algebra.ring.prod | Mathlib porting status

(last sync)

feat(*/prod): prod_prod_prod equivs (#19235)

These send ((a, b), (c, d)) to ((a, c), (b, d)), and this commit provides this bundled as equiv, add_equiv, mul_equiv, ring_equiv, and linear_equiv.

We already have something analogous for tensor_product.

Diff

@@ -212,7 +212,9 @@ end prod_map
 end ring_hom
 
 namespace ring_equiv
-variables {R S} [non_assoc_semiring R] [non_assoc_semiring S]
+variables {R S R' S'}
+variables [non_assoc_semiring R] [non_assoc_semiring S]
+variables [non_assoc_semiring R'] [non_assoc_semiring S']
 
 /-- Swapping components as an equivalence of (semi)rings. -/
 def prod_comm : R × S ≃+* S × R :=
@@ -229,6 +231,31 @@ ring_hom.ext $ λ _, rfl
   (ring_hom.snd S R).comp ↑(prod_comm : R × S ≃+* S × R) = ring_hom.fst R S :=
 ring_hom.ext $ λ _, rfl
 
+section
+variables (R R' S S')
+
+/-- Four-way commutativity of `prod`. The name matches `mul_mul_mul_comm`. -/
+@[simps apply]
+def prod_prod_prod_comm : (R × R') × (S × S') ≃+* (R × S) × (R' × S') :=
+{ to_fun := λ rrss, ((rrss.1.1, rrss.2.1), (rrss.1.2, rrss.2.2)),
+  inv_fun := λ rsrs, ((rsrs.1.1, rsrs.2.1), (rsrs.1.2, rsrs.2.2)),
+  .. add_equiv.prod_prod_prod_comm R R' S S',
+  .. mul_equiv.prod_prod_prod_comm R R' S S' }
+
+@[simp] lemma prod_prod_prod_comm_symm :
+  (prod_prod_prod_comm R R' S S').symm = prod_prod_prod_comm R S R' S' := rfl
+
+@[simp] lemma prod_prod_prod_comm_to_add_equiv :
+  (prod_prod_prod_comm R R' S S').to_add_equiv = add_equiv.prod_prod_prod_comm R R' S S' := rfl
+
+@[simp] lemma prod_prod_prod_comm_to_mul_equiv :
+  (prod_prod_prod_comm R R' S S').to_mul_equiv = mul_equiv.prod_prod_prod_comm R R' S S' := rfl
+
+@[simp] lemma prod_prod_prod_comm_to_equiv :
+  (prod_prod_prod_comm R R' S S').to_equiv = equiv.prod_prod_prod_comm R R' S S' := rfl
+
+end
+
 variables (R S) [subsingleton S]
 
 /-- A ring `R` is isomorphic to `R × S` when `S` is the zero ring -/

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -444,7 +444,7 @@ theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [
   by
   have :=
     NoZeroDivisors.eq_zero_or_eq_zero_of_hMul_eq_zero (show ((0 : R), (1 : S)) * (1, 0) = 0 by simp)
-  rw [Prod.mk_eq_zero, Prod.mk_eq_zero] at this 
+  rw [Prod.mk_eq_zero, Prod.mk_eq_zero] at this
   rcases this with (⟨_, h⟩ | ⟨h, _⟩)
   · exact zero_ne_one h.symm
   · exact zero_ne_one h.symm

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
 -/
-import Mathbin.Data.Int.Cast.Prod
-import Mathbin.Algebra.Group.Prod
-import Mathbin.Algebra.Ring.Equiv
-import Mathbin.Algebra.Order.Monoid.Prod
+import Data.Int.Cast.Prod
+import Algebra.Group.Prod
+import Algebra.Ring.Equiv
+import Algebra.Order.Monoid.Prod
 
 #align_import algebra.ring.prod from "leanprover-community/mathlib"@"cd391184c85986113f8c00844cfe6dda1d34be3d"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -443,7 +443,7 @@ theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [
     [Nontrivial R] [Nontrivial S] : False :=
   by
   have :=
-    NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zero (show ((0 : R), (1 : S)) * (1, 0) = 0 by simp)
+    NoZeroDivisors.eq_zero_or_eq_zero_of_hMul_eq_zero (show ((0 : R), (1 : S)) * (1, 0) = 0 by simp)
   rw [Prod.mk_eq_zero, Prod.mk_eq_zero] at this 
   rcases this with (⟨_, h⟩ | ⟨h, _⟩)
   · exact zero_ne_one h.symm
@@ -469,7 +469,7 @@ instance [OrderedCommSemiring α] [OrderedCommSemiring β] : OrderedCommSemiring
 
 instance [OrderedRing α] [OrderedRing β] : OrderedRing (α × β) :=
   { Prod.ring, Prod.orderedSemiring with
-    mul_nonneg := fun a b ha hb => ⟨mul_nonneg ha.1 hb.1, mul_nonneg ha.2 hb.2⟩ }
+    hMul_nonneg := fun a b ha hb => ⟨mul_nonneg ha.1 hb.1, mul_nonneg ha.2 hb.2⟩ }
 
 instance [OrderedCommRing α] [OrderedCommRing β] : OrderedCommRing (α × β) :=
   { Prod.commRing, Prod.orderedRing with }

bump to nightly-2023-07-27-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11f435d4e34a6cea0a1797d6b625b0c170be845

ae9579d5

Diff

@@ -328,34 +328,34 @@ def prodComm : R × S ≃+* S × R :=
 #align ring_equiv.prod_comm RingEquiv.prodComm
 -/
 
-#print RingEquiv.coe_prod_comm /-
+#print RingEquiv.coe_prodComm /-
 @[simp]
-theorem coe_prod_comm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
+theorem coe_prodComm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
   rfl
-#align ring_equiv.coe_prod_comm RingEquiv.coe_prod_comm
+#align ring_equiv.coe_prod_comm RingEquiv.coe_prodComm
 -/
 
-#print RingEquiv.coe_prod_comm_symm /-
+#print RingEquiv.coe_prodComm_symm /-
 @[simp]
-theorem coe_prod_comm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
+theorem coe_prodComm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
   rfl
-#align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prod_comm_symm
+#align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prodComm_symm
 -/
 
-#print RingEquiv.fst_comp_coe_prod_comm /-
+#print RingEquiv.fst_comp_coe_prodComm /-
 @[simp]
-theorem fst_comp_coe_prod_comm :
+theorem fst_comp_coe_prodComm :
     (RingHom.fst S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.snd R S :=
   RingHom.ext fun _ => rfl
-#align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prod_comm
+#align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prodComm
 -/
 
-#print RingEquiv.snd_comp_coe_prod_comm /-
+#print RingEquiv.snd_comp_coe_prodComm /-
 @[simp]
-theorem snd_comp_coe_prod_comm :
+theorem snd_comp_coe_prodComm :
     (RingHom.snd S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.fst R S :=
   RingHom.ext fun _ => rfl
-#align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prod_comm
+#align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prodComm
 -/
 
 section

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.ring.prod
-! leanprover-community/mathlib commit cd391184c85986113f8c00844cfe6dda1d34be3d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Int.Cast.Prod
 import Mathbin.Algebra.Group.Prod
 import Mathbin.Algebra.Ring.Equiv
 import Mathbin.Algebra.Order.Monoid.Prod
 
+#align_import algebra.ring.prod from "leanprover-community/mathlib"@"cd391184c85986113f8c00844cfe6dda1d34be3d"
+
 /-!
 # Semiring, ring etc structures on `R × S`

bump to nightly-2023-07-18-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

a4aa5276

Diff

@@ -365,6 +365,7 @@ section
 
 variable (R R' S S')
 
+#print RingEquiv.prodProdProdComm /-
 /-- Four-way commutativity of `prod`. The name matches `mul_mul_mul_comm`. -/
 @[simps apply]
 def prodProdProdComm : (R × R') × S × S' ≃+* (R × S) × R' × S' :=
@@ -374,29 +375,38 @@ def prodProdProdComm : (R × R') × S × S' ≃+* (R × S) × R' × S' :=
     toFun := fun rrss => ((rrss.1.1, rrss.2.1), (rrss.1.2, rrss.2.2))
     invFun := fun rsrs => ((rsrs.1.1, rsrs.2.1), (rsrs.1.2, rsrs.2.2)) }
 #align ring_equiv.prod_prod_prod_comm RingEquiv.prodProdProdComm
+-/
 
+#print RingEquiv.prodProdProdComm_symm /-
 @[simp]
 theorem prodProdProdComm_symm : (prodProdProdComm R R' S S').symm = prodProdProdComm R S R' S' :=
   rfl
 #align ring_equiv.prod_prod_prod_comm_symm RingEquiv.prodProdProdComm_symm
+-/
 
+#print RingEquiv.prodProdProdComm_toAddEquiv /-
 @[simp]
 theorem prodProdProdComm_toAddEquiv :
     (prodProdProdComm R R' S S').toAddEquiv = AddEquiv.prodProdProdComm R R' S S' :=
   rfl
 #align ring_equiv.prod_prod_prod_comm_to_add_equiv RingEquiv.prodProdProdComm_toAddEquiv
+-/
 
+#print RingEquiv.prodProdProdComm_toMulEquiv /-
 @[simp]
 theorem prodProdProdComm_toMulEquiv :
     (prodProdProdComm R R' S S').toMulEquiv = MulEquiv.prodProdProdComm R R' S S' :=
   rfl
 #align ring_equiv.prod_prod_prod_comm_to_mul_equiv RingEquiv.prodProdProdComm_toMulEquiv
+-/
 
+#print RingEquiv.prodProdProdComm_toEquiv /-
 @[simp]
 theorem prodProdProdComm_toEquiv :
     (prodProdProdComm R R' S S').toEquiv = Equiv.prodProdProdComm R R' S S' :=
   rfl
 #align ring_equiv.prod_prod_prod_comm_to_equiv RingEquiv.prodProdProdComm_toEquiv
+-/
 
 end

bump to nightly-2023-07-14-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/d608fc5d4e69d4cc21885913fb573a88b0deb521

3a6084c4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.ring.prod
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
+! leanprover-community/mathlib commit cd391184c85986113f8c00844cfe6dda1d34be3d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -318,7 +318,11 @@ end RingHom
 
 namespace RingEquiv
 
-variable {R S} [NonAssocSemiring R] [NonAssocSemiring S]
+variable {R S R' S'}
+
+variable [NonAssocSemiring R] [NonAssocSemiring S]
+
+variable [NonAssocSemiring R'] [NonAssocSemiring S']
 
 #print RingEquiv.prodComm /-
 /-- Swapping components as an equivalence of (semi)rings. -/
@@ -357,6 +361,45 @@ theorem snd_comp_coe_prod_comm :
 #align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prod_comm
 -/
 
+section
+
+variable (R R' S S')
+
+/-- Four-way commutativity of `prod`. The name matches `mul_mul_mul_comm`. -/
+@[simps apply]
+def prodProdProdComm : (R × R') × S × S' ≃+* (R × S) × R' × S' :=
+  { AddEquiv.prodProdProdComm R R' S S',
+    MulEquiv.prodProdProdComm R R' S
+      S' with
+    toFun := fun rrss => ((rrss.1.1, rrss.2.1), (rrss.1.2, rrss.2.2))
+    invFun := fun rsrs => ((rsrs.1.1, rsrs.2.1), (rsrs.1.2, rsrs.2.2)) }
+#align ring_equiv.prod_prod_prod_comm RingEquiv.prodProdProdComm
+
+@[simp]
+theorem prodProdProdComm_symm : (prodProdProdComm R R' S S').symm = prodProdProdComm R S R' S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_symm RingEquiv.prodProdProdComm_symm
+
+@[simp]
+theorem prodProdProdComm_toAddEquiv :
+    (prodProdProdComm R R' S S').toAddEquiv = AddEquiv.prodProdProdComm R R' S S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_to_add_equiv RingEquiv.prodProdProdComm_toAddEquiv
+
+@[simp]
+theorem prodProdProdComm_toMulEquiv :
+    (prodProdProdComm R R' S S').toMulEquiv = MulEquiv.prodProdProdComm R R' S S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_to_mul_equiv RingEquiv.prodProdProdComm_toMulEquiv
+
+@[simp]
+theorem prodProdProdComm_toEquiv :
+    (prodProdProdComm R R' S S').toEquiv = Equiv.prodProdProdComm R R' S S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_to_equiv RingEquiv.prodProdProdComm_toEquiv
+
+end
+
 variable (R S) [Subsingleton S]
 
 #print RingEquiv.prodZeroRing /-

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -94,57 +94,75 @@ namespace NonUnitalRingHom
 
 variable (R S) [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S]
 
+#print NonUnitalRingHom.fst /-
 /-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`.-/
 def fst : R × S →ₙ+* R :=
   { MulHom.fst R S, AddMonoidHom.fst R S with toFun := Prod.fst }
 #align non_unital_ring_hom.fst NonUnitalRingHom.fst
+-/
 
+#print NonUnitalRingHom.snd /-
 /-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`.-/
 def snd : R × S →ₙ+* S :=
   { MulHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
 #align non_unital_ring_hom.snd NonUnitalRingHom.snd
+-/
 
 variable {R S}
 
+#print NonUnitalRingHom.coe_fst /-
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
   rfl
 #align non_unital_ring_hom.coe_fst NonUnitalRingHom.coe_fst
+-/
 
+#print NonUnitalRingHom.coe_snd /-
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
   rfl
 #align non_unital_ring_hom.coe_snd NonUnitalRingHom.coe_snd
+-/
 
 section Prod
 
 variable [NonUnitalNonAssocSemiring T] (f : R →ₙ+* S) (g : R →ₙ+* T)
 
+#print NonUnitalRingHom.prod /-
 /-- Combine two non-unital ring homomorphisms `f : R →ₙ+* S`, `g : R →ₙ+* T` into
 `f.prod g : R →ₙ+* S × T` given by `(f.prod g) x = (f x, g x)` -/
 protected def prod (f : R →ₙ+* S) (g : R →ₙ+* T) : R →ₙ+* S × T :=
   { MulHom.prod (f : MulHom R S) (g : MulHom R T), AddMonoidHom.prod (f : R →+ S) (g : R →+ T) with
     toFun := fun x => (f x, g x) }
 #align non_unital_ring_hom.prod NonUnitalRingHom.prod
+-/
 
+#print NonUnitalRingHom.prod_apply /-
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
   rfl
 #align non_unital_ring_hom.prod_apply NonUnitalRingHom.prod_apply
+-/
 
+#print NonUnitalRingHom.fst_comp_prod /-
 @[simp]
 theorem fst_comp_prod : (fst S T).comp (f.Prod g) = f :=
   ext fun x => rfl
 #align non_unital_ring_hom.fst_comp_prod NonUnitalRingHom.fst_comp_prod
+-/
 
+#print NonUnitalRingHom.snd_comp_prod /-
 @[simp]
 theorem snd_comp_prod : (snd S T).comp (f.Prod g) = g :=
   ext fun x => rfl
 #align non_unital_ring_hom.snd_comp_prod NonUnitalRingHom.snd_comp_prod
+-/
 
+#print NonUnitalRingHom.prod_unique /-
 theorem prod_unique (f : R →ₙ+* S × T) : ((fst S T).comp f).Prod ((snd S T).comp f) = f :=
   ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply, Prod.mk.eta]
 #align non_unital_ring_hom.prod_unique NonUnitalRingHom.prod_unique
+-/
 
 end Prod
 
@@ -154,24 +172,32 @@ variable [NonUnitalNonAssocSemiring R'] [NonUnitalNonAssocSemiring S'] [NonUnita
 
 variable (f : R →ₙ+* R') (g : S →ₙ+* S')
 
+#print NonUnitalRingHom.prodMap /-
 /-- `prod.map` as a `non_unital_ring_hom`. -/
 def prodMap : R × S →ₙ+* R' × S' :=
   (f.comp (fst R S)).Prod (g.comp (snd R S))
 #align non_unital_ring_hom.prod_map NonUnitalRingHom.prodMap
+-/
 
+#print NonUnitalRingHom.prodMap_def /-
 theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :=
   rfl
 #align non_unital_ring_hom.prod_map_def NonUnitalRingHom.prodMap_def
+-/
 
+#print NonUnitalRingHom.coe_prodMap /-
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
   rfl
 #align non_unital_ring_hom.coe_prod_map NonUnitalRingHom.coe_prodMap
+-/
 
+#print NonUnitalRingHom.prod_comp_prodMap /-
 theorem prod_comp_prodMap (f : T →ₙ+* R) (g : T →ₙ+* S) (f' : R →ₙ+* R') (g' : S →ₙ+* S') :
     (f'.Prod_map g').comp (f.Prod g) = (f'.comp f).Prod (g'.comp g) :=
   rfl
 #align non_unital_ring_hom.prod_comp_prod_map NonUnitalRingHom.prod_comp_prodMap
+-/
 
 end Prod_map
 
@@ -181,57 +207,75 @@ namespace RingHom
 
 variable (R S) [NonAssocSemiring R] [NonAssocSemiring S]
 
+#print RingHom.fst /-
 /-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`.-/
 def fst : R × S →+* R :=
   { MonoidHom.fst R S, AddMonoidHom.fst R S with toFun := Prod.fst }
 #align ring_hom.fst RingHom.fst
+-/
 
+#print RingHom.snd /-
 /-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`.-/
 def snd : R × S →+* S :=
   { MonoidHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
 #align ring_hom.snd RingHom.snd
+-/
 
 variable {R S}
 
+#print RingHom.coe_fst /-
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
   rfl
 #align ring_hom.coe_fst RingHom.coe_fst
+-/
 
+#print RingHom.coe_snd /-
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
   rfl
 #align ring_hom.coe_snd RingHom.coe_snd
+-/
 
 section Prod
 
 variable [NonAssocSemiring T] (f : R →+* S) (g : R →+* T)
 
+#print RingHom.prod /-
 /-- Combine two ring homomorphisms `f : R →+* S`, `g : R →+* T` into `f.prod g : R →+* S × T`
 given by `(f.prod g) x = (f x, g x)` -/
 protected def prod (f : R →+* S) (g : R →+* T) : R →+* S × T :=
   { MonoidHom.prod (f : R →* S) (g : R →* T), AddMonoidHom.prod (f : R →+ S) (g : R →+ T) with
     toFun := fun x => (f x, g x) }
 #align ring_hom.prod RingHom.prod
+-/
 
+#print RingHom.prod_apply /-
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
   rfl
 #align ring_hom.prod_apply RingHom.prod_apply
+-/
 
+#print RingHom.fst_comp_prod /-
 @[simp]
 theorem fst_comp_prod : (fst S T).comp (f.Prod g) = f :=
   ext fun x => rfl
 #align ring_hom.fst_comp_prod RingHom.fst_comp_prod
+-/
 
+#print RingHom.snd_comp_prod /-
 @[simp]
 theorem snd_comp_prod : (snd S T).comp (f.Prod g) = g :=
   ext fun x => rfl
 #align ring_hom.snd_comp_prod RingHom.snd_comp_prod
+-/
 
+#print RingHom.prod_unique /-
 theorem prod_unique (f : R →+* S × T) : ((fst S T).comp f).Prod ((snd S T).comp f) = f :=
   ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply, Prod.mk.eta]
 #align ring_hom.prod_unique RingHom.prod_unique
+-/
 
 end Prod
 
@@ -241,24 +285,32 @@ variable [NonAssocSemiring R'] [NonAssocSemiring S'] [NonAssocSemiring T]
 
 variable (f : R →+* R') (g : S →+* S')
 
+#print RingHom.prodMap /-
 /-- `prod.map` as a `ring_hom`. -/
 def prodMap : R × S →+* R' × S' :=
   (f.comp (fst R S)).Prod (g.comp (snd R S))
 #align ring_hom.prod_map RingHom.prodMap
+-/
 
+#print RingHom.prodMap_def /-
 theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :=
   rfl
 #align ring_hom.prod_map_def RingHom.prodMap_def
+-/
 
+#print RingHom.coe_prodMap /-
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
   rfl
 #align ring_hom.coe_prod_map RingHom.coe_prodMap
+-/
 
+#print RingHom.prod_comp_prodMap /-
 theorem prod_comp_prodMap (f : T →+* R) (g : T →+* S) (f' : R →+* R') (g' : S →+* S') :
     (f'.Prod_map g').comp (f.Prod g) = (f'.comp f).Prod (g'.comp g) :=
   rfl
 #align ring_hom.prod_comp_prod_map RingHom.prod_comp_prodMap
+-/
 
 end Prod_map
 
@@ -268,35 +320,46 @@ namespace RingEquiv
 
 variable {R S} [NonAssocSemiring R] [NonAssocSemiring S]
 
+#print RingEquiv.prodComm /-
 /-- Swapping components as an equivalence of (semi)rings. -/
 def prodComm : R × S ≃+* S × R :=
   { AddEquiv.prodComm, MulEquiv.prodComm with }
 #align ring_equiv.prod_comm RingEquiv.prodComm
+-/
 
+#print RingEquiv.coe_prod_comm /-
 @[simp]
 theorem coe_prod_comm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
   rfl
 #align ring_equiv.coe_prod_comm RingEquiv.coe_prod_comm
+-/
 
+#print RingEquiv.coe_prod_comm_symm /-
 @[simp]
 theorem coe_prod_comm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
   rfl
 #align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prod_comm_symm
+-/
 
+#print RingEquiv.fst_comp_coe_prod_comm /-
 @[simp]
 theorem fst_comp_coe_prod_comm :
     (RingHom.fst S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.snd R S :=
   RingHom.ext fun _ => rfl
 #align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prod_comm
+-/
 
+#print RingEquiv.snd_comp_coe_prod_comm /-
 @[simp]
 theorem snd_comp_coe_prod_comm :
     (RingHom.snd S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.fst R S :=
   RingHom.ext fun _ => rfl
 #align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prod_comm
+-/
 
 variable (R S) [Subsingleton S]
 
+#print RingEquiv.prodZeroRing /-
 /-- A ring `R` is isomorphic to `R × S` when `S` is the zero ring -/
 @[simps]
 def prodZeroRing : R ≃+* R × S where
@@ -307,7 +370,9 @@ def prodZeroRing : R ≃+* R × S where
   left_inv x := rfl
   right_inv x := by cases x <;> simp
 #align ring_equiv.prod_zero_ring RingEquiv.prodZeroRing
+-/
 
+#print RingEquiv.zeroRingProd /-
 /-- A ring `R` is isomorphic to `S × R` when `S` is the zero ring -/
 @[simps]
 def zeroRingProd : R ≃+* S × R where
@@ -318,9 +383,11 @@ def zeroRingProd : R ≃+* S × R where
   left_inv x := rfl
   right_inv x := by cases x <;> simp
 #align ring_equiv.zero_ring_prod RingEquiv.zeroRingProd
+-/
 
 end RingEquiv
 
+#print false_of_nontrivial_of_product_domain /-
 /-- The product of two nontrivial rings is not a domain -/
 theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [IsDomain (R × S)]
     [Nontrivial R] [Nontrivial S] : False :=
@@ -332,6 +399,7 @@ theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [
   · exact zero_ne_one h.symm
   · exact zero_ne_one h.symm
 #align false_of_nontrivial_of_product_domain false_of_nontrivial_of_product_domain
+-/
 
 /-! ### Order -/

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -327,7 +327,7 @@ theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [
   by
   have :=
     NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zero (show ((0 : R), (1 : S)) * (1, 0) = 0 by simp)
-  rw [Prod.mk_eq_zero, Prod.mk_eq_zero] at this
+  rw [Prod.mk_eq_zero, Prod.mk_eq_zero] at this 
   rcases this with (⟨_, h⟩ | ⟨h, _⟩)
   · exact zero_ne_one h.symm
   · exact zero_ne_one h.symm

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -94,23 +94,11 @@ namespace NonUnitalRingHom
 
 variable (R S) [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S]
 
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 /-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`.-/
 def fst : R × S →ₙ+* R :=
   { MulHom.fst R S, AddMonoidHom.fst R S with toFun := Prod.fst }
 #align non_unital_ring_hom.fst NonUnitalRingHom.fst
 
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 /-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`.-/
 def snd : R × S →ₙ+* S :=
   { MulHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
@@ -118,23 +106,11 @@ def snd : R × S →ₙ+* S :=
 
 variable {R S}
 
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 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
   rfl
 #align non_unital_ring_hom.coe_fst NonUnitalRingHom.coe_fst
 
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 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
   rfl
@@ -144,12 +120,6 @@ section Prod
 
 variable [NonUnitalNonAssocSemiring T] (f : R →ₙ+* S) (g : R →ₙ+* T)
 
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 /-- Combine two non-unital ring homomorphisms `f : R →ₙ+* S`, `g : R →ₙ+* T` into
 `f.prod g : R →ₙ+* S × T` given by `(f.prod g) x = (f x, g x)` -/
 protected def prod (f : R →ₙ+* S) (g : R →ₙ+* T) : R →ₙ+* S × T :=
@@ -157,45 +127,21 @@ protected def prod (f : R →ₙ+* S) (g : R →ₙ+* T) : R →ₙ+* S × T :=
     toFun := fun x => (f x, g x) }
 #align non_unital_ring_hom.prod NonUnitalRingHom.prod
 
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 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
   rfl
 #align non_unital_ring_hom.prod_apply NonUnitalRingHom.prod_apply
 
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 @[simp]
 theorem fst_comp_prod : (fst S T).comp (f.Prod g) = f :=
   ext fun x => rfl
 #align non_unital_ring_hom.fst_comp_prod NonUnitalRingHom.fst_comp_prod
 
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 @[simp]
 theorem snd_comp_prod : (snd S T).comp (f.Prod g) = g :=
   ext fun x => rfl
 #align non_unital_ring_hom.snd_comp_prod NonUnitalRingHom.snd_comp_prod
 
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 theorem prod_unique (f : R →ₙ+* S × T) : ((fst S T).comp f).Prod ((snd S T).comp f) = f :=
   ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply, Prod.mk.eta]
 #align non_unital_ring_hom.prod_unique NonUnitalRingHom.prod_unique
@@ -208,44 +154,20 @@ variable [NonUnitalNonAssocSemiring R'] [NonUnitalNonAssocSemiring S'] [NonUnita
 
 variable (f : R →ₙ+* R') (g : S →ₙ+* S')
 
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 /-- `prod.map` as a `non_unital_ring_hom`. -/
 def prodMap : R × S →ₙ+* R' × S' :=
   (f.comp (fst R S)).Prod (g.comp (snd R S))
 #align non_unital_ring_hom.prod_map NonUnitalRingHom.prodMap
 
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 theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :=
   rfl
 #align non_unital_ring_hom.prod_map_def NonUnitalRingHom.prodMap_def
 
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 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
   rfl
 #align non_unital_ring_hom.coe_prod_map NonUnitalRingHom.coe_prodMap
 
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 theorem prod_comp_prodMap (f : T →ₙ+* R) (g : T →ₙ+* S) (f' : R →ₙ+* R') (g' : S →ₙ+* S') :
     (f'.Prod_map g').comp (f.Prod g) = (f'.comp f).Prod (g'.comp g) :=
   rfl
@@ -259,23 +181,11 @@ namespace RingHom
 
 variable (R S) [NonAssocSemiring R] [NonAssocSemiring S]
 
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 /-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`.-/
 def fst : R × S →+* R :=
   { MonoidHom.fst R S, AddMonoidHom.fst R S with toFun := Prod.fst }
 #align ring_hom.fst RingHom.fst
 
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 /-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`.-/
 def snd : R × S →+* S :=
   { MonoidHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
@@ -283,23 +193,11 @@ def snd : R × S →+* S :=
 
 variable {R S}
 
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 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
   rfl
 #align ring_hom.coe_fst RingHom.coe_fst
 
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 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
   rfl
@@ -309,12 +207,6 @@ section Prod
 
 variable [NonAssocSemiring T] (f : R →+* S) (g : R →+* T)
 
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 /-- Combine two ring homomorphisms `f : R →+* S`, `g : R →+* T` into `f.prod g : R →+* S × T`
 given by `(f.prod g) x = (f x, g x)` -/
 protected def prod (f : R →+* S) (g : R →+* T) : R →+* S × T :=
@@ -322,45 +214,21 @@ protected def prod (f : R →+* S) (g : R →+* T) : R →+* S × T :=
     toFun := fun x => (f x, g x) }
 #align ring_hom.prod RingHom.prod
 
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 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
   rfl
 #align ring_hom.prod_apply RingHom.prod_apply
 
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 @[simp]
 theorem fst_comp_prod : (fst S T).comp (f.Prod g) = f :=
   ext fun x => rfl
 #align ring_hom.fst_comp_prod RingHom.fst_comp_prod
 
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 @[simp]
 theorem snd_comp_prod : (snd S T).comp (f.Prod g) = g :=
   ext fun x => rfl
 #align ring_hom.snd_comp_prod RingHom.snd_comp_prod
 
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 theorem prod_unique (f : R →+* S × T) : ((fst S T).comp f).Prod ((snd S T).comp f) = f :=
   ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply, Prod.mk.eta]
 #align ring_hom.prod_unique RingHom.prod_unique
@@ -373,44 +241,20 @@ variable [NonAssocSemiring R'] [NonAssocSemiring S'] [NonAssocSemiring T]
 
 variable (f : R →+* R') (g : S →+* S')
 
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 /-- `prod.map` as a `ring_hom`. -/
 def prodMap : R × S →+* R' × S' :=
   (f.comp (fst R S)).Prod (g.comp (snd R S))
 #align ring_hom.prod_map RingHom.prodMap
 
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 theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :=
   rfl
 #align ring_hom.prod_map_def RingHom.prodMap_def
 
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 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
   rfl
 #align ring_hom.coe_prod_map RingHom.coe_prodMap
 
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 theorem prod_comp_prodMap (f : T →+* R) (g : T →+* S) (f' : R →+* R') (g' : S →+* S') :
     (f'.Prod_map g').comp (f.Prod g) = (f'.comp f).Prod (g'.comp g) :=
   rfl
@@ -424,45 +268,27 @@ namespace RingEquiv
 
 variable {R S} [NonAssocSemiring R] [NonAssocSemiring S]
 
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 /-- Swapping components as an equivalence of (semi)rings. -/
 def prodComm : R × S ≃+* S × R :=
   { AddEquiv.prodComm, MulEquiv.prodComm with }
 #align ring_equiv.prod_comm RingEquiv.prodComm
 
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 @[simp]
 theorem coe_prod_comm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
   rfl
 #align ring_equiv.coe_prod_comm RingEquiv.coe_prod_comm
 
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 @[simp]
 theorem coe_prod_comm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
   rfl
 #align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prod_comm_symm
 
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 @[simp]
 theorem fst_comp_coe_prod_comm :
     (RingHom.fst S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.snd R S :=
   RingHom.ext fun _ => rfl
 #align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prod_comm
 
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 @[simp]
 theorem snd_comp_coe_prod_comm :
     (RingHom.snd S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.fst R S :=
@@ -471,12 +297,6 @@ theorem snd_comp_coe_prod_comm :
 
 variable (R S) [Subsingleton S]
 
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 /-- A ring `R` is isomorphic to `R × S` when `S` is the zero ring -/
 @[simps]
 def prodZeroRing : R ≃+* R × S where
@@ -488,12 +308,6 @@ def prodZeroRing : R ≃+* R × S where
   right_inv x := by cases x <;> simp
 #align ring_equiv.prod_zero_ring RingEquiv.prodZeroRing
 
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 /-- A ring `R` is isomorphic to `S × R` when `S` is the zero ring -/
 @[simps]
 def zeroRingProd : R ≃+* S × R where
@@ -507,12 +321,6 @@ def zeroRingProd : R ≃+* S × R where
 
 end RingEquiv
 
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 /-- The product of two nontrivial rings is not a domain -/
 theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [IsDomain (R × S)]
     [Nontrivial R] [Nontrivial S] : False :=

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -436,10 +436,7 @@ def prodComm : R × S ≃+* S × R :=
 #align ring_equiv.prod_comm RingEquiv.prodComm
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_equiv.coe_prod_comm RingEquiv.coe_prod_commₓ'. -/
 @[simp]
 theorem coe_prod_comm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
@@ -447,10 +444,7 @@ theorem coe_prod_comm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
 #align ring_equiv.coe_prod_comm RingEquiv.coe_prod_comm
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prod_comm_symmₓ'. -/
 @[simp]
 theorem coe_prod_comm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
@@ -458,10 +452,7 @@ theorem coe_prod_comm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swa
 #align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prod_comm_symm
 
 /- warning: ring_equiv.fst_comp_coe_prod_comm -> RingEquiv.fst_comp_coe_prod_comm is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prod_commₓ'. -/
 @[simp]
 theorem fst_comp_coe_prod_comm :
@@ -470,10 +461,7 @@ theorem fst_comp_coe_prod_comm :
 #align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prod_comm
 
 /- warning: ring_equiv.snd_comp_coe_prod_comm -> RingEquiv.snd_comp_coe_prod_comm is a dubious translation:
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(NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))))) (Prod.{u1, u2} R S) (Prod.{u2, u1} S R) (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u1} S R _inst_2 _inst_1) (RingEquiv.ringEquivClass.{max u1 u2, max u2 u1} (Prod.{u1, u2} R S) (Prod.{u2, u1} S R) (Prod.hasMul.{u1, u2} R S (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)))) (Prod.hasAdd.{u1, u2} R S (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)))) (Prod.hasMul.{u2, u1} S R (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))) (Prod.hasAdd.{u2, u1} S R (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))))))))) (RingEquiv.prodComm.{u1, u2} R S _inst_1 _inst_2))) (RingHom.fst.{u1, u2} R S _inst_1 _inst_2)
-but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (RingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (RingHom.comp.{max u2 u1, max u2 u1, u2} (Prod.{u2, u1} R S) (Prod.{u1, u2} S R) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u1, u2} S R _inst_2 _inst_1) _inst_1 (RingHom.snd.{u1, u2} S R _inst_2 _inst_1) (RingHomClass.toRingHom.{max u2 u1, max u2 u1, max u2 u1} (RingEquiv.{max u1 u2, max u2 u1} (Prod.{u2, u1} R S) (Prod.{u1, u2} S R) (Prod.instMulProd.{u2, u1} R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2))) (Prod.instMulProd.{u1, u2} S R (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))) (Prod.instAddSum.{u2, u1} R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)))) (Prod.instAddSum.{u1, u2} S R (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2))) (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))))) (Prod.{u2, u1} R S) (Prod.{u1, u2} S R) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u1, u2} S R _inst_2 _inst_1) (RingEquivClass.toRingHomClass.{max u2 u1, max u2 u1, max u2 u1} (RingEquiv.{max u1 u2, max u2 u1} (Prod.{u2, u1} R S) (Prod.{u1, u2} S R) (Prod.instMulProd.{u2, u1} R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2))) (Prod.instMulProd.{u1, u2} S R (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))) (Prod.instAddSum.{u2, u1} R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)))) (Prod.instAddSum.{u1, u2} S R (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2))) (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))))) (Prod.{u2, u1} R S) (Prod.{u1, u2} S R) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u1, u2} S R _inst_2 _inst_1) (RingEquiv.instRingEquivClassRingEquiv.{max u2 u1, max u2 u1} (Prod.{u2, u1} R S) (Prod.{u1, u2} S R) (Prod.instMulProd.{u2, u1} R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2))) (Prod.instMulProd.{u1, u2} S R (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))) (Prod.instAddSum.{u2, u1} R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)))) (Prod.instAddSum.{u1, u2} S R (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2))) (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)))))) (RingEquiv.prodComm.{u2, u1} R S _inst_1 _inst_2))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prod_commₓ'. -/
 @[simp]
 theorem snd_comp_coe_prod_comm :

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -122,7 +122,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u1)} ((Prod.{u1, u2} R S) -> R) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ (max u1 u2)) (succ u1)} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (fun (_x : NonUnitalRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) => (Prod.{u1, u2} R S) -> R) (NonUnitalRingHom.hasCoeToFun.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (NonUnitalRingHom.fst.{u1, u2} R S _inst_1 _inst_2)) (Prod.fst.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_1) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1))) (NonUnitalRingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_1) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1))) (NonUnitalRingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_fst NonUnitalRingHom.coe_fstₓ'. -/
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
@@ -133,7 +133,7 @@ theorem coe_fst : ⇑(fst R S) = Prod.fst :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u2)} ((Prod.{u1, u2} R S) -> S) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (fun (_x : NonUnitalRingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) => (Prod.{u1, u2} R S) -> S) (NonUnitalRingHom.hasCoeToFun.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (NonUnitalRingHom.snd.{u1, u2} R S _inst_1 _inst_2)) (Prod.snd.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2))) (NonUnitalRingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2))) (NonUnitalRingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_snd NonUnitalRingHom.coe_sndₓ'. -/
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
@@ -161,7 +161,7 @@ protected def prod (f : R →ₙ+* S) (g : R →ₙ+* T) : R →ₙ+* S × T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} T] (f : NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} S T) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (fun (_x : NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) => R -> (Prod.{u2, u3} S T)) (NonUnitalRingHom.hasCoeToFun.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (NonUnitalRingHom.prod.{u1, u2, u3} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u2, u3} S T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) (fun (_x : NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) => R -> S) (NonUnitalRingHom.hasCoeToFun.{u1, u2} R S _inst_1 _inst_2) f x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) (fun (_x : NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) => R -> T) (NonUnitalRingHom.hasCoeToFun.{u1, u3} R T _inst_1 _inst_3) g x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} T] (f : NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)))) (NonUnitalRingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} T _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3))) g x))
+  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} T] (f : NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)))) (NonUnitalRingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} T _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3))) g x))
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.prod_apply NonUnitalRingHom.prod_applyₓ'. -/
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
@@ -233,7 +233,7 @@ theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R' : Type.{u2}} {S : Type.{u3}} {S' : Type.{u4}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u4} S'] (f : NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4), Eq.{max (succ (max u1 u3)) (succ (max u2 u4))} ((Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u4)), max (succ (max u1 u3)) (succ (max u2 u4))} (NonUnitalRingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (fun (_x : NonUnitalRingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) => (Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (NonUnitalRingHom.hasCoeToFun.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (NonUnitalRingHom.prodMap.{u1, u2, u3, u4} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u1, u2, u3, u4} R R' S S' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) (fun (_x : NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) => R -> R') (NonUnitalRingHom.hasCoeToFun.{u1, u2} R R' _inst_1 _inst_3) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4) (fun (_x : NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4) => S -> S') (NonUnitalRingHom.hasCoeToFun.{u3, u4} S S' _inst_2 _inst_4) g))
 but is expected to have type
-  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u4} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u1} S'] (f : NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)))) (NonUnitalRingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} R' _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} S' _inst_4) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4))) g))
+  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u4} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u1} S'] (f : NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)))) (NonUnitalRingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} R' _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} S' _inst_4) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4))) g))
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_prod_map NonUnitalRingHom.coe_prodMapₓ'. -/
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
@@ -287,7 +287,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u1)} ((Prod.{u1, u2} R S) -> R) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ (max u1 u2)) (succ u1)} (RingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (fun (_x : RingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) => (Prod.{u1, u2} R S) -> R) (RingHom.hasCoeToFun.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (RingHom.fst.{u1, u2} R S _inst_1 _inst_2)) (Prod.fst.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (RingHom.instRingHomClassRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1)))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (RingHom.instRingHomClassRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1)))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_fst RingHom.coe_fstₓ'. -/
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
@@ -298,7 +298,7 @@ theorem coe_fst : ⇑(fst R S) = Prod.fst :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u2)} ((Prod.{u1, u2} R S) -> S) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (fun (_x : RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) => (Prod.{u1, u2} R S) -> S) (RingHom.hasCoeToFun.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (RingHom.snd.{u1, u2} R S _inst_1 _inst_2)) (Prod.snd.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2)))) (RingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2)))) (RingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_snd RingHom.coe_sndₓ'. -/
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
@@ -326,7 +326,7 @@ protected def prod (f : R →+* S) (g : R →+* T) : R →+* S × T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} T] (f : RingHom.{u1, u2} R S _inst_1 _inst_2) (g : RingHom.{u1, u3} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} S T) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (RingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (fun (_x : RingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) => R -> (Prod.{u2, u3} S T)) (RingHom.hasCoeToFun.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (RingHom.prod.{u1, u2, u3} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u2, u3} S T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S _inst_1 _inst_2) (fun (_x : RingHom.{u1, u2} R S _inst_1 _inst_2) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S _inst_1 _inst_2) f x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R T _inst_1 _inst_3) (fun (_x : RingHom.{u1, u3} R T _inst_1 _inst_3) => R -> T) (RingHom.hasCoeToFun.{u1, u3} R T _inst_1 _inst_3) g x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} T] (f : RingHom.{u1, u3} R S _inst_1 _inst_2) (g : RingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (RingHom.instRingHomClassRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))))) (RingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (RingHom.instRingHomClassRingHom.{u1, u3} R S _inst_1 _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u1, u2} R T _inst_1 _inst_3)))) g x))
+  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} T] (f : RingHom.{u1, u3} R S _inst_1 _inst_2) (g : RingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (RingHom.instRingHomClassRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))))) (RingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (RingHom.instRingHomClassRingHom.{u1, u3} R S _inst_1 _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u1, u2} R T _inst_1 _inst_3)))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.prod_apply RingHom.prod_applyₓ'. -/
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
@@ -398,7 +398,7 @@ theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R' : Type.{u2}} {S : Type.{u3}} {S' : Type.{u4}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} R'] [_inst_4 : NonAssocSemiring.{u4} S'] (f : RingHom.{u1, u2} R R' _inst_1 _inst_3) (g : RingHom.{u3, u4} S S' _inst_2 _inst_4), Eq.{max (succ (max u1 u3)) (succ (max u2 u4))} ((Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u4)), max (succ (max u1 u3)) (succ (max u2 u4))} (RingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (fun (_x : RingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) => (Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (RingHom.hasCoeToFun.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (RingHom.prodMap.{u1, u2, u3, u4} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u1, u2, u3, u4} R R' S S' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R R' _inst_1 _inst_3) (fun (_x : RingHom.{u1, u2} R R' _inst_1 _inst_3) => R -> R') (RingHom.hasCoeToFun.{u1, u2} R R' _inst_1 _inst_3) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} S S' _inst_2 _inst_4) (fun (_x : RingHom.{u3, u4} S S' _inst_2 _inst_4) => S -> S') (RingHom.hasCoeToFun.{u3, u4} S S' _inst_2 _inst_4) g))
 but is expected to have type
-  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonAssocSemiring.{u4} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} R'] [_inst_4 : NonAssocSemiring.{u1} S'] (f : RingHom.{u4, u3} R R' _inst_1 _inst_3) (g : RingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))))) (RingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u4, u3} R R' _inst_1 _inst_3)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (RingHom.instRingHomClassRingHom.{u2, u1} S S' _inst_2 _inst_4)))) g))
+  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonAssocSemiring.{u4} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} R'] [_inst_4 : NonAssocSemiring.{u1} S'] (f : RingHom.{u4, u3} R R' _inst_1 _inst_3) (g : RingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))))) (RingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u4, u3} R R' _inst_1 _inst_3)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (RingHom.instRingHomClassRingHom.{u2, u1} S S' _inst_2 _inst_4)))) g))
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_prod_map RingHom.coe_prodMapₓ'. -/
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -122,7 +122,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u1)} ((Prod.{u1, u2} R S) -> R) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ (max u1 u2)) (succ u1)} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (fun (_x : NonUnitalRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) => (Prod.{u1, u2} R S) -> R) (NonUnitalRingHom.hasCoeToFun.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (NonUnitalRingHom.fst.{u1, u2} R S _inst_1 _inst_2)) (Prod.fst.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_1) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1))) (NonUnitalRingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_1) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1))) (NonUnitalRingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_fst NonUnitalRingHom.coe_fstₓ'. -/
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
@@ -133,7 +133,7 @@ theorem coe_fst : ⇑(fst R S) = Prod.fst :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u2)} ((Prod.{u1, u2} R S) -> S) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (fun (_x : NonUnitalRingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) => (Prod.{u1, u2} R S) -> S) (NonUnitalRingHom.hasCoeToFun.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (NonUnitalRingHom.snd.{u1, u2} R S _inst_1 _inst_2)) (Prod.snd.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2))) (NonUnitalRingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2))) (NonUnitalRingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_snd NonUnitalRingHom.coe_sndₓ'. -/
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
@@ -161,7 +161,7 @@ protected def prod (f : R →ₙ+* S) (g : R →ₙ+* T) : R →ₙ+* S × T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} T] (f : NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} S T) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (fun (_x : NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) => R -> (Prod.{u2, u3} S T)) (NonUnitalRingHom.hasCoeToFun.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (NonUnitalRingHom.prod.{u1, u2, u3} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u2, u3} S T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) (fun (_x : NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) => R -> S) (NonUnitalRingHom.hasCoeToFun.{u1, u2} R S _inst_1 _inst_2) f x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) (fun (_x : NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) => R -> T) (NonUnitalRingHom.hasCoeToFun.{u1, u3} R T _inst_1 _inst_3) g x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} T] (f : NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)))) (NonUnitalRingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} T _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3))) g x))
+  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} T] (f : NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)))) (NonUnitalRingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} T _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3))) g x))
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.prod_apply NonUnitalRingHom.prod_applyₓ'. -/
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
@@ -233,7 +233,7 @@ theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R' : Type.{u2}} {S : Type.{u3}} {S' : Type.{u4}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u4} S'] (f : NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4), Eq.{max (succ (max u1 u3)) (succ (max u2 u4))} ((Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u4)), max (succ (max u1 u3)) (succ (max u2 u4))} (NonUnitalRingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (fun (_x : NonUnitalRingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) => (Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (NonUnitalRingHom.hasCoeToFun.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (NonUnitalRingHom.prodMap.{u1, u2, u3, u4} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u1, u2, u3, u4} R R' S S' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) (fun (_x : NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) => R -> R') (NonUnitalRingHom.hasCoeToFun.{u1, u2} R R' _inst_1 _inst_3) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4) (fun (_x : NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4) => S -> S') (NonUnitalRingHom.hasCoeToFun.{u3, u4} S S' _inst_2 _inst_4) g))
 but is expected to have type
-  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u4} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u1} S'] (f : NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)))) (NonUnitalRingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} R' _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} S' _inst_4) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4))) g))
+  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u4} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u1} S'] (f : NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)))) (NonUnitalRingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} R' _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} S' _inst_4) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4))) g))
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_prod_map NonUnitalRingHom.coe_prodMapₓ'. -/
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
@@ -287,7 +287,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u1)} ((Prod.{u1, u2} R S) -> R) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ (max u1 u2)) (succ u1)} (RingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (fun (_x : RingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) => (Prod.{u1, u2} R S) -> R) (RingHom.hasCoeToFun.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (RingHom.fst.{u1, u2} R S _inst_1 _inst_2)) (Prod.fst.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (RingHom.instRingHomClassRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1)))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (RingHom.instRingHomClassRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1)))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_fst RingHom.coe_fstₓ'. -/
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
@@ -298,7 +298,7 @@ theorem coe_fst : ⇑(fst R S) = Prod.fst :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u2)} ((Prod.{u1, u2} R S) -> S) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (fun (_x : RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) => (Prod.{u1, u2} R S) -> S) (RingHom.hasCoeToFun.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (RingHom.snd.{u1, u2} R S _inst_1 _inst_2)) (Prod.snd.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2)))) (RingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2)))) (RingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_snd RingHom.coe_sndₓ'. -/
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
@@ -326,7 +326,7 @@ protected def prod (f : R →+* S) (g : R →+* T) : R →+* S × T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} T] (f : RingHom.{u1, u2} R S _inst_1 _inst_2) (g : RingHom.{u1, u3} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} S T) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (RingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (fun (_x : RingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) => R -> (Prod.{u2, u3} S T)) (RingHom.hasCoeToFun.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (RingHom.prod.{u1, u2, u3} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u2, u3} S T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S _inst_1 _inst_2) (fun (_x : RingHom.{u1, u2} R S _inst_1 _inst_2) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S _inst_1 _inst_2) f x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R T _inst_1 _inst_3) (fun (_x : RingHom.{u1, u3} R T _inst_1 _inst_3) => R -> T) (RingHom.hasCoeToFun.{u1, u3} R T _inst_1 _inst_3) g x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} T] (f : RingHom.{u1, u3} R S _inst_1 _inst_2) (g : RingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (RingHom.instRingHomClassRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))))) (RingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (RingHom.instRingHomClassRingHom.{u1, u3} R S _inst_1 _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u1, u2} R T _inst_1 _inst_3)))) g x))
+  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} T] (f : RingHom.{u1, u3} R S _inst_1 _inst_2) (g : RingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (RingHom.instRingHomClassRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))))) (RingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (RingHom.instRingHomClassRingHom.{u1, u3} R S _inst_1 _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u1, u2} R T _inst_1 _inst_3)))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.prod_apply RingHom.prod_applyₓ'. -/
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
@@ -398,7 +398,7 @@ theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R' : Type.{u2}} {S : Type.{u3}} {S' : Type.{u4}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} R'] [_inst_4 : NonAssocSemiring.{u4} S'] (f : RingHom.{u1, u2} R R' _inst_1 _inst_3) (g : RingHom.{u3, u4} S S' _inst_2 _inst_4), Eq.{max (succ (max u1 u3)) (succ (max u2 u4))} ((Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u4)), max (succ (max u1 u3)) (succ (max u2 u4))} (RingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (fun (_x : RingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) => (Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (RingHom.hasCoeToFun.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (RingHom.prodMap.{u1, u2, u3, u4} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u1, u2, u3, u4} R R' S S' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R R' _inst_1 _inst_3) (fun (_x : RingHom.{u1, u2} R R' _inst_1 _inst_3) => R -> R') (RingHom.hasCoeToFun.{u1, u2} R R' _inst_1 _inst_3) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} S S' _inst_2 _inst_4) (fun (_x : RingHom.{u3, u4} S S' _inst_2 _inst_4) => S -> S') (RingHom.hasCoeToFun.{u3, u4} S S' _inst_2 _inst_4) g))
 but is expected to have type
-  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonAssocSemiring.{u4} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} R'] [_inst_4 : NonAssocSemiring.{u1} S'] (f : RingHom.{u4, u3} R R' _inst_1 _inst_3) (g : RingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))))) (RingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u4, u3} R R' _inst_1 _inst_3)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (RingHom.instRingHomClassRingHom.{u2, u1} S S' _inst_2 _inst_4)))) g))
+  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonAssocSemiring.{u4} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} R'] [_inst_4 : NonAssocSemiring.{u1} S'] (f : RingHom.{u4, u3} R R' _inst_1 _inst_3) (g : RingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))))) (RingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u4, u3} R R' _inst_1 _inst_3)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (RingHom.instRingHomClassRingHom.{u2, u1} S S' _inst_2 _inst_4)))) g))
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_prod_map RingHom.coe_prodMapₓ'. -/
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=

bump to nightly-2023-03-08-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

10f15343

Diff

@@ -122,7 +122,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u1)} ((Prod.{u1, u2} R S) -> R) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ (max u1 u2)) (succ u1)} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (fun (_x : NonUnitalRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) => (Prod.{u1, u2} R S) -> R) (NonUnitalRingHom.hasCoeToFun.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (NonUnitalRingHom.fst.{u1, u2} R S _inst_1 _inst_2)) (Prod.fst.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_1) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1))) (NonUnitalRingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_1) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1))) (NonUnitalRingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_fst NonUnitalRingHom.coe_fstₓ'. -/
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
@@ -133,7 +133,7 @@ theorem coe_fst : ⇑(fst R S) = Prod.fst :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u2)} ((Prod.{u1, u2} R S) -> S) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (NonUnitalRingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (fun (_x : NonUnitalRingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) => (Prod.{u1, u2} R S) -> S) (NonUnitalRingHom.hasCoeToFun.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonUnitalNonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (NonUnitalRingHom.snd.{u1, u2} R S _inst_1 _inst_2)) (Prod.snd.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2))) (NonUnitalRingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u2} R] [_inst_2 : NonUnitalNonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (NonUnitalRingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonUnitalNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2))) (NonUnitalRingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_snd NonUnitalRingHom.coe_sndₓ'. -/
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
@@ -161,7 +161,7 @@ protected def prod (f : R →ₙ+* S) (g : R →ₙ+* T) : R →ₙ+* S × T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} T] (f : NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} S T) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (fun (_x : NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) => R -> (Prod.{u2, u3} S T)) (NonUnitalRingHom.hasCoeToFun.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonUnitalNonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (NonUnitalRingHom.prod.{u1, u2, u3} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u2, u3} S T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) (fun (_x : NonUnitalRingHom.{u1, u2} R S _inst_1 _inst_2) => R -> S) (NonUnitalRingHom.hasCoeToFun.{u1, u2} R S _inst_1 _inst_2) f x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) (fun (_x : NonUnitalRingHom.{u1, u3} R T _inst_1 _inst_3) => R -> T) (NonUnitalRingHom.hasCoeToFun.{u1, u3} R T _inst_1 _inst_3) g x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} T] (f : NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)))) (NonUnitalRingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} T _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3))) g x))
+  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} T] (f : NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) (g : NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (NonUnitalRingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonUnitalNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)))) (NonUnitalRingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} S _inst_2) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (NonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u3} R S _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u2} T _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (NonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u1, u2} R T _inst_1 _inst_3))) g x))
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.prod_apply NonUnitalRingHom.prod_applyₓ'. -/
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
@@ -233,7 +233,7 @@ theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R' : Type.{u2}} {S : Type.{u3}} {S' : Type.{u4}} [_inst_1 : NonUnitalNonAssocSemiring.{u1} R] [_inst_2 : NonUnitalNonAssocSemiring.{u3} S] [_inst_3 : NonUnitalNonAssocSemiring.{u2} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u4} S'] (f : NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4), Eq.{max (succ (max u1 u3)) (succ (max u2 u4))} ((Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u4)), max (succ (max u1 u3)) (succ (max u2 u4))} (NonUnitalRingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (fun (_x : NonUnitalRingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) => (Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (NonUnitalRingHom.hasCoeToFun.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonUnitalNonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonUnitalNonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (NonUnitalRingHom.prodMap.{u1, u2, u3, u4} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u1, u2, u3, u4} R R' S S' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) (fun (_x : NonUnitalRingHom.{u1, u2} R R' _inst_1 _inst_3) => R -> R') (NonUnitalRingHom.hasCoeToFun.{u1, u2} R R' _inst_1 _inst_3) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4) (fun (_x : NonUnitalRingHom.{u3, u4} S S' _inst_2 _inst_4) => S -> S') (NonUnitalRingHom.hasCoeToFun.{u3, u4} S S' _inst_2 _inst_4) g))
 but is expected to have type
-  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u4} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u1} S'] (f : NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)))) (NonUnitalRingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} R' _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} S' _inst_4) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4))) g))
+  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonUnitalNonAssocSemiring.{u4} R] [_inst_2 : NonUnitalNonAssocSemiring.{u2} S] [_inst_3 : NonUnitalNonAssocSemiring.{u3} R'] [_inst_4 : NonUnitalNonAssocSemiring.{u1} S'] (f : NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) (g : NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (NonUnitalRingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonUnitalNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonUnitalNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)))) (NonUnitalRingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u3} R' _inst_3) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (NonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u4, u3} R R' _inst_1 _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} S' _inst_4) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (NonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (NonUnitalRingHom.instNonUnitalRingHomClassNonUnitalRingHom.{u2, u1} S S' _inst_2 _inst_4))) g))
 Case conversion may be inaccurate. Consider using '#align non_unital_ring_hom.coe_prod_map NonUnitalRingHom.coe_prodMapₓ'. -/
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=
@@ -287,7 +287,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u1)} ((Prod.{u1, u2} R S) -> R) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ (max u1 u2)) (succ u1)} (RingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (fun (_x : RingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) => (Prod.{u1, u2} R S) -> R) (RingHom.hasCoeToFun.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_1) (RingHom.fst.{u1, u2} R S _inst_1 _inst_2)) (Prod.fst.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (RingHom.instRingHomClassRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1)))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => R) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R _inst_1) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u2} (RingHom.{max u1 u2, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1) (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1 (RingHom.instRingHomClassRingHom.{max u2 u1, u2} (Prod.{u2, u1} R S) R (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_1)))) (RingHom.fst.{u2, u1} R S _inst_1 _inst_2)) (Prod.fst.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_fst RingHom.coe_fstₓ'. -/
 @[simp]
 theorem coe_fst : ⇑(fst R S) = Prod.fst :=
@@ -298,7 +298,7 @@ theorem coe_fst : ⇑(fst R S) = Prod.fst :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S], Eq.{max (succ (max u1 u2)) (succ u2)} ((Prod.{u1, u2} R S) -> S) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (fun (_x : RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) => (Prod.{u1, u2} R S) -> S) (RingHom.hasCoeToFun.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S _inst_1 _inst_2) _inst_2) (RingHom.snd.{u1, u2} R S _inst_1 _inst_2)) (Prod.snd.{u1, u2} R S)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2)))) (RingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : NonAssocSemiring.{u2} R] [_inst_2 : NonAssocSemiring.{u1} S], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Prod.{u2, u1} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) (fun (_x : Prod.{u2, u1} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u2, u1} R S) => S) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Prod.{u2, u1} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Prod.{u2, u1} R S) (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, max u2 u1, u1} (RingHom.{max u1 u2, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2) (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2 (RingHom.instRingHomClassRingHom.{max u2 u1, u1} (Prod.{u2, u1} R S) S (Prod.instNonAssocSemiringProd.{u2, u1} R S _inst_1 _inst_2) _inst_2)))) (RingHom.snd.{u2, u1} R S _inst_1 _inst_2)) (Prod.snd.{u2, u1} R S)
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_snd RingHom.coe_sndₓ'. -/
 @[simp]
 theorem coe_snd : ⇑(snd R S) = Prod.snd :=
@@ -326,7 +326,7 @@ protected def prod (f : R →+* S) (g : R →+* T) : R →+* S × T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} T] (f : RingHom.{u1, u2} R S _inst_1 _inst_2) (g : RingHom.{u1, u3} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} S T) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (RingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (fun (_x : RingHom.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) => R -> (Prod.{u2, u3} S T)) (RingHom.hasCoeToFun.{u1, max u2 u3} R (Prod.{u2, u3} S T) _inst_1 (Prod.nonAssocSemiring.{u2, u3} S T _inst_2 _inst_3)) (RingHom.prod.{u1, u2, u3} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u2, u3} S T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S _inst_1 _inst_2) (fun (_x : RingHom.{u1, u2} R S _inst_1 _inst_2) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S _inst_1 _inst_2) f x) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R T _inst_1 _inst_3) (fun (_x : RingHom.{u1, u3} R T _inst_1 _inst_3) => R -> T) (RingHom.hasCoeToFun.{u1, u3} R T _inst_1 _inst_3) g x))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} T] (f : RingHom.{u1, u3} R S _inst_1 _inst_2) (g : RingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (RingHom.instRingHomClassRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))))) (RingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (RingHom.instRingHomClassRingHom.{u1, u3} R S _inst_1 _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u1, u2} R T _inst_1 _inst_3)))) g x))
+  forall {R : Type.{u1}} {S : Type.{u3}} {T : Type.{u2}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} T] (f : RingHom.{u1, u3} R S _inst_1 _inst_2) (g : RingHom.{u1, u2} R T _inst_1 _inst_3) (x : R), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Prod.{u3, u2} S T) _x) (MulHomClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Prod.{u3, u2} S T) (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u3) u2, u1, max u3 u2} (RingHom.{u1, max u2 u3} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3)) R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3) (RingHom.instRingHomClassRingHom.{u1, max u3 u2} R (Prod.{u3, u2} S T) _inst_1 (Prod.instNonAssocSemiringProd.{u3, u2} S T _inst_2 _inst_3))))) (RingHom.prod.{u1, u3, u2} R S T _inst_1 _inst_2 _inst_3 f g) x) (Prod.mk.{u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S _inst_2) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R S _inst_1 _inst_2) R S _inst_1 _inst_2 (RingHom.instRingHomClassRingHom.{u1, u3} R S _inst_1 _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T _inst_1 _inst_3) R T _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u1, u2} R T _inst_1 _inst_3)))) g x))
 Case conversion may be inaccurate. Consider using '#align ring_hom.prod_apply RingHom.prod_applyₓ'. -/
 @[simp]
 theorem prod_apply (x) : f.Prod g x = (f x, g x) :=
@@ -398,7 +398,7 @@ theorem prodMap_def : prodMap f g = (f.comp (fst R S)).Prod (g.comp (snd R S)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R' : Type.{u2}} {S : Type.{u3}} {S' : Type.{u4}} [_inst_1 : NonAssocSemiring.{u1} R] [_inst_2 : NonAssocSemiring.{u3} S] [_inst_3 : NonAssocSemiring.{u2} R'] [_inst_4 : NonAssocSemiring.{u4} S'] (f : RingHom.{u1, u2} R R' _inst_1 _inst_3) (g : RingHom.{u3, u4} S S' _inst_2 _inst_4), Eq.{max (succ (max u1 u3)) (succ (max u2 u4))} ((Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u4)), max (succ (max u1 u3)) (succ (max u2 u4))} (RingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (fun (_x : RingHom.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) => (Prod.{u1, u3} R S) -> (Prod.{u2, u4} R' S')) (RingHom.hasCoeToFun.{max u1 u3, max u2 u4} (Prod.{u1, u3} R S) (Prod.{u2, u4} R' S') (Prod.nonAssocSemiring.{u1, u3} R S _inst_1 _inst_2) (Prod.nonAssocSemiring.{u2, u4} R' S' _inst_3 _inst_4)) (RingHom.prodMap.{u1, u2, u3, u4} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u1, u2, u3, u4} R R' S S' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R R' _inst_1 _inst_3) (fun (_x : RingHom.{u1, u2} R R' _inst_1 _inst_3) => R -> R') (RingHom.hasCoeToFun.{u1, u2} R R' _inst_1 _inst_3) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} S S' _inst_2 _inst_4) (fun (_x : RingHom.{u3, u4} S S' _inst_2 _inst_4) => S -> S') (RingHom.hasCoeToFun.{u3, u4} S S' _inst_2 _inst_4) g))
 but is expected to have type
-  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonAssocSemiring.{u4} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} R'] [_inst_4 : NonAssocSemiring.{u1} S'] (f : RingHom.{u4, u3} R R' _inst_1 _inst_3) (g : RingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))))) (RingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u4, u3} R R' _inst_1 _inst_3)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (RingHom.instRingHomClassRingHom.{u2, u1} S S' _inst_2 _inst_4)))) g))
+  forall {R : Type.{u4}} {R' : Type.{u3}} {S : Type.{u2}} {S' : Type.{u1}} [_inst_1 : NonAssocSemiring.{u4} R] [_inst_2 : NonAssocSemiring.{u2} S] [_inst_3 : NonAssocSemiring.{u3} R'] [_inst_4 : NonAssocSemiring.{u1} S'] (f : RingHom.{u4, u3} R R' _inst_1 _inst_3) (g : RingHom.{u2, u1} S S' _inst_2 _inst_4), Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (forall (ᾰ : Prod.{u4, u2} R S), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u2), max (succ u3) (succ u1)} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (fun (_x : Prod.{u4, u2} R S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Prod.{u4, u2} R S) => Prod.{u3, u1} R' S') _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonUnitalNonAssocSemiring.toMul.{max u4 u2} (Prod.{u4, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))) (NonUnitalRingHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Prod.{u4, u2} R S) (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (RingHomClass.toNonUnitalRingHomClass.{max (max (max u4 u3) u2) u1, max u4 u2, max u3 u1} (RingHom.{max u2 u4, max u1 u3} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4)) (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4) (RingHom.instRingHomClassRingHom.{max u4 u2, max u3 u1} (Prod.{u4, u2} R S) (Prod.{u3, u1} R' S') (Prod.instNonAssocSemiringProd.{u4, u2} R S _inst_1 _inst_2) (Prod.instNonAssocSemiringProd.{u3, u1} R' S' _inst_3 _inst_4))))) (RingHom.prodMap.{u4, u3, u2, u1} R R' S S' _inst_1 _inst_2 _inst_3 _inst_4 f g)) (Prod.map.{u4, u3, u2, u1} R R' S S' (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => R') _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u3} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3)) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R' _inst_3) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R R' _inst_1 _inst_3) R R' _inst_1 _inst_3 (RingHom.instRingHomClassRingHom.{u4, u3} R R' _inst_1 _inst_3)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : S) => S') _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4)) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' _inst_4) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} S S' _inst_2 _inst_4) S S' _inst_2 _inst_4 (RingHom.instRingHomClassRingHom.{u2, u1} S S' _inst_2 _inst_4)))) g))
 Case conversion may be inaccurate. Consider using '#align ring_hom.coe_prod_map RingHom.coe_prodMapₓ'. -/
 @[simp]
 theorem coe_prodMap : ⇑(prodMap f g) = Prod.map f g :=

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -106,12 +106,12 @@ namespace NonUnitalRingHom
 
 variable (R S) [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S]
 
-/-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`.-/
+/-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`. -/
 def fst : R × S →ₙ+* R :=
   { MulHom.fst R S, AddMonoidHom.fst R S with toFun := Prod.fst }
 #align non_unital_ring_hom.fst NonUnitalRingHom.fst
 
-/-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`.-/
+/-- Given non-unital semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`. -/
 def snd : R × S →ₙ+* S :=
   { MulHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
 #align non_unital_ring_hom.snd NonUnitalRingHom.snd
@@ -192,12 +192,12 @@ namespace RingHom
 
 variable (R S) [NonAssocSemiring R] [NonAssocSemiring S]
 
-/-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`.-/
+/-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `R`. -/
 def fst : R × S →+* R :=
   { MonoidHom.fst R S, AddMonoidHom.fst R S with toFun := Prod.fst }
 #align ring_hom.fst RingHom.fst
 
-/-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`.-/
+/-- Given semirings `R`, `S`, the natural projection homomorphism from `R × S` to `S`. -/
 def snd : R × S →+* S :=
   { MonoidHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
 #align ring_hom.snd RingHom.snd

doc(Algebra,AlgebraicGeometry): remove mathlib3 names in doc comments (#11955)

Mostly automatic, with a few manual corrections.

11516514

Diff

@@ -312,7 +312,7 @@ section
 
 variable (R R' S S')
 
-/-- Four-way commutativity of `prod`. The name matches `mul_mul_mul_comm`. -/
+/-- Four-way commutativity of `Prod`. The name matches `mul_mul_mul_comm`. -/
 @[simps apply]
 def prodProdProdComm : (R × R') × S × S' ≃+* (R × S) × R' × S' :=
   { AddEquiv.prodProdProdComm R R' S S', MulEquiv.prodProdProdComm R R' S S' with

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

@@ -163,7 +163,6 @@ end Prod
 section Prod_map
 
 variable [NonUnitalNonAssocSemiring R'] [NonUnitalNonAssocSemiring S'] [NonUnitalNonAssocSemiring T]
-
 variable (f : R →ₙ+* R') (g : S →ₙ+* S')
 
 /-- `Prod.map` as a `NonUnitalRingHom`. -/
@@ -253,7 +252,6 @@ end Prod
 section Prod_map
 
 variable [NonAssocSemiring R'] [NonAssocSemiring S'] [NonAssocSemiring T]
-
 variable (f : R →+* R') (g : S →+* S')
 
 /-- `Prod.map` as a `RingHom`. -/

feat: sum and product of commuting semisimple endomorphisms (#10808)

Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.
In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).
The annihilator of a semisimple module is a radical ideal.
Any module over a semisimple ring is semisimple.
A finite product of semisimple rings is semisimple.
Any quotient of a semisimple ring is semisimple.
Add Artin--Wedderburn as a TODO (proof_wanted).
Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair
Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.
Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.
RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.
Algebra/Module/Torsion.lean: add a lemma and an instance (unused)
Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma
LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv
LinearAlgebra/Span.lean: add two lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

0b52a6a5

Diff

@@ -5,6 +5,7 @@ Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
 -/
 import Mathlib.Data.Int.Cast.Prod
 import Mathlib.Algebra.Group.Prod
+import Mathlib.Algebra.Ring.CompTypeclasses
 import Mathlib.Algebra.Ring.Equiv
 import Mathlib.Algebra.Order.Group.Prod
 import Mathlib.Algebra.Order.Ring.Defs
@@ -202,6 +203,9 @@ def snd : R × S →+* S :=
   { MonoidHom.snd R S, AddMonoidHom.snd R S with toFun := Prod.snd }
 #align ring_hom.snd RingHom.snd
 
+instance (R S) [Semiring R] [Semiring S] : RingHomSurjective (fst R S) := ⟨(⟨⟨·, 0⟩, rfl⟩)⟩
+instance (R S) [Semiring R] [Semiring S] : RingHomSurjective (snd R S) := ⟨(⟨⟨0, ·⟩, rfl⟩)⟩
+
 variable {R S}
 
 @[simp]

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

@@ -398,7 +398,7 @@ instance [OrderedSemiring α] [OrderedSemiring β] : OrderedSemiring (α × β)
 instance [OrderedCommSemiring α] [OrderedCommSemiring β] : OrderedCommSemiring (α × β) :=
   { inferInstanceAs (OrderedSemiring (α × β)), inferInstanceAs (CommSemiring (α × β)) with }
 
--- porting note: compile fails with `inferInstanceAs (OrderedSemiring (α × β))`
+-- Porting note: compile fails with `inferInstanceAs (OrderedSemiring (α × β))`
 instance [OrderedRing α] [OrderedRing β] : OrderedRing (α × β) :=
   { inferInstanceAs (Ring (α × β)), inferInstanceAs (OrderedAddCommGroup (α × β)) with
     zero_le_one := ⟨zero_le_one, zero_le_one⟩

chore: reduce imports (#9830)

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>

f4c4ca61

Diff

@@ -7,6 +7,7 @@ import Mathlib.Data.Int.Cast.Prod
 import Mathlib.Algebra.Group.Prod
 import Mathlib.Algebra.Ring.Equiv
 import Mathlib.Algebra.Order.Group.Prod
+import Mathlib.Algebra.Order.Ring.Defs
 
 #align_import algebra.ring.prod from "leanprover-community/mathlib"@"cd391184c85986113f8c00844cfe6dda1d34be3d"

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

fix: attribute [simp] ... in -> attribute [local simp] ... in (#7678)

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

1fe87718

Diff

@@ -352,7 +352,7 @@ def prodZeroRing : R ≃+* R × S where
   map_add' := by simp
   map_mul' := by simp
   left_inv x := rfl
-  right_inv x := by cases x; simp
+  right_inv x := by cases x; simp [eq_iff_true_of_subsingleton]
 #align ring_equiv.prod_zero_ring RingEquiv.prodZeroRing
 #align ring_equiv.prod_zero_ring_symm_apply RingEquiv.prodZeroRing_symm_apply
 #align ring_equiv.prod_zero_ring_apply RingEquiv.prodZeroRing_apply
@@ -365,7 +365,7 @@ def zeroRingProd : R ≃+* S × R where
   map_add' := by simp
   map_mul' := by simp
   left_inv x := rfl
-  right_inv x := by cases x; simp
+  right_inv x := by cases x; simp [eq_iff_true_of_subsingleton]
 #align ring_equiv.zero_ring_prod RingEquiv.zeroRingProd
 #align ring_equiv.zero_ring_prod_symm_apply RingEquiv.zeroRingProd_symm_apply
 #align ring_equiv.zero_ring_prod_apply RingEquiv.zeroRingProd_apply

chore: cleanup Mathlib.Init.Data.Prod (#6972)

Removing from Mathlib.Init.Data.Prod from the early parts of the import hierarchy.

While at it, remove unnecessary uses of Prod.mk.eta across the library.

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

b5528b3b

Diff

@@ -153,7 +153,7 @@ theorem snd_comp_prod : (snd S T).comp (f.prod g) = g :=
 #align non_unital_ring_hom.snd_comp_prod NonUnitalRingHom.snd_comp_prod
 
 theorem prod_unique (f : R →ₙ+* S × T) : ((fst S T).comp f).prod ((snd S T).comp f) = f :=
-  ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply, Prod.mk.eta]
+  ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply]
 #align non_unital_ring_hom.prod_unique NonUnitalRingHom.prod_unique
 
 end Prod
@@ -240,7 +240,7 @@ theorem snd_comp_prod : (snd S T).comp (f.prod g) = g :=
 #align ring_hom.snd_comp_prod RingHom.snd_comp_prod
 
 theorem prod_unique (f : R →+* S × T) : ((fst S T).comp f).prod ((snd S T).comp f) = f :=
-  ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply, Prod.mk.eta]
+  ext fun x => by simp only [prod_apply, coe_fst, coe_snd, comp_apply]
 #align ring_hom.prod_unique RingHom.prod_unique
 
 end Prod

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

@@ -25,7 +25,7 @@ trivial `simp` lemmas, and define the following operations on `RingHom`s and sim
 -/
 
 
-variable {α β R R' S S' T T' : Type _}
+variable {α β R R' S S' T T' : Type*}
 
 namespace Prod
 
@@ -373,7 +373,7 @@ def zeroRingProd : R ≃+* S × R where
 end RingEquiv
 
 /-- The product of two nontrivial rings is not a domain -/
-theorem false_of_nontrivial_of_product_domain (R S : Type _) [Ring R] [Ring S] [IsDomain (R × S)]
+theorem false_of_nontrivial_of_product_domain (R S : Type*) [Ring R] [Ring S] [IsDomain (R × S)]
     [Nontrivial R] [Nontrivial S] : False := by
   have :=
     NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zero (show ((0 : R), (1 : S)) * (1, 0) = 0 by simp)

chore: tidy various files (#5999)

415165ea

Diff

@@ -30,67 +30,72 @@ variable {α β R R' S S' T T' : Type _}
 namespace Prod
 
 /-- Product of two distributive types is distributive. -/
-instance [Distrib R] [Distrib S] : Distrib (R × S) :=
+instance instDistrib [Distrib R] [Distrib S] : Distrib (R × S) :=
   { left_distrib := fun _ _ _ => mk.inj_iff.mpr ⟨left_distrib _ _ _, left_distrib _ _ _⟩
     right_distrib := fun _ _ _ => mk.inj_iff.mpr ⟨right_distrib _ _ _, right_distrib _ _ _⟩ }
 
 /-- Product of two `NonUnitalNonAssocSemiring`s is a `NonUnitalNonAssocSemiring`. -/
-instance [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S] :
+instance instNonUnitalNonAssocSemiring [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S] :
     NonUnitalNonAssocSemiring (R × S) :=
   { inferInstanceAs (AddCommMonoid (R × S)),
     inferInstanceAs (Distrib (R × S)),
     inferInstanceAs (MulZeroClass (R × S)) with }
 
 /-- Product of two `NonUnitalSemiring`s is a `NonUnitalSemiring`. -/
-instance [NonUnitalSemiring R] [NonUnitalSemiring S] : NonUnitalSemiring (R × S) :=
+instance instNonUnitalSemiring [NonUnitalSemiring R] [NonUnitalSemiring S] :
+    NonUnitalSemiring (R × S) :=
   { inferInstanceAs (NonUnitalNonAssocSemiring (R × S)),
     inferInstanceAs (SemigroupWithZero (R × S)) with }
 
 /-- Product of two `NonAssocSemiring`s is a `NonAssocSemiring`. -/
-instance [NonAssocSemiring R] [NonAssocSemiring S] : NonAssocSemiring (R × S) :=
+instance instNonAssocSemiring [NonAssocSemiring R] [NonAssocSemiring S] :
+    NonAssocSemiring (R × S) :=
   { inferInstanceAs (NonUnitalNonAssocSemiring (R × S)),
     inferInstanceAs (MulZeroOneClass (R × S)),
     inferInstanceAs (AddMonoidWithOne (R × S)) with }
 
 /-- Product of two semirings is a semiring. -/
-instance [Semiring R] [Semiring S] : Semiring (R × S) :=
+instance instSemiring [Semiring R] [Semiring S] : Semiring (R × S) :=
   { inferInstanceAs (NonUnitalSemiring (R × S)),
     inferInstanceAs (NonAssocSemiring (R × S)),
     inferInstanceAs (MonoidWithZero (R × S)) with }
 
 /-- Product of two `NonUnitalCommSemiring`s is a `NonUnitalCommSemiring`. -/
-instance [NonUnitalCommSemiring R] [NonUnitalCommSemiring S] : NonUnitalCommSemiring (R × S) :=
+instance instNonUnitalCommSemiring [NonUnitalCommSemiring R] [NonUnitalCommSemiring S] :
+    NonUnitalCommSemiring (R × S) :=
   { inferInstanceAs (NonUnitalSemiring (R × S)), inferInstanceAs (CommSemigroup (R × S)) with }
 
 /-- Product of two commutative semirings is a commutative semiring. -/
-instance [CommSemiring R] [CommSemiring S] : CommSemiring (R × S) :=
+instance instCommSemiring [CommSemiring R] [CommSemiring S] : CommSemiring (R × S) :=
   { inferInstanceAs (Semiring (R × S)), inferInstanceAs (CommMonoid (R × S)) with }
 
-instance [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] : NonUnitalNonAssocRing (R × S) :=
+instance instNonUnitalNonAssocRing [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] :
+    NonUnitalNonAssocRing (R × S) :=
   { inferInstanceAs (AddCommGroup (R × S)),
     inferInstanceAs (NonUnitalNonAssocSemiring (R × S)) with }
 
-instance [NonUnitalRing R] [NonUnitalRing S] : NonUnitalRing (R × S) :=
+instance instNonUnitalRing [NonUnitalRing R] [NonUnitalRing S] : NonUnitalRing (R × S) :=
   { inferInstanceAs (NonUnitalNonAssocRing (R × S)),
     inferInstanceAs (NonUnitalSemiring (R × S)) with }
 
-instance [NonAssocRing R] [NonAssocRing S] : NonAssocRing (R × S) :=
+instance instNonAssocRing [NonAssocRing R] [NonAssocRing S] : NonAssocRing (R × S) :=
   { inferInstanceAs (NonUnitalNonAssocRing (R × S)),
     inferInstanceAs (NonAssocSemiring (R × S)),
     inferInstanceAs (AddGroupWithOne (R × S)) with }
 
 /-- Product of two rings is a ring. -/
-instance [Ring R] [Ring S] : Ring (R × S) :=
+instance instRing [Ring R] [Ring S] : Ring (R × S) :=
   { inferInstanceAs (Semiring (R × S)),
     inferInstanceAs (AddCommGroup (R × S)),
     inferInstanceAs (AddGroupWithOne (R × S)) with }
 
 /-- Product of two `NonUnitalCommRing`s is a `NonUnitalCommRing`. -/
-instance [NonUnitalCommRing R] [NonUnitalCommRing S] : NonUnitalCommRing (R × S) :=
+instance instNonUnitalCommRing [NonUnitalCommRing R] [NonUnitalCommRing S] :
+    NonUnitalCommRing (R × S) :=
   { inferInstanceAs (NonUnitalRing (R × S)), inferInstanceAs (CommSemigroup (R × S)) with }
 
 /-- Product of two commutative rings is a commutative ring. -/
-instance [CommRing R] [CommRing S] : CommRing (R × S) :=
+instance instCommRing [CommRing R] [CommRing S] : CommRing (R × S) :=
   { inferInstanceAs (Ring (R × S)), inferInstanceAs (CommMonoid (R × S)) with }
 
 end Prod
@@ -159,7 +164,7 @@ variable [NonUnitalNonAssocSemiring R'] [NonUnitalNonAssocSemiring S'] [NonUnita
 
 variable (f : R →ₙ+* R') (g : S →ₙ+* S')
 
-/-- `prod.map` as a `NonUnitalRingHom`. -/
+/-- `Prod.map` as a `NonUnitalRingHom`. -/
 def prodMap : R × S →ₙ+* R' × S' :=
   (f.comp (fst R S)).prod (g.comp (snd R S))
 #align non_unital_ring_hom.prod_map NonUnitalRingHom.prodMap
@@ -279,26 +284,26 @@ def prodComm : R × S ≃+* S × R :=
 #align ring_equiv.prod_comm RingEquiv.prodComm
 
 @[simp]
-theorem coe_prod_comm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
+theorem coe_prodComm : ⇑(prodComm : R × S ≃+* S × R) = Prod.swap :=
   rfl
-#align ring_equiv.coe_prod_comm RingEquiv.coe_prod_comm
+#align ring_equiv.coe_prod_comm RingEquiv.coe_prodComm
 
 @[simp]
-theorem coe_prod_comm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
+theorem coe_prodComm_symm : ⇑(prodComm : R × S ≃+* S × R).symm = Prod.swap :=
   rfl
-#align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prod_comm_symm
+#align ring_equiv.coe_prod_comm_symm RingEquiv.coe_prodComm_symm
 
 @[simp]
-theorem fst_comp_coe_prod_comm :
+theorem fst_comp_coe_prodComm :
     (RingHom.fst S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.snd R S :=
   RingHom.ext fun _ => rfl
-#align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prod_comm
+#align ring_equiv.fst_comp_coe_prod_comm RingEquiv.fst_comp_coe_prodComm
 
 @[simp]
-theorem snd_comp_coe_prod_comm :
+theorem snd_comp_coe_prodComm :
     (RingHom.snd S R).comp ↑(prodComm : R × S ≃+* S × R) = RingHom.fst R S :=
   RingHom.ext fun _ => rfl
-#align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prod_comm
+#align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prodComm
 
 section

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.ring.prod
-! leanprover-community/mathlib commit cd391184c85986113f8c00844cfe6dda1d34be3d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Int.Cast.Prod
 import Mathlib.Algebra.Group.Prod
 import Mathlib.Algebra.Ring.Equiv
 import Mathlib.Algebra.Order.Group.Prod
 
+#align_import algebra.ring.prod from "leanprover-community/mathlib"@"cd391184c85986113f8c00844cfe6dda1d34be3d"
+
 /-!
 # Semiring, ring etc structures on `R × S`

chore: forward-port leanprover-community/mathlib#19234 (#5887)

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

48029e81

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.ring.prod
-! leanprover-community/mathlib commit 207cfac9fcd06138865b5d04f7091e46d9320432
+! leanprover-community/mathlib commit cd391184c85986113f8c00844cfe6dda1d34be3d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -274,7 +274,7 @@ end RingHom
 
 namespace RingEquiv
 
-variable [NonAssocSemiring R] [NonAssocSemiring S]
+variable [NonAssocSemiring R] [NonAssocSemiring S] [NonAssocSemiring R'] [NonAssocSemiring S']
 
 /-- Swapping components as an equivalence of (semi)rings. -/
 def prodComm : R × S ≃+* S × R :=
@@ -303,6 +303,43 @@ theorem snd_comp_coe_prod_comm :
   RingHom.ext fun _ => rfl
 #align ring_equiv.snd_comp_coe_prod_comm RingEquiv.snd_comp_coe_prod_comm
 
+section
+
+variable (R R' S S')
+
+/-- Four-way commutativity of `prod`. The name matches `mul_mul_mul_comm`. -/
+@[simps apply]
+def prodProdProdComm : (R × R') × S × S' ≃+* (R × S) × R' × S' :=
+  { AddEquiv.prodProdProdComm R R' S S', MulEquiv.prodProdProdComm R R' S S' with
+    toFun := fun rrss => ((rrss.1.1, rrss.2.1), (rrss.1.2, rrss.2.2))
+    invFun := fun rsrs => ((rsrs.1.1, rsrs.2.1), (rsrs.1.2, rsrs.2.2)) }
+#align ring_equiv.prod_prod_prod_comm RingEquiv.prodProdProdComm
+
+@[simp]
+theorem prodProdProdComm_symm : (prodProdProdComm R R' S S').symm = prodProdProdComm R S R' S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_symm RingEquiv.prodProdProdComm_symm
+
+@[simp]
+theorem prodProdProdComm_toAddEquiv :
+    (prodProdProdComm R R' S S' : _ ≃+ _) = AddEquiv.prodProdProdComm R R' S S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_to_add_equiv RingEquiv.prodProdProdComm_toAddEquiv
+
+@[simp]
+theorem prodProdProdComm_toMulEquiv :
+    (prodProdProdComm R R' S S' : _ ≃* _) = MulEquiv.prodProdProdComm R R' S S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_to_mul_equiv RingEquiv.prodProdProdComm_toMulEquiv
+
+@[simp]
+theorem prodProdProdComm_toEquiv :
+    (prodProdProdComm R R' S S' : _ ≃ _) = Equiv.prodProdProdComm R R' S S' :=
+  rfl
+#align ring_equiv.prod_prod_prod_comm_to_equiv RingEquiv.prodProdProdComm_toEquiv
+
+end
+
 variable (R S) [Subsingleton S]
 
 /-- A ring `R` is isomorphic to `R × S` when `S` is the zero ring -/

fix: replace symmApply by symm_apply (#2560)

9aade17b

Diff

@@ -315,7 +315,7 @@ def prodZeroRing : R ≃+* R × S where
   left_inv x := rfl
   right_inv x := by cases x; simp
 #align ring_equiv.prod_zero_ring RingEquiv.prodZeroRing
-#align ring_equiv.prod_zero_ring_symm_apply RingEquiv.prodZeroRing_symmApply
+#align ring_equiv.prod_zero_ring_symm_apply RingEquiv.prodZeroRing_symm_apply
 #align ring_equiv.prod_zero_ring_apply RingEquiv.prodZeroRing_apply
 
 /-- A ring `R` is isomorphic to `S × R` when `S` is the zero ring -/
@@ -328,7 +328,7 @@ def zeroRingProd : R ≃+* S × R where
   left_inv x := rfl
   right_inv x := by cases x; simp
 #align ring_equiv.zero_ring_prod RingEquiv.zeroRingProd
-#align ring_equiv.zero_ring_prod_symm_apply RingEquiv.zeroRingProd_symmApply
+#align ring_equiv.zero_ring_prod_symm_apply RingEquiv.zeroRingProd_symm_apply
 #align ring_equiv.zero_ring_prod_apply RingEquiv.zeroRingProd_apply
 
 end RingEquiv

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -315,6 +315,8 @@ def prodZeroRing : R ≃+* R × S where
   left_inv x := rfl
   right_inv x := by cases x; simp
 #align ring_equiv.prod_zero_ring RingEquiv.prodZeroRing
+#align ring_equiv.prod_zero_ring_symm_apply RingEquiv.prodZeroRing_symmApply
+#align ring_equiv.prod_zero_ring_apply RingEquiv.prodZeroRing_apply
 
 /-- A ring `R` is isomorphic to `S × R` when `S` is the zero ring -/
 @[simps]
@@ -326,6 +328,8 @@ def zeroRingProd : R ≃+* S × R where
   left_inv x := rfl
   right_inv x := by cases x; simp
 #align ring_equiv.zero_ring_prod RingEquiv.zeroRingProd
+#align ring_equiv.zero_ring_prod_symm_apply RingEquiv.zeroRingProd_symmApply
+#align ring_equiv.zero_ring_prod_apply RingEquiv.zeroRingProd_apply
 
 end RingEquiv

chore: tidy various files (#1247)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

0690e5fb

Diff

@@ -16,14 +16,14 @@ import Mathlib.Algebra.Order.Group.Prod
 /-!
 # Semiring, ring etc structures on `R × S`
 
-In this file we define two-binop (`semiring`, `ring` etc) structures on `R × S`. We also prove
-trivial `simp` lemmas, and define the following operations on `ring_hom`s and similarly for
-`non_unital_ring_hom`s:
-
-* `fst R S : R × S →+* R`, `snd R S : R × S →+* S`: projections `prod.fst` and `prod.snd`
-  as `ring_hom`s;
-* `f.prod g : `R →+* S × T`: sends `x` to `(f x, g x)`;
-* `f.prod_map g : `R × S → R' × S'`: `prod.map f g` as a `ring_hom`,
+In this file we define two-binop (`Semiring`, `Ring` etc) structures on `R × S`. We also prove
+trivial `simp` lemmas, and define the following operations on `RingHom`s and similarly for
+`NonUnitalRingHom`s:
+
+* `fst R S : R × S →+* R`, `snd R S : R × S →+* S`: projections `Prod.fst` and `Prod.snd`
+  as `RingHom`s;
+* `f.prod g : R →+* S × T`: sends `x` to `(f x, g x)`;
+* `f.prod_map g : R × S → R' × S'`: `Prod.map f g` as a `RingHom`,
   sends `(x, y)` to `(f x, g y)`.
 -/
 
@@ -37,19 +37,19 @@ instance [Distrib R] [Distrib S] : Distrib (R × S) :=
   { left_distrib := fun _ _ _ => mk.inj_iff.mpr ⟨left_distrib _ _ _, left_distrib _ _ _⟩
     right_distrib := fun _ _ _ => mk.inj_iff.mpr ⟨right_distrib _ _ _, right_distrib _ _ _⟩ }
 
-/-- Product of two `non_unital_non_assoc_semiring`s is a `non_unital_non_assoc_semiring`. -/
+/-- Product of two `NonUnitalNonAssocSemiring`s is a `NonUnitalNonAssocSemiring`. -/
 instance [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S] :
     NonUnitalNonAssocSemiring (R × S) :=
   { inferInstanceAs (AddCommMonoid (R × S)),
     inferInstanceAs (Distrib (R × S)),
     inferInstanceAs (MulZeroClass (R × S)) with }
 
-/-- Product of two `non_unital_semiring`s is a `non_unital_semiring`. -/
+/-- Product of two `NonUnitalSemiring`s is a `NonUnitalSemiring`. -/
 instance [NonUnitalSemiring R] [NonUnitalSemiring S] : NonUnitalSemiring (R × S) :=
   { inferInstanceAs (NonUnitalNonAssocSemiring (R × S)),
     inferInstanceAs (SemigroupWithZero (R × S)) with }
 
-/-- Product of two `non_assoc_semiring`s is a `non_assoc_semiring`. -/
+/-- Product of two `NonAssocSemiring`s is a `NonAssocSemiring`. -/
 instance [NonAssocSemiring R] [NonAssocSemiring S] : NonAssocSemiring (R × S) :=
   { inferInstanceAs (NonUnitalNonAssocSemiring (R × S)),
     inferInstanceAs (MulZeroOneClass (R × S)),
@@ -61,7 +61,7 @@ instance [Semiring R] [Semiring S] : Semiring (R × S) :=
     inferInstanceAs (NonAssocSemiring (R × S)),
     inferInstanceAs (MonoidWithZero (R × S)) with }
 
-/-- Product of two `non_unital_comm_semiring`s is a `non_unital_comm_semiring`. -/
+/-- Product of two `NonUnitalCommSemiring`s is a `NonUnitalCommSemiring`. -/
 instance [NonUnitalCommSemiring R] [NonUnitalCommSemiring S] : NonUnitalCommSemiring (R × S) :=
   { inferInstanceAs (NonUnitalSemiring (R × S)), inferInstanceAs (CommSemigroup (R × S)) with }
 
@@ -88,7 +88,7 @@ instance [Ring R] [Ring S] : Ring (R × S) :=
     inferInstanceAs (AddCommGroup (R × S)),
     inferInstanceAs (AddGroupWithOne (R × S)) with }
 
-/-- Product of two `non_unital_comm_ring`s is a `non_unital_comm_ring`. -/
+/-- Product of two `NonUnitalCommRing`s is a `NonUnitalCommRing`. -/
 instance [NonUnitalCommRing R] [NonUnitalCommRing S] : NonUnitalCommRing (R × S) :=
   { inferInstanceAs (NonUnitalRing (R × S)), inferInstanceAs (CommSemigroup (R × S)) with }
 
@@ -162,7 +162,7 @@ variable [NonUnitalNonAssocSemiring R'] [NonUnitalNonAssocSemiring S'] [NonUnita
 
 variable (f : R →ₙ+* R') (g : S →ₙ+* S')
 
-/-- `prod.map` as a `non_unital_ring_hom`. -/
+/-- `prod.map` as a `NonUnitalRingHom`. -/
 def prodMap : R × S →ₙ+* R' × S' :=
   (f.comp (fst R S)).prod (g.comp (snd R S))
 #align non_unital_ring_hom.prod_map NonUnitalRingHom.prodMap
@@ -249,7 +249,7 @@ variable [NonAssocSemiring R'] [NonAssocSemiring S'] [NonAssocSemiring T]
 
 variable (f : R →+* R') (g : S →+* S')
 
-/-- `prod.map` as a `ring_hom`. -/
+/-- `Prod.map` as a `RingHom`. -/
 def prodMap : R × S →+* R' × S' :=
   (f.comp (fst R S)).prod (g.comp (snd R S))
 #align ring_hom.prod_map RingHom.prodMap
@@ -307,7 +307,7 @@ variable (R S) [Subsingleton S]
 
 /-- A ring `R` is isomorphic to `R × S` when `S` is the zero ring -/
 @[simps]
-def prodZeroRing : R ≃+* R × S where 
+def prodZeroRing : R ≃+* R × S where
   toFun x := (x, 0)
   invFun := Prod.fst
   map_add' := by simp
@@ -318,7 +318,7 @@ def prodZeroRing : R ≃+* R × S where
 
 /-- A ring `R` is isomorphic to `S × R` when `S` is the zero ring -/
 @[simps]
-def zeroRingProd : R ≃+* S × R where 
+def zeroRingProd : R ≃+* S × R where
   toFun x := (0, x)
   invFun := Prod.snd
   map_add' := by simp