ring_theory.valuation.integers | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

7b7da893

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1dac236e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathbin.RingTheory.Valuation.Basic
+import RingTheory.Valuation.Basic
 
 #align_import ring_theory.valuation.integers from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"

1dac236e

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -34,7 +34,7 @@ variable (v : Valuation R Γ₀)
 def integer : Subring R where
   carrier := {x | v x ≤ 1}
   one_mem' := le_of_eq v.map_one
-  mul_mem' x y hx hy := trans_rel_right (· ≤ ·) (v.map_mul x y) (mul_le_one' hx hy)
+  hMul_mem' x y hx hy := trans_rel_right (· ≤ ·) (v.map_hMul x y) (mul_le_one' hx hy)
   zero_mem' := trans_rel_right (· ≤ ·) v.map_zero zero_le_one
   add_mem' x y hx hy := le_trans (v.map_add x y) (max_le hx hy)
   neg_mem' x hx := trans_rel_right (· ≤ ·) (v.map_neg x) hx
@@ -83,7 +83,7 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   le_antisymm (hv.2 _) <|
     by
     rw [← v.map_one, ← (algebraMap O R).map_one, ← u.mul_inv, ← mul_one (v (algebraMap O R x)), hu,
-      (algebraMap O R).map_mul, v.map_mul]
+      (algebraMap O R).map_hMul, v.map_mul]
     exact mul_le_mul_left' (hv.2 (u⁻¹ : Units O)) _
 #align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnit
 -/
@@ -136,7 +136,7 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
     have : v ((algebraMap O F y)⁻¹ * algebraMap O F x) ≤ 1 := by
       rw [← v.map_one, ← inv_mul_cancel hy, v.map_mul, v.map_mul]; exact mul_le_mul_left' h _
     let ⟨z, hz⟩ := hv.3 this
-    ⟨z, hv.1 <| ((algebraMap O F).map_mul y z).symm ▸ hz.symm ▸ (mul_inv_cancel_left₀ hy _).symm⟩
+    ⟨z, hv.1 <| ((algebraMap O F).map_hMul y z).symm ▸ hz.symm ▸ (mul_inv_cancel_left₀ hy _).symm⟩
 #align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_le
 -/

1dac236e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.valuation.integers
-! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Valuation.Basic
 
+#align_import ring_theory.valuation.integers from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"
+
 /-!
 # Ring of integers under a given valuation

1dac236e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -68,18 +68,19 @@ structure Integers : Prop where
 instance : Algebra v.integer R :=
   Algebra.ofSubring v.integer
 
+#print Valuation.integer.integers /-
 theorem integer.integers : v.Integers v.integer :=
   { hom_inj := Subtype.coe_injective
     map_le_one := fun r => r.2
     exists_of_le_one := fun r hr => ⟨⟨r, hr⟩, rfl⟩ }
 #align valuation.integer.integers Valuation.integer.integers
+-/
 
 namespace Integers
 
 variable {v O} (hv : Integers v O)
 
-include hv
-
+#print Valuation.Integers.one_of_isUnit /-
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
   le_antisymm (hv.2 _) <|
@@ -88,7 +89,9 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
       (algebraMap O R).map_mul, v.map_mul]
     exact mul_le_mul_left' (hv.2 (u⁻¹ : Units O)) _
 #align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnit
+-/
 
+#print Valuation.Integers.isUnit_of_one /-
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=
   let ⟨u, hu⟩ := hx
@@ -101,13 +104,16 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
       hv.1 <| by rw [RingHom.map_mul, RingHom.map_one, hr1, hr2, Units.inv_mul]⟩,
     hv.1 <| hr1.trans hu⟩
 #align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_one
+-/
 
+#print Valuation.Integers.le_of_dvd /-
 theorem le_of_dvd {x y : O} (h : x ∣ y) : v (algebraMap O R y) ≤ v (algebraMap O R x) :=
   by
   let ⟨z, hz⟩ := h
   rw [← mul_one (v (algebraMap O R x)), hz, RingHom.map_mul, v.map_mul]
   exact mul_le_mul_left' (hv.2 z) _
 #align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvd
+-/
 
 end Integers
 
@@ -119,10 +125,9 @@ variable {F : Type u} {Γ₀ : Type v} [Field F] [LinearOrderedCommGroupWithZero
 
 variable {v : Valuation F Γ₀} {O : Type w} [CommRing O] [Algebra O F] (hv : Integers v O)
 
-include hv
-
 namespace Integers
 
+#print Valuation.Integers.dvd_of_le /-
 theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y)) : y ∣ x :=
   by_cases
     (fun hy : algebraMap O F y = 0 =>
@@ -136,14 +141,19 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
     let ⟨z, hz⟩ := hv.3 this
     ⟨z, hv.1 <| ((algebraMap O F).map_mul y z).symm ▸ hz.symm ▸ (mul_inv_cancel_left₀ hy _).symm⟩
 #align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_le
+-/
 
+#print Valuation.Integers.dvd_iff_le /-
 theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMap O F x) :=
   ⟨hv.le_of_dvd, hv.dvd_of_le⟩
 #align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_le
+-/
 
+#print Valuation.Integers.le_iff_dvd /-
 theorem le_iff_dvd {x y : O} : v (algebraMap O F x) ≤ v (algebraMap O F y) ↔ y ∣ x :=
   ⟨hv.dvd_of_le, hv.le_of_dvd⟩
 #align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvd
+-/
 
 end Integers

1dac236e

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -35,7 +35,7 @@ variable (v : Valuation R Γ₀)
 #print Valuation.integer /-
 /-- The ring of integers under a given valuation is the subring of elements with valuation ≤ 1. -/
 def integer : Subring R where
-  carrier := { x | v x ≤ 1 }
+  carrier := {x | v x ≤ 1}
   one_mem' := le_of_eq v.map_one
   mul_mem' x y hx hy := trans_rel_right (· ≤ ·) (v.map_mul x y) (mul_le_one' hx hy)
   zero_mem' := trans_rel_right (· ≤ ·) v.map_zero zero_le_one

1dac236e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -68,12 +68,6 @@ structure Integers : Prop where
 instance : Algebra v.integer R :=
   Algebra.ofSubring v.integer
 
-/- warning: valuation.integer.integers -> Valuation.integer.integers is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.algebra.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
-but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_1))) x (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v))) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.instAlgebraSubtypeMemSubringToRingInstMembershipInstSetLikeSubringIntegerToCommSemiringToCommSemiringToSubsemiringToSemiring.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
-Case conversion may be inaccurate. Consider using '#align valuation.integer.integers Valuation.integer.integersₓ'. -/
 theorem integer.integers : v.Integers v.integer :=
   { hom_inj := Subtype.coe_injective
     map_le_one := fun r => r.2
@@ -86,9 +80,6 @@ variable {v O} (hv : Integers v O)
 
 include hv
 
-/- warning: valuation.integers.one_of_is_unit -> Valuation.Integers.one_of_isUnit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnitₓ'. -/
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
   le_antisymm (hv.2 _) <|
@@ -98,9 +89,6 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
     exact mul_le_mul_left' (hv.2 (u⁻¹ : Units O)) _
 #align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnit
 
-/- warning: valuation.integers.is_unit_of_one -> Valuation.Integers.isUnit_of_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_oneₓ'. -/
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=
   let ⟨u, hu⟩ := hx
@@ -114,9 +102,6 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
     hv.1 <| hr1.trans hu⟩
 #align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_one
 
-/- warning: valuation.integers.le_of_dvd -> Valuation.Integers.le_of_dvd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvdₓ'. -/
 theorem le_of_dvd {x y : O} (h : x ∣ y) : v (algebraMap O R y) ≤ v (algebraMap O R x) :=
   by
   let ⟨z, hz⟩ := h
@@ -138,9 +123,6 @@ include hv
 
 namespace Integers
 
-/- warning: valuation.integers.dvd_of_le -> Valuation.Integers.dvd_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_leₓ'. -/
 theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y)) : y ∣ x :=
   by_cases
     (fun hy : algebraMap O F y = 0 =>
@@ -155,16 +137,10 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
     ⟨z, hv.1 <| ((algebraMap O F).map_mul y z).symm ▸ hz.symm ▸ (mul_inv_cancel_left₀ hy _).symm⟩
 #align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_le
 
-/- warning: valuation.integers.dvd_iff_le -> Valuation.Integers.dvd_iff_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_leₓ'. -/
 theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMap O F x) :=
   ⟨hv.le_of_dvd, hv.dvd_of_le⟩
 #align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_le
 
-/- warning: valuation.integers.le_iff_dvd -> Valuation.Integers.le_iff_dvd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvdₓ'. -/
 theorem le_iff_dvd {x y : O} : v (algebraMap O F x) ≤ v (algebraMap O F y) ↔ y ∣ x :=
   ⟨hv.dvd_of_le, hv.le_of_dvd⟩
 #align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvd

1dac236e

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -149,10 +149,8 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
           (algebraMap O F).map_zero.symm ▸ (v.zero_iff.1 <| le_zero_iff.1 (v.map_zero ▸ hy ▸ h))
       hx.symm ▸ dvd_zero y)
     fun hy : algebraMap O F y ≠ 0 =>
-    have : v ((algebraMap O F y)⁻¹ * algebraMap O F x) ≤ 1 :=
-      by
-      rw [← v.map_one, ← inv_mul_cancel hy, v.map_mul, v.map_mul]
-      exact mul_le_mul_left' h _
+    have : v ((algebraMap O F y)⁻¹ * algebraMap O F x) ≤ 1 := by
+      rw [← v.map_one, ← inv_mul_cancel hy, v.map_mul, v.map_mul]; exact mul_le_mul_left' h _
     let ⟨z, hz⟩ := hv.3 this
     ⟨z, hv.1 <| ((algebraMap O F).map_mul y z).symm ▸ hz.symm ▸ (mul_inv_cancel_left₀ hy _).symm⟩
 #align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_le

1dac236e

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -87,10 +87,7 @@ variable {v O} (hv : Integers v O)
 include hv
 
 /- warning: valuation.integers.one_of_is_unit -> Valuation.Integers.one_of_isUnit is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (Ring.toMonoid.{u3} O (CommRing.toRing.{u3} O _inst_3)) x) -> (Eq.{succ u2} Γ₀ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} Γ₀ 1 (OfNat.mk.{u2} Γ₀ 1 (One.one.{u2} Γ₀ (MulOneClass.toHasOne.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (GroupWithZero.toMonoidWithZero.{u2} Γ₀ (CommGroupWithZero.toGroupWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} Γ₀ _inst_2)))))))))))
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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnitₓ'. -/
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
@@ -102,10 +99,7 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
 #align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnit
 
 /- warning: valuation.integers.is_unit_of_one -> Valuation.Integers.isUnit_of_one is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_oneₓ'. -/
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=
@@ -121,10 +115,7 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
 #align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvdₓ'. -/
 theorem le_of_dvd {x y : O} (h : x ∣ y) : v (algebraMap O R y) ≤ v (algebraMap O R x) :=
   by
@@ -148,10 +139,7 @@ include hv
 namespace Integers
 
 /- warning: valuation.integers.dvd_of_le -> Valuation.Integers.dvd_of_le is a dubious translation:
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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_leₓ'. -/
 theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y)) : y ∣ x :=
   by_cases
@@ -170,20 +158,14 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
 #align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_le
 
 /- warning: valuation.integers.dvd_iff_le -> Valuation.Integers.dvd_iff_le is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_leₓ'. -/
 theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMap O F x) :=
   ⟨hv.le_of_dvd, hv.dvd_of_le⟩
 #align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_le
 
 /- warning: valuation.integers.le_iff_dvd -> Valuation.Integers.le_iff_dvd is a dubious translation:
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_inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvdₓ'. -/
 theorem le_iff_dvd {x y : O} : v (algebraMap O F x) ≤ v (algebraMap O F y) ↔ y ∣ x :=
   ⟨hv.dvd_of_le, hv.le_of_dvd⟩

1dac236e

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -90,7 +90,7 @@ include hv
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (Ring.toMonoid.{u3} O (CommRing.toRing.{u3} O _inst_3)) x) -> (Eq.{succ u2} Γ₀ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} Γ₀ 1 (OfNat.mk.{u2} Γ₀ 1 (One.one.{u2} Γ₀ (MulOneClass.toHasOne.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (GroupWithZero.toMonoidWithZero.{u2} Γ₀ (CommGroupWithZero.toGroupWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} Γ₀ _inst_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) x) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (DivisionCommMonoid.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (CommGroupWithZero.toDivisionCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ 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(CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))))
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) x) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (DivisionMonoid.toDivInvOneMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (DivisionCommMonoid.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (CommGroupWithZero.toDivisionCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnitₓ'. -/
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
@@ -105,7 +105,7 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) -> (Eq.{succ u2} Γ₀ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} Γ₀ 1 (OfNat.mk.{u2} Γ₀ 1 (One.one.{u2} Γ₀ (MulOneClass.toHasOne.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (GroupWithZero.toMonoidWithZero.{u2} Γ₀ (CommGroupWithZero.toGroupWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} Γ₀ _inst_2)))))))))) -> (IsUnit.{u3} O (Ring.toMonoid.{u3} O (CommRing.toRing.{u3} O _inst_3)) x))
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))) -> (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) x))
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))) -> (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_oneₓ'. -/
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=
@@ -124,7 +124,7 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x))))
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R 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(NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x))))
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R 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(LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvdₓ'. -/
 theorem le_of_dvd {x y : O} (h : x ∣ y) : v (algebraMap O R y) ≤ v (algebraMap O R x) :=
   by
@@ -151,7 +151,7 @@ namespace Integers
 lean 3 declaration is
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 but is expected to have type
-  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun 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O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) 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(DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_leₓ'. -/
 theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y)) : y ∣ x :=
   by_cases
@@ -173,7 +173,7 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
 lean 3 declaration is
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x))))
 but is expected to have type
-  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O 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(Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) _inst_2)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x))))
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) _inst_2)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_leₓ'. -/
 theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMap O F x) :=
   ⟨hv.le_of_dvd, hv.dvd_of_le⟩
@@ -183,7 +183,7 @@ theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMa
 lean 3 declaration is
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 but is expected to have type
-  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F 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_inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Γ₀) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) 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 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvdₓ'. -/
 theorem le_iff_dvd {x y : O} : v (algebraMap O F x) ≤ v (algebraMap O F y) ↔ y ∣ x :=
   ⟨hv.dvd_of_le, hv.le_of_dvd⟩

1dac236e

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -122,7 +122,7 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
 
 /- warning: valuation.integers.le_of_dvd -> Valuation.Integers.le_of_dvd is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x))))
 but is expected to have type
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvdₓ'. -/
@@ -149,7 +149,7 @@ namespace Integers
 
 /- warning: valuation.integers.dvd_of_le -> Valuation.Integers.dvd_of_le is a dubious translation:
 lean 3 declaration is
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+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 but is expected to have type
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O 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_inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_leₓ'. -/
@@ -171,7 +171,7 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
 
 /- warning: valuation.integers.dvd_iff_le -> Valuation.Integers.dvd_iff_le is a dubious translation:
 lean 3 declaration is
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+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x))))
 but is expected to have type
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F 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(CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) 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u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_leₓ'. -/
@@ -181,7 +181,7 @@ theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMa
 
 /- warning: valuation.integers.le_iff_dvd -> Valuation.Integers.le_iff_dvd is a dubious translation:
 lean 3 declaration is
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+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} Γ₀ (Preorder.toHasLe.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 but is expected to have type
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O 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_inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvdₓ'. -/

1dac236e

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -72,7 +72,7 @@ instance : Algebra v.integer R :=
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.algebra.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_1))) x (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v))) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.instAlgebraSubtypeMemSubringToRingInstMembershipInstSetLikeSubringIntegerToCommSemiringToCommRingToSemiring.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_1))) x (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v))) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.instAlgebraSubtypeMemSubringToRingInstMembershipInstSetLikeSubringIntegerToCommSemiringToCommSemiringToSubsemiringToSemiring.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
 Case conversion may be inaccurate. Consider using '#align valuation.integer.integers Valuation.integer.integersₓ'. -/
 theorem integer.integers : v.Integers v.integer :=
   { hom_inj := Subtype.coe_injective
@@ -90,7 +90,7 @@ include hv
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (Ring.toMonoid.{u3} O (CommRing.toRing.{u3} O _inst_3)) x) -> (Eq.{succ u2} Γ₀ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} Γ₀ 1 (OfNat.mk.{u2} Γ₀ 1 (One.one.{u2} Γ₀ (MulOneClass.toHasOne.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (GroupWithZero.toMonoidWithZero.{u2} Γ₀ (CommGroupWithZero.toGroupWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} Γ₀ _inst_2)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (Ring.toSemiring.{u3} O (CommRing.toRing.{u3} O _inst_3)))) x) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O 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(CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (DivisionMonoid.toDivInvOneMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (DivisionCommMonoid.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (CommGroupWithZero.toDivisionCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))))
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) x) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) 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(CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (DivisionCommMonoid.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (CommGroupWithZero.toDivisionCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnitₓ'. -/
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
@@ -105,7 +105,7 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) -> (Eq.{succ u2} Γ₀ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} Γ₀ 1 (OfNat.mk.{u2} Γ₀ 1 (One.one.{u2} Γ₀ (MulOneClass.toHasOne.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (GroupWithZero.toMonoidWithZero.{u2} Γ₀ (CommGroupWithZero.toGroupWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} Γ₀ _inst_2)))))))))) -> (IsUnit.{u3} O (Ring.toMonoid.{u3} O (CommRing.toRing.{u3} O _inst_3)) x))
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O 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(CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))) -> (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (Ring.toSemiring.{u3} O (CommRing.toRing.{u3} O _inst_3)))) x))
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R 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O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (CommGroupWithZero.toDivisionCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ 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(CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))) -> (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_oneₓ'. -/
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=
@@ -124,7 +124,7 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
 lean 3 declaration is
   forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} Γ₀ (Preorder.toLE.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x))))
 but is expected to have type
-  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R 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_inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) y)) _inst_2)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x))))
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) -> (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun 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(CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) _inst_2)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1) (Valuation.instValuationClassValuation.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4) x))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvdₓ'. -/
 theorem le_of_dvd {x y : O} (h : x ∣ y) : v (algebraMap O R y) ≤ v (algebraMap O R x) :=
   by
@@ -151,7 +151,7 @@ namespace Integers
 lean 3 declaration is
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} Γ₀ (Preorder.toLE.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 but is expected to have type
-  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) 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: F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_leₓ'. -/
 theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y)) : y ∣ x :=
   by_cases
@@ -173,7 +173,7 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
 lean 3 declaration is
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} Γ₀ (Preorder.toLE.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x))))
 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F 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(CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) 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(NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x))))
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) x y) (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O 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(Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) _inst_2)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F 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_inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x))))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_leₓ'. -/
 theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMap O F x) :=
   ⟨hv.le_of_dvd, hv.dvd_of_le⟩
@@ -183,7 +183,7 @@ theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMa
 lean 3 declaration is
   forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} Γ₀ (Preorder.toLE.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 but is expected to have type
-  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F 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(Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ 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Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
 Case conversion may be inaccurate. Consider using '#align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvdₓ'. -/
 theorem le_iff_dvd {x y : O} : v (algebraMap O F x) ≤ v (algebraMap O F y) ↔ y ∣ x :=
   ⟨hv.dvd_of_le, hv.le_of_dvd⟩

1dac236e

bump to nightly-2023-03-20-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

2e1f2c13

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.valuation.integers
-! leanprover-community/mathlib commit 7b7da89322fe46a16bf03eeb345b0acfc73fe10e
+! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.Valuation.Basic
 /-!
 # Ring of integers under a given valuation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The elements with valuation less than or equal to 1.
 
 TODO: Define characteristic predicate.

7b7da893

bump to nightly-2023-03-18-10

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

8e568880

Diff

@@ -29,6 +29,7 @@ variable {R : Type u} {Γ₀ : Type v} [Ring R] [LinearOrderedCommGroupWithZero
 
 variable (v : Valuation R Γ₀)
 
+#print Valuation.integer /-
 /-- The ring of integers under a given valuation is the subring of elements with valuation ≤ 1. -/
 def integer : Subring R where
   carrier := { x | v x ≤ 1 }
@@ -38,6 +39,7 @@ def integer : Subring R where
   add_mem' x y hx hy := le_trans (v.map_add x y) (max_le hx hy)
   neg_mem' x hx := trans_rel_right (· ≤ ·) (v.map_neg x) hx
 #align valuation.integer Valuation.integer
+-/
 
 end Ring
 
@@ -49,6 +51,7 @@ variable (v : Valuation R Γ₀)
 
 variable (O : Type w) [CommRing O] [Algebra O R]
 
+#print Valuation.Integers /-
 /-- Given a valuation v : R → Γ₀ and a ring homomorphism O →+* R, we say that O is the integers of v
 if f is injective, and its range is exactly `v.integer`. -/
 structure Integers : Prop where
@@ -56,11 +59,18 @@ structure Integers : Prop where
   map_le_one : ∀ x, v (algebraMap O R x) ≤ 1
   exists_of_le_one : ∀ ⦃r⦄, v r ≤ 1 → ∃ x, algebraMap O R x = r
 #align valuation.integers Valuation.Integers
+-/
 
 -- typeclass shortcut
 instance : Algebra v.integer R :=
   Algebra.ofSubring v.integer
 
+/- warning: valuation.integer.integers -> Valuation.integer.integers is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.algebra.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
+but is expected to have type
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] (v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)), Valuation.Integers.{u1, u2, u1} R Γ₀ _inst_1 _inst_2 v (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_1))) x (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v))) (Subring.toCommRing.{u1} R _inst_1 (Valuation.integer.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) _inst_2 v)) (Valuation.instAlgebraSubtypeMemSubringToRingInstMembershipInstSetLikeSubringIntegerToCommSemiringToCommRingToSemiring.{u1, u2} R Γ₀ _inst_1 _inst_2 v)
+Case conversion may be inaccurate. Consider using '#align valuation.integer.integers Valuation.integer.integersₓ'. -/
 theorem integer.integers : v.Integers v.integer :=
   { hom_inj := Subtype.coe_injective
     map_le_one := fun r => r.2
@@ -73,6 +83,12 @@ variable {v O} (hv : Integers v O)
 
 include hv
 
+/- warning: valuation.integers.one_of_is_unit -> Valuation.Integers.one_of_isUnit is a dubious translation:
+lean 3 declaration is
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_inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (DivisionMonoid.toDivInvOneMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (DivisionCommMonoid.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) 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(CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (CommGroupWithZero.toDivisionCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => R) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))))
+Case conversion may be inaccurate. Consider using '#align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnitₓ'. -/
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
   le_antisymm (hv.2 _) <|
@@ -82,6 +98,12 @@ theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
     exact mul_le_mul_left' (hv.2 (u⁻¹ : Units O)) _
 #align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnit
 
+/- warning: valuation.integers.is_unit_of_one -> Valuation.Integers.isUnit_of_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Valuation.Integers.{u1, u2, u3} R Γ₀ _inst_1 _inst_2 v O _inst_3 _inst_4) -> (forall {x : O}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) -> (Eq.{succ u2} Γ₀ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) (fun (_x : Valuation.{u1, u2} R Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (CommRing.toRing.{u1} R _inst_1)) => R -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} R Γ₀ (CommRing.toRing.{u1} R _inst_1) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => O -> R) (RingHom.hasCoeToFun.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) (OfNat.ofNat.{u2} Γ₀ 1 (OfNat.mk.{u2} Γ₀ 1 (One.one.{u2} Γ₀ (MulOneClass.toHasOne.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (GroupWithZero.toMonoidWithZero.{u2} Γ₀ (CommGroupWithZero.toGroupWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u2} Γ₀ _inst_2)))))))))) -> (IsUnit.{u3} O (Ring.toMonoid.{u3} O (CommRing.toRing.{u3} O _inst_3)) x))
+but is expected to have type
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(CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x)) _inst_2))))))))) -> (IsUnit.{u3} O (MonoidWithZero.toMonoid.{u3} O (Semiring.toMonoidWithZero.{u3} O (Ring.toSemiring.{u3} O (CommRing.toRing.{u3} O _inst_3)))) x))
+Case conversion may be inaccurate. Consider using '#align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_oneₓ'. -/
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=
   let ⟨u, hu⟩ := hx
@@ -95,6 +117,12 @@ theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebra
     hv.1 <| hr1.trans hu⟩
 #align valuation.integers.is_unit_of_one Valuation.Integers.isUnit_of_one
 
+/- warning: valuation.integers.le_of_dvd -> Valuation.Integers.le_of_dvd is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CommRing.toRing.{u1} R _inst_1)))) O R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u1} O R (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (algebraMap.{u3, u1} O R (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4) x))))
+Case conversion may be inaccurate. Consider using '#align valuation.integers.le_of_dvd Valuation.Integers.le_of_dvdₓ'. -/
 theorem le_of_dvd {x y : O} (h : x ∣ y) : v (algebraMap O R y) ≤ v (algebraMap O R x) :=
   by
   let ⟨z, hz⟩ := h
@@ -116,6 +144,12 @@ include hv
 
 namespace Integers
 
+/- warning: valuation.integers.dvd_of_le -> Valuation.Integers.dvd_of_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (OrderedCommMonoid.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (a : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) a) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F 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(Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ 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(NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, 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(Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) -> (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_leₓ'. -/
 theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y)) : y ∣ x :=
   by_cases
     (fun hy : algebraMap O F y = 0 =>
@@ -132,10 +166,22 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
     ⟨z, hv.1 <| ((algebraMap O F).map_mul y z).symm ▸ hz.symm ▸ (mul_inv_cancel_left₀ hy _).symm⟩
 #align valuation.integers.dvd_of_le Valuation.Integers.dvd_of_le
 
+/- warning: valuation.integers.dvd_iff_le -> Valuation.Integers.dvd_iff_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O 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+Case conversion may be inaccurate. Consider using '#align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_leₓ'. -/
 theorem dvd_iff_le {x y : O} : x ∣ y ↔ v (algebraMap O F y) ≤ v (algebraMap O F x) :=
   ⟨hv.le_of_dvd, hv.dvd_of_le⟩
 #align valuation.integers.dvd_iff_le Valuation.Integers.dvd_iff_le
 
+/- warning: valuation.integers.le_iff_dvd -> Valuation.Integers.le_iff_dvd is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} Γ₀ (Preorder.toLE.{u2} Γ₀ (PartialOrder.toPreorder.{u2} Γ₀ (OrderedCommMonoid.toPartialOrder.{u2} Γ₀ (LinearOrderedCommMonoid.toOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toLinearOrderedCommMonoid.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (fun (_x : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) => F -> Γ₀) (Valuation.hasCoeToFun.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)) v (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (fun (_x : RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) => O -> F) (RingHom.hasCoeToFun.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) _inst_4) y))) (Dvd.Dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+but is expected to have type
+  forall {F : Type.{u1}} {Γ₀ : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_2 : LinearOrderedCommGroupWithZero.{u2} Γ₀] {v : Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))} {O : Type.{u3}} [_inst_3 : CommRing.{u3} O] [_inst_4 : Algebra.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))], (Valuation.Integers.{u1, u2, u3} F Γ₀ (Field.toCommRing.{u1} F _inst_1) _inst_2 v O _inst_3 _inst_4) -> (forall {x : O} {y : O}, Iff (LE.le.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F 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(Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O 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(Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => Γ₀) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulOneClass.toMul.{u1} F (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (MulOneClass.toMul.{u2} Γ₀ (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (MulZeroOneClass.toMulOneClass.{u1} F (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (MulZeroOneClass.toMulOneClass.{u2} Γ₀ (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2))))) (MonoidWithZeroHomClass.toMonoidHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (NonAssocSemiring.toMulZeroOneClass.{u1} F (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (MonoidWithZero.toMulZeroOneClass.{u2} Γ₀ (CommMonoidWithZero.toMonoidWithZero.{u2} Γ₀ (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{u2} Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))) (ValuationClass.toMonoidWithZeroHomClass.{max u1 u2, u1, u2} (Valuation.{u1, u2} F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F Γ₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2) (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (Valuation.instValuationClassValuation.{u1, u2} F Γ₀ (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u2} Γ₀ _inst_2)))))) v (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O (fun (_x : O) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : O) => F) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonUnitalNonAssocSemiring.toMul.{u3} O (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} O (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u3, u1} (RingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (RingHom.instRingHomClassRingHom.{u3, u1} O F (Semiring.toNonAssocSemiring.{u3} O (CommSemiring.toSemiring.{u3} O (CommRing.toCommSemiring.{u3} O _inst_3))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (algebraMap.{u3, u1} O F (CommRing.toCommSemiring.{u3} O _inst_3) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) _inst_4) y))) (Dvd.dvd.{u3} O (semigroupDvd.{u3} O (SemigroupWithZero.toSemigroup.{u3} O (NonUnitalSemiring.toSemigroupWithZero.{u3} O (NonUnitalRing.toNonUnitalSemiring.{u3} O (NonUnitalCommRing.toNonUnitalRing.{u3} O (CommRing.toNonUnitalCommRing.{u3} O _inst_3)))))) y x))
+Case conversion may be inaccurate. Consider using '#align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvdₓ'. -/
 theorem le_iff_dvd {x y : O} : v (algebraMap O F x) ≤ v (algebraMap O F y) ↔ y ∣ x :=
   ⟨hv.dvd_of_le, hv.le_of_dvd⟩
 #align valuation.integers.le_iff_dvd Valuation.Integers.le_iff_dvd

7b7da893

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

7b7da893

feat (RingTheory/Valuation/Integers) : add lemma one_of_isUnit' (#12247)

Add lemma one_of_isUnit' , that is a generalization of one_of_isUnit with a slightly weaker assumption.

Co-authored-by: María Inés de Frutos Fernández @mariainesdff

d96c1e7c

Diff

@@ -65,16 +65,20 @@ theorem integer.integers : v.Integers v.integer :=
 
 namespace Integers
 
-variable {v O} [CommRing O] [Algebra O R] (hv : Integers v O)
+variable {v O} [CommRing O] [Algebra O R]
 
-
-theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
+theorem one_of_isUnit' {x : O} (hx : IsUnit x) (H : ∀ x, v (algebraMap O R x) ≤ 1) :
+    v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
-  le_antisymm (hv.2 _) <| by
+  le_antisymm (H _) <| by
     rw [← v.map_one, ← (algebraMap O R).map_one, ← u.mul_inv, ← mul_one (v (algebraMap O R x)), hu,
       (algebraMap O R).map_mul, v.map_mul]
-    exact mul_le_mul_left' (hv.2 (u⁻¹ : Units O)) _
-#align valuation.integers.one_of_is_unit Valuation.Integers.one_of_isUnit
+    exact mul_le_mul_left' (H (u⁻¹ : Units O)) _
+
+variable (hv : Integers v O)
+
+theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
+  one_of_isUnit' hx hv.map_le_one
 
 theorem isUnit_of_one {x : O} (hx : IsUnit (algebraMap O R x)) (hvx : v (algebraMap O R x) = 1) :
     IsUnit x :=

7b7da893

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -23,7 +23,6 @@ namespace Valuation
 section Ring
 
 variable {R : Type u} {Γ₀ : Type v} [Ring R] [LinearOrderedCommGroupWithZero Γ₀]
-
 variable (v : Valuation R Γ₀)
 
 /-- The ring of integers under a given valuation is the subring of elements with valuation ≤ 1. -/
@@ -43,9 +42,7 @@ end Ring
 section CommRing
 
 variable {R : Type u} {Γ₀ : Type v} [CommRing R] [LinearOrderedCommGroupWithZero Γ₀]
-
 variable (v : Valuation R Γ₀)
-
 variable (O : Type w) [CommRing O] [Algebra O R]
 
 /-- Given a valuation v : R → Γ₀ and a ring homomorphism O →+* R, we say that O is the integers of v
@@ -105,7 +102,6 @@ end CommRing
 section Field
 
 variable {F : Type u} {Γ₀ : Type v} [Field F] [LinearOrderedCommGroupWithZero Γ₀]
-
 variable {v : Valuation F Γ₀} {O : Type w} [CommRing O] [Algebra O F] (hv : Integers v O)
 
 namespace Integers

7b7da893

feat(Topology.Algebra.Valuation): add integer_isOpen (#8148)

The unit ball in a valued ring is open.

cbef07bb

Diff

@@ -36,6 +36,8 @@ def integer : Subring R where
   neg_mem' {x} hx := by simp only [Set.mem_setOf_eq] at hx; simpa only [Set.mem_setOf_eq, map_neg]
 #align valuation.integer Valuation.integer
 
+lemma mem_integer_iff (r : R) : r ∈ v.integer ↔ v r ≤ 1 := by rfl
+
 end Ring
 
 section CommRing

7b7da893

chore: cleanup some spaces (#7490)

Purely cosmetic PR

39a866a8

Diff

@@ -33,7 +33,7 @@ def integer : Subring R where
   mul_mem' {x y} hx hy := by simp only [Set.mem_setOf_eq, _root_.map_mul, mul_le_one' hx hy]
   zero_mem' := by simp only [Set.mem_setOf_eq, _root_.map_zero, zero_le']
   add_mem' {x y} hx hy := le_trans (v.map_add x y) (max_le hx hy)
-  neg_mem' {x} hx :=by simp only [Set.mem_setOf_eq] at hx; simpa only [Set.mem_setOf_eq, map_neg]
+  neg_mem' {x} hx := by simp only [Set.mem_setOf_eq] at hx; simpa only [Set.mem_setOf_eq, map_neg]
 #align valuation.integer Valuation.integer
 
 end Ring

7b7da893

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.valuation.integers
-! leanprover-community/mathlib commit 7b7da89322fe46a16bf03eeb345b0acfc73fe10e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Valuation.Basic
 
+#align_import ring_theory.valuation.integers from "leanprover-community/mathlib"@"7b7da89322fe46a16bf03eeb345b0acfc73fe10e"
+
 /-!
 # Ring of integers under a given valuation

7b7da893

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -74,8 +74,7 @@ variable {v O} [CommRing O] [Algebra O R] (hv : Integers v O)
 
 theorem one_of_isUnit {x : O} (hx : IsUnit x) : v (algebraMap O R x) = 1 :=
   let ⟨u, hu⟩ := hx
-  le_antisymm (hv.2 _) <|
-    by
+  le_antisymm (hv.2 _) <| by
     rw [← v.map_one, ← (algebraMap O R).map_one, ← u.mul_inv, ← mul_one (v (algebraMap O R x)), hu,
       (algebraMap O R).map_mul, v.map_mul]
     exact mul_le_mul_left' (hv.2 (u⁻¹ : Units O)) _
@@ -120,8 +119,7 @@ theorem dvd_of_le {x y : O} (h : v (algebraMap O F x) ≤ v (algebraMap O F y))
           (algebraMap O F).map_zero.symm ▸ (v.zero_iff.1 <| le_zero_iff.1 (v.map_zero ▸ hy ▸ h))
       hx.symm ▸ dvd_zero y)
     fun hy : algebraMap O F y ≠ 0 =>
-    have : v ((algebraMap O F y)⁻¹ * algebraMap O F x) ≤ 1 :=
-      by
+    have : v ((algebraMap O F y)⁻¹ * algebraMap O F x) ≤ 1 := by
       rw [← v.map_one, ← inv_mul_cancel hy, v.map_mul, v.map_mul]
       exact mul_le_mul_left' h _
     let ⟨z, hz⟩ := hv.3 this

7b7da893

feat: Port/RingTheory.Valuation.Integers (#2966)

mostly simple fixes: proofs to sub for trans_rel_right and moving instance declarations into namespace.

21c773a1

`ring_theory.valuation.integers` ⟷ `Mathlib.RingTheory.Valuation.Integers`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 452

ring_theory.valuation.integers ⟷ Mathlib.RingTheory.Valuation.Integers

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 452

`ring_theory.valuation.integers` ⟷ `Mathlib.RingTheory.Valuation.Integers`