_exists_add _ _ h,

This doesn't have any significant downstream fallout, and removes some subsingleton elimination from one or two proofs.

This enables some trivial computations on factorizations, eg finding the odd prime factors:

/-- info: fun₀ | 3 => 2 | 5 => 1 -/
#guard_msgs in
#eval (Nat.factorization 720).filter Odd

Zulip thread

@@ -123,6 +123,7 @@ theorem of'_divOf (a : G) : of' k G a /ᵒᶠ a = 1 := by
 
 /-- The remainder upon division by `of' k G g`. -/
 noncomputable def modOf (x : k[G]) (g : G) : k[G] :=
+  letI := Classical.decPred fun g₁ => ∃ g₂, g₁ = g + g₂
   x.filter fun g₁ => ¬∃ g₂, g₁ = g + g₂
 #align add_monoid_algebra.mod_of AddMonoidAlgebra.modOf
 
@@ -130,14 +131,14 @@ local infixl:70 " %ᵒᶠ " => modOf
 
 @[simp]
 theorem modOf_apply_of_not_exists_add (x : k[G]) (g : G) (g' : G)
-    (h : ¬∃ d, g' = g + d) : (x %ᵒᶠ g) g' = x g' :=
-  Finsupp.filter_apply_pos _ _ h
+    (h : ¬∃ d, g' = g + d) : (x %ᵒᶠ g) g' = x g' := by
+  classical exact Finsupp.filter_apply_pos _ _ h
 #align add_monoid_algebra.mod_of_apply_of_not_exists_add AddMonoidAlgebra.modOf_apply_of_not_exists_add
 
 @[simp]
 theorem modOf_apply_of_exists_add (x : k[G]) (g : G) (g' : G)
-    (h : ∃ d, g' = g + d) : (x %ᵒᶠ g) g' = 0 :=
-  Finsupp.filter_apply_neg _ _ <| by rwa [Classical.not_not]
+    (h : ∃ d, g' = g + d) : (x %ᵒᶠ g) g' = 0 := by
+  classical exact Finsupp.filter_apply_neg _ _ <| by rwa [Classical.not_not]
 #align add_monoid_algebra.mod_of_apply_of_exists_add AddMonoidAlgebra.modOf_apply_of_exists_add
 
 @[simp]

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -145,7 +145,7 @@ theorem modOf_apply_add_self (x : k[G]) (g : G) (d : G) : (x %ᵒᶠ g) (d + g)
   modOf_apply_of_exists_add _ _ _ ⟨_, add_comm _ _⟩
 #align add_monoid_algebra.mod_of_apply_add_self AddMonoidAlgebra.modOf_apply_add_self
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem modOf_apply_self_add (x : k[G]) (g : G) (d : G) : (x %ᵒᶠ g) (g + d) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, rfl⟩
 #align add_monoid_algebra.mod_of_apply_self_add AddMonoidAlgebra.modOf_apply_self_add

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>

@@ -70,7 +70,7 @@ theorem support_divOf (g : G) (x : k[G]) :
 
 @[simp]
 theorem zero_divOf (g : G) : (0 : k[G]) /ᵒᶠ g = 0 :=
-  map_zero _
+  map_zero (Finsupp.comapDomain.addMonoidHom _)
 #align add_monoid_algebra.zero_div_of AddMonoidAlgebra.zero_divOf
 
 @[simp]
@@ -80,7 +80,7 @@ theorem divOf_zero (x : k[G]) : x /ᵒᶠ 0 = x := by
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
 
 theorem add_divOf (x y : k[G]) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /ᵒᶠ g :=
-  map_add _ _ _
+  map_add (Finsupp.comapDomain.addMonoidHom _) _ _
 #align add_monoid_algebra.add_div_of AddMonoidAlgebra.add_divOf
 
 theorem divOf_add (x : k[G]) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
 import Mathlib.Algebra.MonoidAlgebra.Basic
-import Mathlib.Data.Finsupp.Order
 
 #align_import algebra.monoid_algebra.division from "leanprover-community/mathlib"@"72c366d0475675f1309d3027d3d7d47ee4423951"
 

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -52,7 +52,7 @@ noncomputable def divOf (x : k[G]) (g : G) : k[G] :=
   -- the support, and discarding the elements of the support from which `g` can't be subtracted.
   -- If `G` is an additive group, such as `ℤ` when used for `LaurentPolynomial`,
   -- then no discarding occurs.
-  @Finsupp.comapDomain.addMonoidHom _ _ _ _ ((· + ·) g) (add_right_injective g) x
+  @Finsupp.comapDomain.addMonoidHom _ _ _ _ (g + ·) (add_right_injective g) x
 #align add_monoid_algebra.div_of AddMonoidAlgebra.divOf
 
 local infixl:70 " /ᵒᶠ " => divOf
@@ -65,7 +65,7 @@ theorem divOf_apply (g : G) (x : k[G]) (g' : G) : (x /ᵒᶠ g) g' = x (g + g')
 @[simp]
 theorem support_divOf (g : G) (x : k[G]) :
     (x /ᵒᶠ g).support =
-      x.support.preimage ((· + ·) g) (Function.Injective.injOn (add_right_injective g) _) :=
+      x.support.preimage (g + ·) (Function.Injective.injOn (add_right_injective g) _) :=
   rfl
 #align add_monoid_algebra.support_div_of AddMonoidAlgebra.support_divOf
 

Introduce the notation R[A] for AddMonoidAlgebra R A. This is to align Mathlibs notation with the standard notation for group ring.

The notation is scoped in AddMonoidAlgebra and there is no analogous notation for MonoidAlgebra.

I only used the notation for single-character R and As and only in the range [a-zA-Z].

The extra lines are all in Mathlib/Algebra/MonoidAlgebra/Basic.lean. They are accounted for by extra text in the doc-module and the actual notation.

Affected files:

Counterexamples/ZeroDivisorsInAddMonoidAlgebras
Algebra/AlgebraicCard
Algebra/MonoidAlgebra/Basic
Algebra/MonoidAlgebra/Degree
Algebra/MonoidAlgebra/Division
Algebra/MonoidAlgebra/Grading
Algebra/MonoidAlgebra/NoZeroDivisors
Algebra/MonoidAlgebra/Support
Data/Polynomial/AlgebraMap
Data/Polynomial/Basic
Data/Polynomial/Eval
Data/Polynomial/Laurent
RingTheory/FiniteType

@@ -47,7 +47,7 @@ section
 variable [AddCancelCommMonoid G]
 
 /-- Divide by `of' k G g`, discarding terms not divisible by this. -/
-noncomputable def divOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k G :=
+noncomputable def divOf (x : k[G]) (g : G) : k[G] :=
   -- note: comapping by `+ g` has the effect of subtracting `g` from every element in
   -- the support, and discarding the elements of the support from which `g` can't be subtracted.
   -- If `G` is an additive group, such as `ℤ` when used for `LaurentPolynomial`,
@@ -58,40 +58,40 @@ noncomputable def divOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k
 local infixl:70 " /ᵒᶠ " => divOf
 
 @[simp]
-theorem divOf_apply (g : G) (x : AddMonoidAlgebra k G) (g' : G) : (x /ᵒᶠ g) g' = x (g + g') :=
+theorem divOf_apply (g : G) (x : k[G]) (g' : G) : (x /ᵒᶠ g) g' = x (g + g') :=
   rfl
 #align add_monoid_algebra.div_of_apply AddMonoidAlgebra.divOf_apply
 
 @[simp]
-theorem support_divOf (g : G) (x : AddMonoidAlgebra k G) :
+theorem support_divOf (g : G) (x : k[G]) :
     (x /ᵒᶠ g).support =
       x.support.preimage ((· + ·) g) (Function.Injective.injOn (add_right_injective g) _) :=
   rfl
 #align add_monoid_algebra.support_div_of AddMonoidAlgebra.support_divOf
 
 @[simp]
-theorem zero_divOf (g : G) : (0 : AddMonoidAlgebra k G) /ᵒᶠ g = 0 :=
+theorem zero_divOf (g : G) : (0 : k[G]) /ᵒᶠ g = 0 :=
   map_zero _
 #align add_monoid_algebra.zero_div_of AddMonoidAlgebra.zero_divOf
 
 @[simp]
-theorem divOf_zero (x : AddMonoidAlgebra k G) : x /ᵒᶠ 0 = x := by
+theorem divOf_zero (x : k[G]) : x /ᵒᶠ 0 = x := by
   refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
   simp only [AddMonoidAlgebra.divOf_apply, zero_add]
 #align add_monoid_algebra.div_of_zero AddMonoidAlgebra.divOf_zero
 
-theorem add_divOf (x y : AddMonoidAlgebra k G) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /ᵒᶠ g :=
+theorem add_divOf (x y : k[G]) (g : G) : (x + y) /ᵒᶠ g = x /ᵒᶠ g + y /ᵒᶠ g :=
   map_add _ _ _
 #align add_monoid_algebra.add_div_of AddMonoidAlgebra.add_divOf
 
-theorem divOf_add (x : AddMonoidAlgebra k G) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by
+theorem divOf_add (x : k[G]) (a b : G) : x /ᵒᶠ (a + b) = x /ᵒᶠ a /ᵒᶠ b := by
   refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
   simp only [AddMonoidAlgebra.divOf_apply, add_assoc]
 #align add_monoid_algebra.div_of_add AddMonoidAlgebra.divOf_add
 
 /-- A bundled version of `AddMonoidAlgebra.divOf`. -/
 @[simps]
-noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgebra k G) where
+noncomputable def divOfHom : Multiplicative G →* AddMonoid.End k[G] where
   toFun g :=
     { toFun := fun x => divOf x (Multiplicative.toAdd g)
       map_zero' := zero_divOf _
@@ -103,14 +103,14 @@ noncomputable def divOfHom : Multiplicative G →* AddMonoid.End (AddMonoidAlgeb
         (divOf_add _ _ _)
 #align add_monoid_algebra.div_of_hom AddMonoidAlgebra.divOfHom
 
-theorem of'_mul_divOf (a : G) (x : AddMonoidAlgebra k G) : of' k G a * x /ᵒᶠ a = x := by
+theorem of'_mul_divOf (a : G) (x : k[G]) : of' k G a * x /ᵒᶠ a = x := by
   refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
   rw [AddMonoidAlgebra.divOf_apply, of'_apply, single_mul_apply_aux, one_mul]
   intro c
   exact add_right_inj _
 #align add_monoid_algebra.of'_mul_div_of AddMonoidAlgebra.of'_mul_divOf
 
-theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ a = x := by
+theorem mul_of'_divOf (x : k[G]) (a : G) : x * of' k G a /ᵒᶠ a = x := by
   refine Finsupp.ext fun _ => ?_  -- porting note: `ext` doesn't work
   rw [AddMonoidAlgebra.divOf_apply, of'_apply, mul_single_apply_aux, mul_one]
   intro c
@@ -119,39 +119,39 @@ theorem mul_of'_divOf (x : AddMonoidAlgebra k G) (a : G) : x * of' k G a /ᵒᶠ
 #align add_monoid_algebra.mul_of'_div_of AddMonoidAlgebra.mul_of'_divOf
 
 theorem of'_divOf (a : G) : of' k G a /ᵒᶠ a = 1 := by
-  simpa only [one_mul] using mul_of'_divOf (1 : AddMonoidAlgebra k G) a
+  simpa only [one_mul] using mul_of'_divOf (1 : k[G]) a
 #align add_monoid_algebra.of'_div_of AddMonoidAlgebra.of'_divOf
 
 /-- The remainder upon division by `of' k G g`. -/
-noncomputable def modOf (x : AddMonoidAlgebra k G) (g : G) : AddMonoidAlgebra k G :=
+noncomputable def modOf (x : k[G]) (g : G) : k[G] :=
   x.filter fun g₁ => ¬∃ g₂, g₁ = g + g₂
 #align add_monoid_algebra.mod_of AddMonoidAlgebra.modOf
 
 local infixl:70 " %ᵒᶠ " => modOf
 
 @[simp]
-theorem modOf_apply_of_not_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
+theorem modOf_apply_of_not_exists_add (x : k[G]) (g : G) (g' : G)
     (h : ¬∃ d, g' = g + d) : (x %ᵒᶠ g) g' = x g' :=
   Finsupp.filter_apply_pos _ _ h
 #align add_monoid_algebra.mod_of_apply_of_not_exists_add AddMonoidAlgebra.modOf_apply_of_not_exists_add
 
 @[simp]
-theorem modOf_apply_of_exists_add (x : AddMonoidAlgebra k G) (g : G) (g' : G)
+theorem modOf_apply_of_exists_add (x : k[G]) (g : G) (g' : G)
     (h : ∃ d, g' = g + d) : (x %ᵒᶠ g) g' = 0 :=
   Finsupp.filter_apply_neg _ _ <| by rwa [Classical.not_not]
 #align add_monoid_algebra.mod_of_apply_of_exists_add AddMonoidAlgebra.modOf_apply_of_exists_add
 
 @[simp]
-theorem modOf_apply_add_self (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (d + g) = 0 :=
+theorem modOf_apply_add_self (x : k[G]) (g : G) (d : G) : (x %ᵒᶠ g) (d + g) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, add_comm _ _⟩
 #align add_monoid_algebra.mod_of_apply_add_self AddMonoidAlgebra.modOf_apply_add_self
 
 -- @[simp] -- Porting note: simp can prove this
-theorem modOf_apply_self_add (x : AddMonoidAlgebra k G) (g : G) (d : G) : (x %ᵒᶠ g) (g + d) = 0 :=
+theorem modOf_apply_self_add (x : k[G]) (g : G) (d : G) : (x %ᵒᶠ g) (g + d) = 0 :=
   modOf_apply_of_exists_add _ _ _ ⟨_, rfl⟩
 #align add_monoid_algebra.mod_of_apply_self_add AddMonoidAlgebra.modOf_apply_self_add
 
-theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ g = 0 := by
+theorem of'_mul_modOf (g : G) (x : k[G]) : of' k G g * x %ᵒᶠ g = 0 := by
   refine Finsupp.ext fun g' => ?_  -- porting note: `ext g'` doesn't work
   rw [Finsupp.zero_apply]
   obtain ⟨d, rfl⟩ | h := em (∃ d, g' = g + d)
@@ -159,7 +159,7 @@ theorem of'_mul_modOf (g : G) (x : AddMonoidAlgebra k G) : of' k G g * x %ᵒᶠ
   · rw [modOf_apply_of_not_exists_add _ _ _ h, of'_apply, single_mul_apply_of_not_exists_add _ _ h]
 #align add_monoid_algebra.of'_mul_mod_of AddMonoidAlgebra.of'_mul_modOf
 
-theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ g = 0 := by
+theorem mul_of'_modOf (x : k[G]) (g : G) : x * of' k G g %ᵒᶠ g = 0 := by
   refine Finsupp.ext fun g' => ?_  -- porting note: `ext g'` doesn't work
   rw [Finsupp.zero_apply]
   obtain ⟨d, rfl⟩ | h := em (∃ d, g' = g + d)
@@ -169,10 +169,10 @@ theorem mul_of'_modOf (x : AddMonoidAlgebra k G) (g : G) : x * of' k G g %ᵒᶠ
 #align add_monoid_algebra.mul_of'_mod_of AddMonoidAlgebra.mul_of'_modOf
 
 theorem of'_modOf (g : G) : of' k G g %ᵒᶠ g = 0 := by
-  simpa only [one_mul] using mul_of'_modOf (1 : AddMonoidAlgebra k G) g
+  simpa only [one_mul] using mul_of'_modOf (1 : k[G]) g
 #align add_monoid_algebra.of'_mod_of AddMonoidAlgebra.of'_modOf
 
-theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) :
+theorem divOf_add_modOf (x : k[G]) (g : G) :
     of' k G g * (x /ᵒᶠ g) + x %ᵒᶠ g = x := by
   refine Finsupp.ext fun g' => ?_  -- porting note: `ext` doesn't work
   rw [Finsupp.add_apply] -- porting note: changed from `simp_rw` which can't see through the type
@@ -186,11 +186,11 @@ theorem divOf_add_modOf (x : AddMonoidAlgebra k G) (g : G) :
     exact add_right_inj _
 #align add_monoid_algebra.div_of_add_mod_of AddMonoidAlgebra.divOf_add_modOf
 
-theorem modOf_add_divOf (x : AddMonoidAlgebra k G) (g : G) : x %ᵒᶠ g + of' k G g * (x /ᵒᶠ g) = x :=
+theorem modOf_add_divOf (x : k[G]) (g : G) : x %ᵒᶠ g + of' k G g * (x /ᵒᶠ g) = x :=
   by rw [add_comm, divOf_add_modOf]
 #align add_monoid_algebra.mod_of_add_div_of AddMonoidAlgebra.modOf_add_divOf
 
-theorem of'_dvd_iff_modOf_eq_zero {x : AddMonoidAlgebra k G} {g : G} :
+theorem of'_dvd_iff_modOf_eq_zero {x : k[G]} {g : G} :
     of' k G g ∣ x ↔ x %ᵒᶠ g = 0 := by
   constructor
   · rintro ⟨x, rfl⟩

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

This has nice performance benefits.

@@ -38,7 +38,7 @@ likely to be very useful.
 -/
 
 
-variable {k G : Type _} [Semiring k]
+variable {k G : Type*} [Semiring k]
 
 namespace AddMonoidAlgebra
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 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.monoid_algebra.division
-! leanprover-community/mathlib commit 72c366d0475675f1309d3027d3d7d47ee4423951
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.MonoidAlgebra.Basic
 import Mathlib.Data.Finsupp.Order
 
+#align_import algebra.monoid_algebra.division from "leanprover-community/mathlib"@"72c366d0475675f1309d3027d3d7d47ee4423951"
+
 /-!
 # Division of `AddMonoidAlgebra` by monomials
 

This is the second part of the forward port of leanprover-community/mathlib#15905.

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