field_theory.mv_polynomial ⟷ Mathlib.FieldTheory.MvPolynomial

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

@@ -3,7 +3,7 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Data.MvPolynomial.CommRing
+import Algebra.MvPolynomial.CommRing
 import LinearAlgebra.Dimension.Basic
 import RingTheory.Ideal.Quotient
 import RingTheory.MvPolynomial.Basic

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
 import Data.MvPolynomial.CommRing
-import LinearAlgebra.Dimension
+import LinearAlgebra.Dimension.Basic
 import RingTheory.Ideal.Quotient
 import RingTheory.MvPolynomial.Basic
 

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

@@ -43,10 +43,10 @@ theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=
   by
   refine' (injective_iff_map_eq_zero _).2 fun x hx => _
-  rw [RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem] at hx 
+  rw [RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem] at hx
   refine' by_contradiction fun hx0 => absurd (I.eq_top_iff_one.2 _) hI
   have := I.mul_mem_left (MvPolynomial.C x⁻¹) hx
-  rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this 
+  rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this
 #align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injective
 -/
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.Data.MvPolynomial.CommRing
-import Mathbin.LinearAlgebra.Dimension
-import Mathbin.RingTheory.Ideal.Quotient
-import Mathbin.RingTheory.MvPolynomial.Basic
+import Data.MvPolynomial.CommRing
+import LinearAlgebra.Dimension
+import RingTheory.Ideal.Quotient
+import RingTheory.MvPolynomial.Basic
 
 #align_import field_theory.mv_polynomial from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module field_theory.mv_polynomial
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.CommRing
 import Mathbin.LinearAlgebra.Dimension
 import Mathbin.RingTheory.Ideal.Quotient
 import Mathbin.RingTheory.MvPolynomial.Basic
 
+#align_import field_theory.mv_polynomial from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
+
 /-!
 # Multivariate polynomials over fields
 

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

@@ -41,6 +41,7 @@ variable {σ : Type u} {K : Type v}
 
 variable (σ K) [Field K]
 
+#print MvPolynomial.quotient_mk_comp_C_injective /-
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=
   by
@@ -50,6 +51,7 @@ theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠
   have := I.mul_mem_left (MvPolynomial.C x⁻¹) hx
   rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this 
 #align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injective
+-/
 
 end MvPolynomial
 

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

@@ -45,10 +45,10 @@ theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=
   by
   refine' (injective_iff_map_eq_zero _).2 fun x hx => _
-  rw [RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem] at hx
+  rw [RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem] at hx 
   refine' by_contradiction fun hx0 => absurd (I.eq_top_iff_one.2 _) hI
   have := I.mul_mem_left (MvPolynomial.C x⁻¹) hx
-  rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this
+  rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this 
 #align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injective
 
 end MvPolynomial

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

@@ -27,11 +27,11 @@ finitely supported functions from the indexing set to `ℕ`.
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 open Set LinearMap Submodule
 
-open BigOperators
+open scoped BigOperators
 
 namespace MvPolynomial
 
@@ -59,7 +59,7 @@ universe u
 
 variable {σ : Type u} {K : Type u} [Field K]
 
-open Classical
+open scoped Classical
 
 #print MvPolynomial.rank_mvPolynomial /-
 theorem rank_mvPolynomial : Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ) := by

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

@@ -41,9 +41,6 @@ variable {σ : Type u} {K : Type v}
 
 variable (σ K) [Field K]
 
-/- warning: mv_polynomial.quotient_mk_comp_C_injective -> MvPolynomial.quotient_mk_comp_C_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injectiveₓ'. -/
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=
   by

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

@@ -42,10 +42,7 @@ variable {σ : Type u} {K : Type v}
 variable (σ K) [Field K]
 
 /- warning: mv_polynomial.quotient_mk_comp_C_injective -> MvPolynomial.quotient_mk_comp_C_injective is a dubious translation:
-lean 3 declaration is
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_inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K 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u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) => K -> (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I)) (RingHom.hasCoeToFun.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
-but is expected to have type
-  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 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_inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} 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(MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ 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(MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K 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(HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injectiveₓ'. -/
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=

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

@@ -45,7 +45,7 @@ variable (σ K) [Field K]
 lean 3 declaration is
   forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))), (Ne.{succ (max u1 u2)} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) I (Top.top.{max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Submodule.hasTop.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))))))) -> (Function.Injective.{succ u2, succ (max u1 u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (fun (_x : RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) => K -> (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I)) (RingHom.hasCoeToFun.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
 but is expected to have type
-  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K 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K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
+  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K 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(MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K 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u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injectiveₓ'. -/
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -45,7 +45,7 @@ variable (σ K) [Field K]
 lean 3 declaration is
   forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))), (Ne.{succ (max u1 u2)} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) I (Top.top.{max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Submodule.hasTop.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))))))) -> (Function.Injective.{succ u2, succ (max u1 u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (fun (_x : RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) => K -> (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I)) (RingHom.hasCoeToFun.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
 but is expected to have type
-  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
+  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K 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(MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K 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u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K 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(MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injectiveₓ'. -/
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -45,7 +45,7 @@ variable (σ K) [Field K]
 lean 3 declaration is
   forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))), (Ne.{succ (max u1 u2)} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) I (Top.top.{max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Submodule.hasTop.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))))))) -> (Function.Injective.{succ u2, succ (max u1 u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (fun (_x : RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) => K -> (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I)) (RingHom.hasCoeToFun.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
 but is expected to have type
-  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
+  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commSemiring.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} 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_inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Semiring.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommSemiring.toSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toCommSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injectiveₓ'. -/
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module field_theory.mv_polynomial
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.RingTheory.MvPolynomial.Basic
 /-!
 # Multivariate polynomials over fields
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains basic facts about multivariate polynomials over fields, for example that the
 dimension of the space of multivariate polynomials over a field is equal to the cardinality of
 finitely supported functions from the indexing set to `ℕ`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -38,7 +38,13 @@ variable {σ : Type u} {K : Type v}
 
 variable (σ K) [Field K]
 
-theorem quotient_mk_comp_c_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
+/- warning: mv_polynomial.quotient_mk_comp_C_injective -> MvPolynomial.quotient_mk_comp_C_injective is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))), (Ne.{succ (max u1 u2)} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) I (Top.top.{max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Submodule.hasTop.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))))))))) -> (Function.Injective.{succ u2, succ (max u1 u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K 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(EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (fun (_x : RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) => K -> (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I)) (RingHom.hasCoeToFun.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))))) (Ideal.hasQuotient.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.commRing.{u2, u1} K σ (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1))) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
+but is expected to have type
+  forall (σ : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u2} K] (I : Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))), (Ne.{max (succ u1) (succ u2)} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) I (Top.top.{max u1 u2} (Ideal.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Submodule.instTopSubmodule.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)))))))) -> (Function.Injective.{succ u2, max (succ u1) (succ u2)} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, max u1 u2} (RingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I))))) K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (RingHom.instRingHomClassRingHom.{u2, max u1 u2} K (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))))))) (RingHom.comp.{u2, max u1 u2, max u1 u2} K (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ring.toNonAssocRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (CommRing.toRing.{max u1 u2} (HasQuotient.Quotient.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))))) (Ideal.instHasQuotientIdealToSemiringToRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1))) I) (Ideal.Quotient.commRing.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I)))) (Ideal.Quotient.mk.{max u1 u2} (MvPolynomial.{u1, u2} σ K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} K σ (Field.toCommRing.{u2} K _inst_1)) I) (MvPolynomial.C.{u2, u1} K σ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injectiveₓ'. -/
+theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
     Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=
   by
   refine' (injective_iff_map_eq_zero _).2 fun x hx => _
@@ -46,7 +52,7 @@ theorem quotient_mk_comp_c_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠
   refine' by_contradiction fun hx0 => absurd (I.eq_top_iff_one.2 _) hI
   have := I.mul_mem_left (MvPolynomial.C x⁻¹) hx
   rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this
-#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_c_injective
+#align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_C_injective
 
 end MvPolynomial
 
@@ -58,9 +64,11 @@ variable {σ : Type u} {K : Type u} [Field K]
 
 open Classical
 
+#print MvPolynomial.rank_mvPolynomial /-
 theorem rank_mvPolynomial : Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ) := by
   rw [← Cardinal.lift_inj, ← (basis_monomials σ K).mk_eq_rank]
 #align mv_polynomial.rank_mv_polynomial MvPolynomial.rank_mvPolynomial
+-/
 
 end MvPolynomial
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module field_theory.mv_polynomial
-! leanprover-community/mathlib commit 59628387770d82eb6f6dd7b7107308aa2509ec95
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -58,9 +58,9 @@ variable {σ : Type u} {K : Type u} [Field K]
 
 open Classical
 
-theorem dim_mvPolynomial : Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ) := by
-  rw [← Cardinal.lift_inj, ← (basis_monomials σ K).mk_eq_dim]
-#align mv_polynomial.dim_mv_polynomial MvPolynomial.dim_mvPolynomial
+theorem rank_mvPolynomial : Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ) := by
+  rw [← Cardinal.lift_inj, ← (basis_monomials σ K).mk_eq_rank]
+#align mv_polynomial.rank_mv_polynomial MvPolynomial.rank_mvPolynomial
 
 end MvPolynomial
 

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

@@ -4,11 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module field_theory.mv_polynomial
-! leanprover-community/mathlib commit 019ead10c09bb91f49b1b7005d442960b1e0485f
+! leanprover-community/mathlib commit 59628387770d82eb6f6dd7b7107308aa2509ec95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.CommRing
+import Mathbin.LinearAlgebra.Dimension
+import Mathbin.RingTheory.Ideal.Quotient
 import Mathbin.RingTheory.MvPolynomial.Basic
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -37,13 +37,13 @@ variable {σ : Type u} {K : Type v}
 variable (σ K) [Field K]
 
 theorem quotient_mk_comp_c_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :
-    Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.c) :=
+    Function.Injective ((Ideal.Quotient.mk I).comp MvPolynomial.C) :=
   by
   refine' (injective_iff_map_eq_zero _).2 fun x hx => _
   rw [RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem] at hx
   refine' by_contradiction fun hx0 => absurd (I.eq_top_iff_one.2 _) hI
-  have := I.mul_mem_left (MvPolynomial.c x⁻¹) hx
-  rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.c_1] at this
+  have := I.mul_mem_left (MvPolynomial.C x⁻¹) hx
+  rwa [← mv_polynomial.C.map_mul, inv_mul_cancel hx0, MvPolynomial.C_1] at this
 #align mv_polynomial.quotient_mk_comp_C_injective MvPolynomial.quotient_mk_comp_c_injective
 
 end MvPolynomial

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

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

@@ -3,9 +3,9 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
+import Mathlib.Algebra.MvPolynomial.CommRing
 import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
 import Mathlib.RingTheory.MvPolynomial.Basic
-import Mathlib.Data.MvPolynomial.CommRing
 
 #align_import field_theory.mv_polynomial from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
 

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)

@@ -31,7 +31,6 @@ namespace MvPolynomial
 universe u v
 
 variable {σ : Type u} {K : Type v}
-
 variable (σ K) [Field K]
 
 theorem quotient_mk_comp_C_injective (I : Ideal (MvPolynomial σ K)) (hI : I ≠ ⊤) :

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -20,7 +20,7 @@ finitely supported functions from the indexing set to `ℕ`.
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 open Set LinearMap Submodule
 
@@ -52,7 +52,7 @@ universe u
 
 variable {σ : Type u} {K : Type u} [Field K]
 
-open Classical
+open scoped Classical
 
 theorem rank_mvPolynomial : Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ) := by
   rw [← Cardinal.lift_inj, ← (basisMonomials σ K).mk_eq_rank]

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>

@@ -5,6 +5,7 @@ Authors: Johannes Hölzl
 -/
 import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
 import Mathlib.RingTheory.MvPolynomial.Basic
+import Mathlib.Data.MvPolynomial.CommRing
 
 #align_import field_theory.mv_polynomial from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
 

The files Mathlib.LinearAlgebra.FreeModule.Rank, Mathlib.LinearAlgebra.FreeModule.Finite.Rank, Mathlib.LinearAlgebra.Dimension and Mathlib.LinearAlgebra.Finrank were reorganized into a folder Mathlib.LinearAlgebra.Dimension, containing the following files

• Basic.lean: Contains the definition of Module.rank.
• Finrank.lean: Contains the definition of FiniteDimensional.finrank.
• StrongRankCondition.lean: Contains results about rank and finrank over rings satisfying strong rank condition
• Free.lean: Contains results about rank and finrank of free modules
• Finite.lean: Contains conditions or consequences for rank to be finite or zero
• Constructions.lean: Contains the calculation of the rank of various constructions.
• DivisionRing.lean: Contains results about rank and finrank of spaces over division rings.
• LinearMap.lean: Contains results about LinearMap.rank

API changes: IsNoetherian.rank_lt_aleph0 and FiniteDimensional.rank_lt_aleph0 are replaced with rank_lt_aleph0. Module.Free.finite_basis was renamed to Module.Finite.finite_basis. FiniteDimensional.finrank_eq_rank was renamed to finrank_eq_rank. rank_eq_cardinal_basis and rank_eq_cardinal_basis' were removed in favour of Basis.mk_eq_mk and Basis.mk_eq_mk''.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -3,9 +3,7 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathlib.Data.MvPolynomial.CommRing
-import Mathlib.LinearAlgebra.Dimension
-import Mathlib.RingTheory.Ideal.Quotient
+import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
 import Mathlib.RingTheory.MvPolynomial.Basic
 
 #align_import field_theory.mv_polynomial from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module field_theory.mv_polynomial
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.LinearAlgebra.Dimension
 import Mathlib.RingTheory.Ideal.Quotient
 import Mathlib.RingTheory.MvPolynomial.Basic
 
+#align_import field_theory.mv_polynomial from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
+
 /-!
 # Multivariate polynomials over fields
 

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -58,7 +58,6 @@ variable {σ : Type u} {K : Type u} [Field K]
 
 open Classical
 
-set_option synthInstance.etaExperiment true in
 theorem rank_mvPolynomial : Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ) := by
   rw [← Cardinal.lift_inj, ← (basisMonomials σ K).mk_eq_rank]
 #align mv_polynomial.rank_mv_polynomial MvPolynomial.rank_mvPolynomial

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>