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

@@ -49,7 +49,7 @@ theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0)
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p :=
   by
   simp_rw [← natCast_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (int.coe_nat_ne_zero.mpr hn),
-    Int.cast_ofNat]
+    Int.cast_natCast]
   rfl
 #align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
 -/
@@ -76,7 +76,7 @@ theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=
   by
   simp_rw [← natCast_zsmul ψ, ← natCast_zsmul θ,
-    zmultiples_zsmul_eq_zsmul_iff (int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
+    zmultiples_zsmul_eq_zsmul_iff (int.coe_nat_ne_zero.mpr hz), Int.cast_natCast]
   rfl
 #align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
 -/

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

@@ -30,7 +30,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
   have hz' : (z : R) ≠ 0 := int.cast_ne_zero.mpr hz
   conv_rhs => simp (config := { singlePass := true }) only [← (mul_right_injective₀ hz').eq_iff]
   simp_rw [← zsmul_eq_mul, smul_add, ← mul_smul_comm, zsmul_eq_mul (z : R)⁻¹, mul_inv_cancel hz',
-    mul_one, ← coe_nat_zsmul, smul_smul, ← add_smul]
+    mul_one, ← natCast_zsmul, smul_smul, ← add_smul]
   constructor
   · rintro ⟨k, h⟩
     simp_rw [← h]
@@ -48,7 +48,7 @@ theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0)
     n • r ∈ AddSubgroup.zmultiples p ↔
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p :=
   by
-  simp_rw [← coe_nat_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (int.coe_nat_ne_zero.mpr hn),
+  simp_rw [← natCast_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (int.coe_nat_ne_zero.mpr hn),
     Int.cast_ofNat]
   rfl
 #align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
@@ -75,7 +75,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=
   by
-  simp_rw [← coe_nat_zsmul ψ, ← coe_nat_zsmul θ,
+  simp_rw [← natCast_zsmul ψ, ← natCast_zsmul θ,
     zmultiples_zsmul_eq_zsmul_iff (int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
 #align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.GroupTheory.QuotientGroup
+import GroupTheory.QuotientGroup
 
 #align_import algebra.char_zero.quotient from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.char_zero.quotient
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.QuotientGroup
 
+#align_import algebra.char_zero.quotient from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
+
 /-!
 # Lemmas about quotients in characteristic zero
 

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

@@ -22,6 +22,7 @@ variable {R : Type _} [DivisionRing R] [CharZero R] {p : R}
 
 namespace AddSubgroup
 
+#print AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div /-
 /-- `z • r` is a multiple of `p` iff `r` is `pk/z` above a multiple of `p`, where `0 ≤ k < |z|`. -/
 theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0) :
     z • r ∈ AddSubgroup.zmultiples p ↔
@@ -43,7 +44,9 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
   · rintro ⟨k, n, h⟩
     exact ⟨_, h⟩
 #align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div
+-/
 
+#print AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div /-
 theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0) :
     n • r ∈ AddSubgroup.zmultiples p ↔
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p :=
@@ -52,11 +55,13 @@ theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0)
     Int.cast_ofNat]
   rfl
 #align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
+-/
 
 end AddSubgroup
 
 namespace quotientAddGroup
 
+#print QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff /-
 theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {z : ℤ} (hz : z ≠ 0) :
     z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + (k : ℕ) • (p / z : R) :=
   by
@@ -67,7 +72,9 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
   simp_rw [← coe_zsmul, ← coe_nsmul, ← coe_add, QuotientAddGroup.eq_iff_sub_mem, ← smul_sub, ←
     sub_sub, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz]
 #align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
+-/
 
+#print QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff /-
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=
   by
@@ -75,6 +82,7 @@ theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
     zmultiples_zsmul_eq_zsmul_iff (int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
 #align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
+-/
 
 end quotientAddGroup
 

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

@@ -22,12 +22,6 @@ variable {R : Type _} [DivisionRing R] [CharZero R] {p : R}
 
 namespace AddSubgroup
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_divₓ'. -/
 /-- `z • r` is a multiple of `p` iff `r` is `pk/z` above a multiple of `p`, where `0 ≤ k < |z|`. -/
 theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0) :
     z • r ∈ AddSubgroup.zmultiples p ↔
@@ -50,12 +44,6 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
     exact ⟨_, h⟩
 #align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_divₓ'. -/
 theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0) :
     n • r ∈ AddSubgroup.zmultiples p ↔
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p :=
@@ -69,9 +57,6 @@ end AddSubgroup
 
 namespace quotientAddGroup
 
-/- warning: quotient_add_group.zmultiples_zsmul_eq_zsmul_iff -> QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iffₓ'. -/
 theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {z : ℤ} (hz : z ≠ 0) :
     z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + (k : ℕ) • (p / z : R) :=
   by
@@ -83,9 +68,6 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
     sub_sub, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz]
 #align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
 
-/- warning: quotient_add_group.zmultiples_nsmul_eq_nsmul_iff -> QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iffₓ'. -/
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=
   by

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

@@ -70,10 +70,7 @@ end AddSubgroup
 namespace quotientAddGroup
 
 /- warning: quotient_add_group.zmultiples_zsmul_eq_zsmul_iff -> QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff is a dubious translation:
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(DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val (Int.natAbs z) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Int.cast.{u1} R (Ring.toIntCast.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) z))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iffₓ'. -/
 theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {z : ℤ} (hz : z ≠ 0) :
     z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + (k : ℕ) • (p / z : R) :=
@@ -87,10 +84,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 #align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
 
 /- warning: quotient_add_group.zmultiples_nsmul_eq_nsmul_iff -> QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) n))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iffₓ'. -/
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=

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

@@ -69,12 +69,12 @@ end AddSubgroup
 
 namespace quotientAddGroup
 
-/- warning: quotient_add_group.zmultiples_zsmul_eq_zsmul_iff -> quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff is a dubious translation:
+/- warning: quotient_add_group.zmultiples_zsmul_eq_zsmul_iff -> QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff is a dubious translation:
 lean 3 declaration is
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(AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (CoeTCₓ.coe.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) z))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HSMul.hSMul.{0, u1, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))) z ψ) (HSMul.hSMul.{0, u1, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))) z θ)) (Exists.{1} (Fin (Int.natAbs z)) (fun (k : Fin (Int.natAbs z)) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))))) θ (QuotientAddGroup.mk.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val (Int.natAbs z) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Int.cast.{u1} R (Ring.toIntCast.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) z))))))))
-Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iffₓ'. -/
+Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iffₓ'. -/
 theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {z : ℤ} (hz : z ≠ 0) :
     z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + (k : ℕ) • (p / z : R) :=
   by
@@ -84,21 +84,21 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
   simp only [this]
   simp_rw [← coe_zsmul, ← coe_nsmul, ← coe_add, QuotientAddGroup.eq_iff_sub_mem, ← smul_sub, ←
     sub_sub, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz]
-#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
+#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
 
-/- warning: quotient_add_group.zmultiples_nsmul_eq_nsmul_iff -> quotientAddGroup.zmultiples_nsmul_eq_nsmul_iff is a dubious translation:
+/- warning: quotient_add_group.zmultiples_nsmul_eq_nsmul_iff -> QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) n ψ) (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) n θ)) (Exists.{1} (Fin n) (fun (k : Fin n) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddZeroClass.toHasAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))))) θ (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) k) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasLiftT.mk.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (CoeTCₓ.coe.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n ψ) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n θ)) (Exists.{1} (Fin n) (fun (k : Fin n) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))))) θ (QuotientAddGroup.mk.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) n))))))))
-Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff quotientAddGroup.zmultiples_nsmul_eq_nsmul_iffₓ'. -/
+Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iffₓ'. -/
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=
   by
   simp_rw [← coe_nat_zsmul ψ, ← coe_nat_zsmul θ,
     zmultiples_zsmul_eq_zsmul_iff (int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
-#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff quotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
+#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
 
 end quotientAddGroup
 

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

@@ -54,7 +54,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {r : R} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) n r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (Exists.{1} (Fin n) (fun (k : Fin n) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) r (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {r : R} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) n r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (Exists.{1} (Fin n) (fun (k : Fin n) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) r (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) n)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {r : R} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) n r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (Exists.{1} (Fin n) (fun (k : Fin n) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) r (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) n)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_divₓ'. -/
 theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0) :
     n • r ∈ AddSubgroup.zmultiples p ↔
@@ -90,7 +90,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R 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(quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (CoeTCₓ.coe.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n ψ) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n θ)) (Exists.{1} (Fin n) (fun (k : Fin n) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))))) θ (QuotientAddGroup.mk.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) n))))))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n ψ) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n θ)) (Exists.{1} (Fin n) (fun (k : Fin n) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))))) θ (QuotientAddGroup.mk.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) n))))))))
 Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff quotientAddGroup.zmultiples_nsmul_eq_nsmul_iffₓ'. -/
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -24,7 +24,7 @@ namespace AddSubgroup
 
 /- warning: add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div -> AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {r : R} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Iff (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (SMul.smul.{0, u1} Int R (SubNegMonoid.SMulInt.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) z r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (Exists.{1} (Fin (Int.natAbs z)) (fun (k : Fin (Int.natAbs z)) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) r (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (Int.natAbs z)) Nat (HasLiftT.mk.{1, 1} (Fin (Int.natAbs z)) Nat (CoeTCₓ.coe.{1, 1} (Fin (Int.natAbs z)) Nat (coeBase.{1, 1} (Fin (Int.natAbs z)) Nat (Fin.coeToNat (Int.natAbs z))))) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) z)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {r : R} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Iff (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (SMul.smul.{0, u1} Int R (SubNegMonoid.SMulInt.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) z r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (Exists.{1} (Fin (Int.natAbs z)) (fun (k : Fin (Int.natAbs z)) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) r (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (Int.natAbs z)) Nat (HasLiftT.mk.{1, 1} (Fin (Int.natAbs z)) Nat (CoeTCₓ.coe.{1, 1} (Fin (Int.natAbs z)) Nat (coeBase.{1, 1} (Fin (Int.natAbs z)) Nat (Fin.coeToNat (Int.natAbs z))))) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) z)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {r : R} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Iff (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSMul.hSMul.{0, u1, u1} Int R R (instHSMul.{0, u1} Int R (SubNegMonoid.SMulInt.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) z r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (Exists.{1} (Fin (Int.natAbs z)) (fun (k : Fin (Int.natAbs z)) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) r (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val (Int.natAbs z) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Int.cast.{u1} R (Ring.toIntCast.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) z)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_divₓ'. -/
@@ -52,7 +52,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
 
 /- warning: add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div -> AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {r : R} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) n r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (Exists.{1} (Fin n) (fun (k : Fin n) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) r (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {r : R} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) n r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (Exists.{1} (Fin n) (fun (k : Fin n) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) r (SMul.smul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {r : R} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) n r) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (Exists.{1} (Fin n) (fun (k : Fin n) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) r (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) n)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_divₓ'. -/
@@ -71,7 +71,7 @@ namespace quotientAddGroup
 
 /- warning: quotient_add_group.zmultiples_zsmul_eq_zsmul_iff -> quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SMul.smul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))) z ψ) (SMul.smul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))) z θ)) (Exists.{1} (Fin (Int.natAbs z)) (fun (k : Fin (Int.natAbs z)) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddZeroClass.toHasAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R 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(Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))))) θ (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (Int.natAbs z)) Nat (HasLiftT.mk.{1, 1} (Fin (Int.natAbs z)) Nat (CoeTCₓ.coe.{1, 1} (Fin (Int.natAbs z)) Nat (coeBase.{1, 1} (Fin (Int.natAbs z)) Nat (Fin.coeToNat (Int.natAbs z))))) k) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasLiftT.mk.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (CoeTCₓ.coe.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) z))))))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SMul.smul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p))))) z ψ) (SMul.smul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))))) θ (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (Int.natAbs z)) Nat (HasLiftT.mk.{1, 1} (Fin (Int.natAbs z)) Nat (CoeTCₓ.coe.{1, 1} (Fin (Int.natAbs z)) Nat (coeBase.{1, 1} (Fin (Int.natAbs z)) Nat (Fin.coeToNat (Int.natAbs z))))) k) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasLiftT.mk.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (CoeTCₓ.coe.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))) z))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {z : Int}, (Ne.{1} Int z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HSMul.hSMul.{0, u1, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} 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(AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Int (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.SMulInt.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))) z θ)) (Exists.{1} (Fin (Int.natAbs z)) (fun (k : Fin (Int.natAbs z)) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))))) θ (QuotientAddGroup.mk.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val (Int.natAbs z) k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Int.cast.{u1} R (Ring.toIntCast.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) z))))))))
 Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iffₓ'. -/
@@ -88,7 +88,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 
 /- warning: quotient_add_group.zmultiples_nsmul_eq_nsmul_iff -> quotientAddGroup.zmultiples_nsmul_eq_nsmul_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R 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(Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) k) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R 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R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n))))))))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) n ψ) (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) n θ)) (Exists.{1} (Fin n) (fun (k : Fin n) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddZeroClass.toHasAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))))) θ (SMul.smul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p) (AddSubgroup.normal_of_comm.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) k) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (HasLiftT.mk.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (CoeTCₓ.coe.{succ u1, succ u1} R (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (quotientAddGroup.Subgroup.hasQuotient.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) p)))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) p ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) n))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {p : R} {ψ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {θ : HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)} {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Iff (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n ψ) (HSMul.hSMul.{0, u1, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHSMul.{0, u1} Nat (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.SMul.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p))))))) n θ)) (Exists.{1} (Fin n) (fun (k : Fin n) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) ψ (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)) (QuotientAddGroup.Quotient.addGroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (AddSubgroup.normal_of_comm.{u1} R (Ring.toAddCommGroup.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p)))))))) θ (QuotientAddGroup.mk.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (AddSubgroup.zmultiples.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) p) (HSMul.hSMul.{0, u1, u1} Nat R R (instHSMul.{0, u1} Nat R (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (Fin.val n k) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivisionRing.toDiv.{u1} R _inst_1)) p (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) n))))))))
 Case conversion may be inaccurate. Consider using '#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff quotientAddGroup.zmultiples_nsmul_eq_nsmul_iffₓ'. -/

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

This renames

• Int.cast_ofNat to Int.cast_natCast
• Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

@@ -43,7 +43,7 @@ theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0)
     n • r ∈ AddSubgroup.zmultiples p ↔
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p := by
   rw [← natCast_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (Int.natCast_ne_zero.mpr hn),
-    Int.cast_ofNat]
+    Int.cast_natCast]
   rfl
 #align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
 
@@ -67,7 +67,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) := by
   rw [← natCast_zsmul ψ, ← natCast_zsmul θ,
-    zmultiples_zsmul_eq_zsmul_iff (Int.natCast_ne_zero.mpr hz), Int.cast_ofNat]
+    zmultiples_zsmul_eq_zsmul_iff (Int.natCast_ne_zero.mpr hz), Int.cast_natCast]
   rfl
 #align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
 

Reduce the diff of #11499

Renames

All in the Int namespace:

• ofNat_eq_cast → ofNat_eq_natCast
• cast_eq_cast_iff_Nat → natCast_inj
• natCast_eq_ofNat → ofNat_eq_natCast
• coe_nat_sub → natCast_sub
• coe_nat_nonneg → natCast_nonneg
• sign_coe_add_one → sign_natCast_add_one
• nat_succ_eq_int_succ → natCast_succ
• succ_neg_nat_succ → succ_neg_natCast_succ
• coe_pred_of_pos → natCast_pred_of_pos
• coe_nat_div → natCast_div
• coe_nat_ediv → natCast_ediv
• sign_coe_nat_of_nonzero → sign_natCast_of_ne_zero
• toNat_coe_nat → toNat_natCast
• toNat_coe_nat_add_one → toNat_natCast_add_one
• coe_nat_dvd → natCast_dvd_natCast
• coe_nat_dvd_left → natCast_dvd
• coe_nat_dvd_right → dvd_natCast
• le_coe_nat_sub → le_natCast_sub
• succ_coe_nat_pos → succ_natCast_pos
• coe_nat_modEq_iff → natCast_modEq_iff
• coe_natAbs → natCast_natAbs
• coe_nat_eq_zero → natCast_eq_zero
• coe_nat_ne_zero → natCast_ne_zero
• coe_nat_ne_zero_iff_pos → natCast_ne_zero_iff_pos
• abs_coe_nat → abs_natCast
• coe_nat_nonpos_iff → natCast_nonpos_iff

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

@@ -42,7 +42,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
 theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0) :
     n • r ∈ AddSubgroup.zmultiples p ↔
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p := by
-  rw [← natCast_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (Int.coe_nat_ne_zero.mpr hn),
+  rw [← natCast_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (Int.natCast_ne_zero.mpr hn),
     Int.cast_ofNat]
   rfl
 #align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
@@ -67,7 +67,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) := by
   rw [← natCast_zsmul ψ, ← natCast_zsmul θ,
-    zmultiples_zsmul_eq_zsmul_iff (Int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
+    zmultiples_zsmul_eq_zsmul_iff (Int.natCast_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
 #align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
 

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

@@ -25,7 +25,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
   have hz' : (z : R) ≠ 0 := Int.cast_ne_zero.mpr hz
   conv_rhs => simp (config := { singlePass := true }) only [← (mul_right_injective₀ hz').eq_iff]
   simp_rw [← zsmul_eq_mul, smul_add, ← mul_smul_comm, zsmul_eq_mul (z : R)⁻¹, mul_inv_cancel hz',
-    mul_one, ← coe_nat_zsmul, smul_smul, ← add_smul]
+    mul_one, ← natCast_zsmul, smul_smul, ← add_smul]
   constructor
   · rintro ⟨k, h⟩
     simp_rw [← h]
@@ -42,7 +42,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
 theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0) :
     n • r ∈ AddSubgroup.zmultiples p ↔
       ∃ k : Fin n, r - (k : ℕ) • (p / n : R) ∈ AddSubgroup.zmultiples p := by
-  rw [← coe_nat_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (Int.coe_nat_ne_zero.mpr hn),
+  rw [← natCast_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (Int.coe_nat_ne_zero.mpr hn),
     Int.cast_ofNat]
   rfl
 #align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
@@ -66,7 +66,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
 
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) := by
-  rw [← coe_nat_zsmul ψ, ← coe_nat_zsmul θ,
+  rw [← natCast_zsmul ψ, ← natCast_zsmul θ,
     zmultiples_zsmul_eq_zsmul_iff (Int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
 #align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -33,9 +33,8 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
     · rw [← Int.ofNat_lt, Int.toNat_of_nonneg (Int.emod_nonneg _ hz)]
       exact (Int.emod_lt _ hz).trans_eq (Int.abs_eq_natAbs _)
     rw [Fin.val_mk, Int.toNat_of_nonneg (Int.emod_nonneg _ hz)]
-    nth_rewrite 3 [← Int.div_add_mod k z]
-    rw [Int.mod_def, ← Int.div_def', Int.emod_def]
-    simp only [add_sub_cancel'_right, zsmul_eq_mul, Int.div_def']
+    nth_rewrite 3 [← Int.ediv_add_emod k z]
+    rfl
   · rintro ⟨k, n, h⟩
     exact ⟨_, h⟩
 #align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -53,7 +53,7 @@ end AddSubgroup
 namespace QuotientAddGroup
 
 theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {z : ℤ} (hz : z ≠ 0) :
-    z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + (k : ℕ) • (p / z : R) := by
+    z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + ((k : ℕ) • (p / z) : R) := by
   induction ψ using Quotient.inductionOn'
   induction θ using Quotient.inductionOn'
   -- Porting note: Introduced Zp notation to shorten lines

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

This has nice performance benefits.

@@ -12,7 +12,7 @@ import Mathlib.GroupTheory.QuotientGroup
 -/
 
 
-variable {R : Type _} [DivisionRing R] [CharZero R] {p : R}
+variable {R : Type*} [DivisionRing R] [CharZero R] {p : R}
 
 namespace AddSubgroup
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.char_zero.quotient
-! leanprover-community/mathlib commit d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.QuotientGroup
 
+#align_import algebra.char_zero.quotient from "leanprover-community/mathlib"@"d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46"
+
 /-!
 # Lemmas about quotients in characteristic zero
 -/

Co-authored-by: David Loeffler <d.loeffler.01@cantab.net>

@@ -53,7 +53,7 @@ theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0)
 
 end AddSubgroup
 
-namespace quotientAddGroup
+namespace QuotientAddGroup
 
 theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {z : ℤ} (hz : z ≠ 0) :
     z • ψ = z • θ ↔ ∃ k : Fin z.natAbs, ψ = θ + (k : ℕ) • (p / z : R) := by
@@ -66,13 +66,13 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
   simp_rw [← QuotientAddGroup.mk_zsmul, ← QuotientAddGroup.mk_add,
     QuotientAddGroup.eq_iff_sub_mem, ← smul_sub, ← sub_sub]
   exact AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz
-#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
+#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
 
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) := by
   rw [← coe_nat_zsmul ψ, ← coe_nat_zsmul θ,
     zmultiples_zsmul_eq_zsmul_iff (Int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
-#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff quotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
+#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
 
-end quotientAddGroup
+end QuotientAddGroup

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -63,7 +63,7 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
   let Zp := AddSubgroup.zmultiples p
   have : (Quotient.mk'' : R → R ⧸ Zp) = ((↑) : R → R ⧸ Zp) := rfl
   simp only [this]
-  simp_rw [← QuotientAddGroup.mk_zsmul, ← QuotientAddGroup.mk_nsmul, ← QuotientAddGroup.mk_add,
+  simp_rw [← QuotientAddGroup.mk_zsmul, ← QuotientAddGroup.mk_add,
     QuotientAddGroup.eq_iff_sub_mem, ← smul_sub, ← sub_sub]
   exact AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz
 #align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -41,8 +41,7 @@ theorem zsmul_mem_zmultiples_iff_exists_sub_div {r : R} {z : ℤ} (hz : z ≠ 0)
     simp only [add_sub_cancel'_right, zsmul_eq_mul, Int.div_def']
   · rintro ⟨k, n, h⟩
     exact ⟨_, h⟩
-#align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div
-    AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div
+#align add_subgroup.zsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div
 
 theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0) :
     n • r ∈ AddSubgroup.zmultiples p ↔
@@ -67,7 +66,6 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
   simp_rw [← QuotientAddGroup.mk_zsmul, ← QuotientAddGroup.mk_nsmul, ← QuotientAddGroup.mk_add,
     QuotientAddGroup.eq_iff_sub_mem, ← smul_sub, ← sub_sub]
   exact AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz
-
 #align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
 
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :

Same as #3103, I missed those before, probably because I didn't rebase on HEAD before. This shouldnow include all cases of aligns with linebreak.

find . -type f -name "*.lean" -exec sed -i -E 'N;s/^#align ([^[:space:]]+)\n *([^[:space:]]+)$/#align \1 \2/' {} \;

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -68,15 +68,13 @@ theorem zmultiples_zsmul_eq_zsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {
     QuotientAddGroup.eq_iff_sub_mem, ← smul_sub, ← sub_sub]
   exact AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div hz
 
-#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff
-    quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
+#align quotient_add_group.zmultiples_zsmul_eq_zsmul_iff quotientAddGroup.zmultiples_zsmul_eq_zsmul_iff
 
 theorem zmultiples_nsmul_eq_nsmul_iff {ψ θ : R ⧸ AddSubgroup.zmultiples p} {n : ℕ} (hz : n ≠ 0) :
     n • ψ = n • θ ↔ ∃ k : Fin n, ψ = θ + (k : ℕ) • (p / n : R) := by
   rw [← coe_nat_zsmul ψ, ← coe_nat_zsmul θ,
     zmultiples_zsmul_eq_zsmul_iff (Int.coe_nat_ne_zero.mpr hz), Int.cast_ofNat]
   rfl
-#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff
-    quotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
+#align quotient_add_group.zmultiples_nsmul_eq_nsmul_iff quotientAddGroup.zmultiples_nsmul_eq_nsmul_iff
 
 end quotientAddGroup

Apparently we have CI scripts that assume those fall on a single line. The command line used to fix the aligns was:

find . -type f -name "*.lean" -exec sed -i -E 'N;s/^#align ([^[:space:]]+)\n *([^[:space:]]+)$/#align \1 \2/' {} \;

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -50,8 +50,7 @@ theorem nsmul_mem_zmultiples_iff_exists_sub_div {r : R} {n : ℕ} (hn : n ≠ 0)
   rw [← coe_nat_zsmul r, zsmul_mem_zmultiples_iff_exists_sub_div (Int.coe_nat_ne_zero.mpr hn),
     Int.cast_ofNat]
   rfl
-#align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div
-    AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
+#align add_subgroup.nsmul_mem_zmultiples_iff_exists_sub_div AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div
 
 end AddSubgroup
 

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Lukas Miaskiwskyi <lukas.mias@gmail.com>