linear_algebra.adic_completion | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

2bbc7e38

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1b0a28e1

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
 import Algebra.GeomSum
-import LinearAlgebra.Smodeq
+import LinearAlgebra.SModEq
 import RingTheory.JacobsonIdeal
 
 #align_import linear_algebra.adic_completion from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"

1b0a28e1

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -186,7 +186,7 @@ instance : IsHausdorff I (Hausdorffification I M) :=
         (mem_iInf _).2 fun n =>
           by
           have := comap_map_mkq (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) (I ^ n • ⊤)
-          simp only [sup_of_le_right (iInf_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this 
+          simp only [sup_of_le_right (iInf_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this
           rw [← this, map_smul'', mem_comap, Submodule.map_top, range_mkq, ← SModEq.zero];
           exact hx n⟩
 
@@ -234,7 +234,7 @@ instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
   · rw [pow_zero, Ideal.one_eq_top, top_smul]; exact SModEq.top
   specialize hf (Nat.le_add_left 1 n)
-  rw [pow_one, bot_smul, SModEq.bot] at hf ; rw [hf]
+  rw [pow_one, bot_smul, SModEq.bot] at hf; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
 -/

1b0a28e1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathbin.Algebra.GeomSum
-import Mathbin.LinearAlgebra.Smodeq
-import Mathbin.RingTheory.JacobsonIdeal
+import Algebra.GeomSum
+import LinearAlgebra.Smodeq
+import RingTheory.JacobsonIdeal
 
 #align_import linear_algebra.adic_completion from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"

1b0a28e1

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module linear_algebra.adic_completion
-! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GeomSum
 import Mathbin.LinearAlgebra.Smodeq
 import Mathbin.RingTheory.JacobsonIdeal
 
+#align_import linear_algebra.adic_completion from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
+
 /-!
 # Completion of a module with respect to an ideal.

1b0a28e1

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -67,22 +67,29 @@ class IsAdicComplete extends IsHausdorff I M, IsPrecomplete I M : Prop
 
 variable {I M}
 
+#print IsHausdorff.haus /-
 theorem IsHausdorff.haus (h : IsHausdorff I M) :
     ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0 :=
   IsHausdorff.haus'
 #align is_Hausdorff.haus IsHausdorff.haus
+-/
 
+#print isHausdorff_iff /-
 theorem isHausdorff_iff :
     IsHausdorff I M ↔ ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0 :=
   ⟨IsHausdorff.haus, fun h => ⟨h⟩⟩
 #align is_Hausdorff_iff isHausdorff_iff
+-/
 
+#print IsPrecomplete.prec /-
 theorem IsPrecomplete.prec (h : IsPrecomplete I M) {f : ℕ → M} :
     (∀ {m n}, m ≤ n → f m ≡ f n [SMOD (I ^ m • ⊤ : Submodule R M)]) →
       ∃ L : M, ∀ n, f n ≡ L [SMOD (I ^ n • ⊤ : Submodule R M)] :=
   IsPrecomplete.prec' _
 #align is_precomplete.prec IsPrecomplete.prec
+-/
 
+#print isPrecomplete_iff /-
 theorem isPrecomplete_iff :
     IsPrecomplete I M ↔
       ∀ f : ℕ → M,
@@ -90,6 +97,7 @@ theorem isPrecomplete_iff :
           ∃ L : M, ∀ n, f n ≡ L [SMOD (I ^ n • ⊤ : Submodule R M)] :=
   ⟨fun h => h.1, fun h => ⟨h⟩⟩
 #align is_precomplete_iff isPrecomplete_iff
+-/
 
 variable (I M)
 
@@ -119,16 +127,20 @@ def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule
 
 namespace IsHausdorff
 
+#print IsHausdorff.bot /-
 instance bot : IsHausdorff (⊥ : Ideal R) M :=
   ⟨fun x hx => by simpa only [pow_one ⊥, bot_smul, SModEq.bot] using hx 1⟩
 #align is_Hausdorff.bot IsHausdorff.bot
+-/
 
 variable {M}
 
+#print IsHausdorff.subsingleton /-
 protected theorem subsingleton (h : IsHausdorff (⊤ : Ideal R) M) : Subsingleton M :=
   ⟨fun x y =>
     eq_of_sub_eq_zero <| h.haus (x - y) fun n => by rw [Ideal.top_pow, top_smul]; exact SModEq.top⟩
 #align is_Hausdorff.subsingleton IsHausdorff.subsingleton
+-/
 
 variable (M)
 
@@ -140,10 +152,12 @@ instance (priority := 100) of_subsingleton [Subsingleton M] : IsHausdorff I M :=
 
 variable {I M}
 
+#print IsHausdorff.iInf_pow_smul /-
 theorem iInf_pow_smul (h : IsHausdorff I M) : (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) = ⊥ :=
   eq_bot_iff.2 fun x hx =>
     (mem_bot _).2 <| h.haus x fun n => SModEq.zero.2 <| (mem_iInf fun n : ℕ => I ^ n • ⊤).1 hx n
 #align is_Hausdorff.infi_pow_smul IsHausdorff.iInf_pow_smul
+-/
 
 end IsHausdorff
 
@@ -158,11 +172,13 @@ def of : M →ₗ[R] Hausdorffification I M :=
 
 variable {I M}
 
+#print Hausdorffification.induction_on /-
 @[elab_as_elim]
 theorem induction_on {C : Hausdorffification I M → Prop} (x : Hausdorffification I M)
     (ih : ∀ x, C (of I M x)) : C x :=
   Quotient.inductionOn' x ih
 #align Hausdorffification.induction_on Hausdorffification.induction_on
+-/
 
 variable (I M)
 
@@ -179,8 +195,6 @@ instance : IsHausdorff I (Hausdorffification I M) :=
 
 variable {M} [h : IsHausdorff I N]
 
-include h
-
 #print Hausdorffification.lift /-
 /-- universal property of Hausdorffification: any linear map to a Hausdorff module extends to a
 unique map from the Hausdorffification. -/
@@ -193,24 +207,31 @@ def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
 #align Hausdorffification.lift Hausdorffification.lift
 -/
 
+#print Hausdorffification.lift_of /-
 theorem lift_of (f : M →ₗ[R] N) (x : M) : lift I f (of I M x) = f x :=
   rfl
 #align Hausdorffification.lift_of Hausdorffification.lift_of
+-/
 
+#print Hausdorffification.lift_comp_of /-
 theorem lift_comp_of (f : M →ₗ[R] N) : (lift I f).comp (of I M) = f :=
   LinearMap.ext fun _ => rfl
 #align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_of
+-/
 
+#print Hausdorffification.lift_eq /-
 /-- Uniqueness of lift. -/
 theorem lift_eq (f : M →ₗ[R] N) (g : Hausdorffification I M →ₗ[R] N) (hg : g.comp (of I M) = f) :
     g = lift I f :=
   LinearMap.ext fun x => induction_on x fun x => by rw [lift_of, ← hg, LinearMap.comp_apply]
 #align Hausdorffification.lift_eq Hausdorffification.lift_eq
+-/
 
 end Hausdorffification
 
 namespace IsPrecomplete
 
+#print IsPrecomplete.bot /-
 instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   by
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
@@ -218,10 +239,13 @@ instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   specialize hf (Nat.le_add_left 1 n)
   rw [pow_one, bot_smul, SModEq.bot] at hf ; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
+-/
 
+#print IsPrecomplete.top /-
 instance top : IsPrecomplete (⊤ : Ideal R) M :=
   ⟨fun f hf => ⟨0, fun n => by rw [Ideal.top_pow, top_smul]; exact SModEq.top⟩⟩
 #align is_precomplete.top IsPrecomplete.top
+-/
 
 #print IsPrecomplete.of_subsingleton /-
 instance (priority := 100) of_subsingleton [Subsingleton M] : IsPrecomplete I M :=
@@ -318,12 +342,16 @@ end adicCompletion
 
 namespace IsAdicComplete
 
+#print IsAdicComplete.bot /-
 instance bot : IsAdicComplete (⊥ : Ideal R) M where
 #align is_adic_complete.bot IsAdicComplete.bot
+-/
 
+#print IsAdicComplete.subsingleton /-
 protected theorem subsingleton (h : IsAdicComplete (⊤ : Ideal R) M) : Subsingleton M :=
   h.1.Subsingleton
 #align is_adic_complete.subsingleton IsAdicComplete.subsingleton
+-/
 
 #print IsAdicComplete.of_subsingleton /-
 instance (priority := 100) of_subsingleton [Subsingleton M] : IsAdicComplete I M where
@@ -334,6 +362,7 @@ open scoped BigOperators
 
 open Finset
 
+#print IsAdicComplete.le_jacobson_bot /-
 theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
   by
   intro x hx
@@ -370,6 +399,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
         sub_self, zero_sub, neg_mem_iff, mul_pow]
       exact Ideal.mul_mem_right _ (I ^ _) (Ideal.pow_mem_pow hx _)
 #align is_adic_complete.le_jacobson_bot IsAdicComplete.le_jacobson_bot
+-/
 
 end IsAdicComplete

1b0a28e1

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -107,9 +107,9 @@ In fact, this is only complete if the ideal is finitely generated. -/
 def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule R M))
     where
   carrier :=
-    { f |
+    {f |
       ∀ {m n} (h : m ≤ n),
-        liftQ _ (mkQ _) (by rw [ker_mkq]; exact smul_mono (Ideal.pow_le_pow h) le_rfl) (f n) = f m }
+        liftQ _ (mkQ _) (by rw [ker_mkq]; exact smul_mono (Ideal.pow_le_pow h) le_rfl) (f n) = f m}
   zero_mem' m n hmn := by rw [Pi.zero_apply, Pi.zero_apply, LinearMap.map_zero]
   add_mem' f g hf hg m n hmn := by
     rw [Pi.add_apply, Pi.add_apply, LinearMap.map_add, hf hmn, hg hmn]

1b0a28e1

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -173,7 +173,7 @@ instance : IsHausdorff I (Hausdorffification I M) :=
         (mem_iInf _).2 fun n =>
           by
           have := comap_map_mkq (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) (I ^ n • ⊤)
-          simp only [sup_of_le_right (iInf_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this
+          simp only [sup_of_le_right (iInf_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this 
           rw [← this, map_smul'', mem_comap, Submodule.map_top, range_mkq, ← SModEq.zero];
           exact hx n⟩
 
@@ -216,7 +216,7 @@ instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
   · rw [pow_zero, Ideal.one_eq_top, top_smul]; exact SModEq.top
   specialize hf (Nat.le_add_left 1 n)
-  rw [pow_one, bot_smul, SModEq.bot] at hf; rw [hf]
+  rw [pow_one, bot_smul, SModEq.bot] at hf ; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
 
 instance top : IsPrecomplete (⊤ : Ideal R) M :=
@@ -357,7 +357,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
     apply IsHausdorff.haus (to_is_Hausdorff : IsHausdorff I R)
     intro n
     specialize hL n
-    rw [SModEq.sub_mem, Algebra.id.smul_eq_mul, Ideal.mul_top] at hL⊢
+    rw [SModEq.sub_mem, Algebra.id.smul_eq_mul, Ideal.mul_top] at hL ⊢
     rw [sub_zero]
     suffices (1 - x * y) * f n - 1 ∈ I ^ n
       by

1b0a28e1

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -330,7 +330,7 @@ instance (priority := 100) of_subsingleton [Subsingleton M] : IsAdicComplete I M
 #align is_adic_complete.of_subsingleton IsAdicComplete.of_subsingleton
 -/
 
-open BigOperators
+open scoped BigOperators
 
 open Finset

1b0a28e1

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -67,40 +67,22 @@ class IsAdicComplete extends IsHausdorff I M, IsPrecomplete I M : Prop
 
 variable {I M}
 
-/- warning: is_Hausdorff.haus -> IsHausdorff.haus is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsHausdorff.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (forall (x : M), (forall (n : Nat), SModEq.{u1, u2} R (CommRing.toRing.{u1} R _inst_1) M _inst_2 _inst_3 (SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsHausdorff.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (forall (x : M), (forall (n : Nat), SModEq.{u2, u1} R (CommRing.toRing.{u2} R _inst_1) M _inst_2 _inst_3 (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2)))))))) -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2)))))))))
-Case conversion may be inaccurate. Consider using '#align is_Hausdorff.haus IsHausdorff.hausₓ'. -/
 theorem IsHausdorff.haus (h : IsHausdorff I M) :
     ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0 :=
   IsHausdorff.haus'
 #align is_Hausdorff.haus IsHausdorff.haus
 
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 theorem isHausdorff_iff :
     IsHausdorff I M ↔ ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0 :=
   ⟨IsHausdorff.haus, fun h => ⟨h⟩⟩
 #align is_Hausdorff_iff isHausdorff_iff
 
-/- warning: is_precomplete.prec -> IsPrecomplete.prec is a dubious translation:
-<too large>
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 theorem IsPrecomplete.prec (h : IsPrecomplete I M) {f : ℕ → M} :
     (∀ {m n}, m ≤ n → f m ≡ f n [SMOD (I ^ m • ⊤ : Submodule R M)]) →
       ∃ L : M, ∀ n, f n ≡ L [SMOD (I ^ n • ⊤ : Submodule R M)] :=
   IsPrecomplete.prec' _
 #align is_precomplete.prec IsPrecomplete.prec
 
-/- warning: is_precomplete_iff -> isPrecomplete_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_precomplete_iff isPrecomplete_iffₓ'. -/
 theorem isPrecomplete_iff :
     IsPrecomplete I M ↔
       ∀ f : ℕ → M,
@@ -137,24 +119,12 @@ def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule
 
 namespace IsHausdorff
 
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 instance bot : IsHausdorff (⊥ : Ideal R) M :=
   ⟨fun x hx => by simpa only [pow_one ⊥, bot_smul, SModEq.bot] using hx 1⟩
 #align is_Hausdorff.bot IsHausdorff.bot
 
 variable {M}
 
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-Case conversion may be inaccurate. Consider using '#align is_Hausdorff.subsingleton IsHausdorff.subsingletonₓ'. -/
 protected theorem subsingleton (h : IsHausdorff (⊤ : Ideal R) M) : Subsingleton M :=
   ⟨fun x y =>
     eq_of_sub_eq_zero <| h.haus (x - y) fun n => by rw [Ideal.top_pow, top_smul]; exact SModEq.top⟩
@@ -170,12 +140,6 @@ instance (priority := 100) of_subsingleton [Subsingleton M] : IsHausdorff I M :=
 
 variable {I M}
 
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-Case conversion may be inaccurate. Consider using '#align is_Hausdorff.infi_pow_smul IsHausdorff.iInf_pow_smulₓ'. -/
 theorem iInf_pow_smul (h : IsHausdorff I M) : (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) = ⊥ :=
   eq_bot_iff.2 fun x hx =>
     (mem_bot _).2 <| h.haus x fun n => SModEq.zero.2 <| (mem_iInf fun n : ℕ => I ^ n • ⊤).1 hx n
@@ -194,9 +158,6 @@ def of : M →ₗ[R] Hausdorffification I M :=
 
 variable {I M}
 
-/- warning: Hausdorffification.induction_on -> Hausdorffification.induction_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Hausdorffification.induction_on Hausdorffification.induction_onₓ'. -/
 @[elab_as_elim]
 theorem induction_on {C : Hausdorffification I M → Prop} (x : Hausdorffification I M)
     (ih : ∀ x, C (of I M x)) : C x :=
@@ -232,23 +193,14 @@ def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
 #align Hausdorffification.lift Hausdorffification.lift
 -/
 
-/- warning: Hausdorffification.lift_of -> Hausdorffification.lift_of is a dubious translation:
-<too large>
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 theorem lift_of (f : M →ₗ[R] N) (x : M) : lift I f (of I M x) = f x :=
   rfl
 #align Hausdorffification.lift_of Hausdorffification.lift_of
 
-/- warning: Hausdorffification.lift_comp_of -> Hausdorffification.lift_comp_of is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_ofₓ'. -/
 theorem lift_comp_of (f : M →ₗ[R] N) : (lift I f).comp (of I M) = f :=
   LinearMap.ext fun _ => rfl
 #align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_of
 
-/- warning: Hausdorffification.lift_eq -> Hausdorffification.lift_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_eq Hausdorffification.lift_eqₓ'. -/
 /-- Uniqueness of lift. -/
 theorem lift_eq (f : M →ₗ[R] N) (g : Hausdorffification I M →ₗ[R] N) (hg : g.comp (of I M) = f) :
     g = lift I f :=
@@ -259,12 +211,6 @@ end Hausdorffification
 
 namespace IsPrecomplete
 
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-Case conversion may be inaccurate. Consider using '#align is_precomplete.bot IsPrecomplete.botₓ'. -/
 instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   by
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
@@ -273,12 +219,6 @@ instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   rw [pow_one, bot_smul, SModEq.bot] at hf; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
 
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-Case conversion may be inaccurate. Consider using '#align is_precomplete.top IsPrecomplete.topₓ'. -/
 instance top : IsPrecomplete (⊤ : Ideal R) M :=
   ⟨fun f hf => ⟨0, fun n => by rw [Ideal.top_pow, top_smul]; exact SModEq.top⟩⟩
 #align is_precomplete.top IsPrecomplete.top
@@ -378,21 +318,9 @@ end adicCompletion
 
 namespace IsAdicComplete
 
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-Case conversion may be inaccurate. Consider using '#align is_adic_complete.bot IsAdicComplete.botₓ'. -/
 instance bot : IsAdicComplete (⊥ : Ideal R) M where
 #align is_adic_complete.bot IsAdicComplete.bot
 
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-Case conversion may be inaccurate. Consider using '#align is_adic_complete.subsingleton IsAdicComplete.subsingletonₓ'. -/
 protected theorem subsingleton (h : IsAdicComplete (⊤ : Ideal R) M) : Subsingleton M :=
   h.1.Subsingleton
 #align is_adic_complete.subsingleton IsAdicComplete.subsingleton
@@ -406,12 +334,6 @@ open BigOperators
 
 open Finset
 
-/- warning: is_adic_complete.le_jacobson_bot -> IsAdicComplete.le_jacobson_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_6 : IsAdicComplete.{u1, u1} R _inst_1 I R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))], LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) I (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) [_inst_6 : IsAdicComplete.{u1, u1} R _inst_1 I R (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))], LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align is_adic_complete.le_jacobson_bot IsAdicComplete.le_jacobson_botₓ'. -/
 theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
   by
   intro x hx

1b0a28e1

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -127,12 +127,7 @@ def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule
   carrier :=
     { f |
       ∀ {m n} (h : m ≤ n),
-        liftQ _ (mkQ _)
-            (by
-              rw [ker_mkq]
-              exact smul_mono (Ideal.pow_le_pow h) le_rfl)
-            (f n) =
-          f m }
+        liftQ _ (mkQ _) (by rw [ker_mkq]; exact smul_mono (Ideal.pow_le_pow h) le_rfl) (f n) = f m }
   zero_mem' m n hmn := by rw [Pi.zero_apply, Pi.zero_apply, LinearMap.map_zero]
   add_mem' f g hf hg m n hmn := by
     rw [Pi.add_apply, Pi.add_apply, LinearMap.map_add, hf hmn, hg hmn]
@@ -162,10 +157,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_Hausdorff.subsingleton IsHausdorff.subsingletonₓ'. -/
 protected theorem subsingleton (h : IsHausdorff (⊤ : Ideal R) M) : Subsingleton M :=
   ⟨fun x y =>
-    eq_of_sub_eq_zero <|
-      h.haus (x - y) fun n => by
-        rw [Ideal.top_pow, top_smul]
-        exact SModEq.top⟩
+    eq_of_sub_eq_zero <| h.haus (x - y) fun n => by rw [Ideal.top_pow, top_smul]; exact SModEq.top⟩
 #align is_Hausdorff.subsingleton IsHausdorff.subsingleton
 
 variable (M)
@@ -236,10 +228,7 @@ def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
     map_le_iff_le_comap.1 <|
       h.iInf_pow_smul ▸
         le_iInf fun n =>
-          le_trans (map_mono <| iInf_le _ n) <|
-            by
-            rw [map_smul'']
-            exact smul_mono le_rfl le_top
+          le_trans (map_mono <| iInf_le _ n) <| by rw [map_smul'']; exact smul_mono le_rfl le_top
 #align Hausdorffification.lift Hausdorffification.lift
 -/
 
@@ -279,8 +268,7 @@ Case conversion may be inaccurate. Consider using '#align is_precomplete.bot IsP
 instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   by
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
-  · rw [pow_zero, Ideal.one_eq_top, top_smul]
-    exact SModEq.top
+  · rw [pow_zero, Ideal.one_eq_top, top_smul]; exact SModEq.top
   specialize hf (Nat.le_add_left 1 n)
   rw [pow_one, bot_smul, SModEq.bot] at hf; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
@@ -292,10 +280,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsPrecomplete.{u1, u2} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M _inst_2 _inst_3
 Case conversion may be inaccurate. Consider using '#align is_precomplete.top IsPrecomplete.topₓ'. -/
 instance top : IsPrecomplete (⊤ : Ideal R) M :=
-  ⟨fun f hf =>
-    ⟨0, fun n => by
-      rw [Ideal.top_pow, top_smul]
-      exact SModEq.top⟩⟩
+  ⟨fun f hf => ⟨0, fun n => by rw [Ideal.top_pow, top_smul]; exact SModEq.top⟩⟩
 #align is_precomplete.top IsPrecomplete.top
 
 #print IsPrecomplete.of_subsingleton /-

1b0a28e1

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -90,10 +90,7 @@ theorem isHausdorff_iff :
 #align is_Hausdorff_iff isHausdorff_iff
 
 /- warning: is_precomplete.prec -> IsPrecomplete.prec is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsPrecomplete.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (forall {f : Nat -> M}, (forall {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (SModEq.{u2, u1} R (CommRing.toRing.{u2} R _inst_1) M _inst_2 _inst_3 (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R 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R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (f n) L)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_precomplete.prec IsPrecomplete.precₓ'. -/
 theorem IsPrecomplete.prec (h : IsPrecomplete I M) {f : ℕ → M} :
     (∀ {m n}, m ≤ n → f m ≡ f n [SMOD (I ^ m • ⊤ : Submodule R M)]) →
@@ -102,10 +99,7 @@ theorem IsPrecomplete.prec (h : IsPrecomplete I M) {f : ℕ → M} :
 #align is_precomplete.prec IsPrecomplete.prec
 
 /- warning: is_precomplete_iff -> isPrecomplete_iff is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_precomplete_iff isPrecomplete_iffₓ'. -/
 theorem isPrecomplete_iff :
     IsPrecomplete I M ↔
@@ -209,10 +203,7 @@ def of : M →ₗ[R] Hausdorffification I M :=
 variable {I M}
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Hausdorffification.induction_on Hausdorffification.induction_onₓ'. -/
 @[elab_as_elim]
 theorem induction_on {C : Hausdorffification I M → Prop} (x : Hausdorffification I M)
@@ -253,30 +244,21 @@ def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
 -/
 
 /- warning: Hausdorffification.lift_of -> Hausdorffification.lift_of is a dubious translation:
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(Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) => (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.lift.{u1, u2, u3} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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_inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (fun (_x : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R 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(CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.lift.{u3, u2, u1} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M 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+<too large>
 Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_of Hausdorffification.lift_ofₓ'. -/
 theorem lift_of (f : M →ₗ[R] N) (x : M) : lift I f (of I M x) = f x :=
   rfl
 #align Hausdorffification.lift_of Hausdorffification.lift_of
 
 /- warning: Hausdorffification.lift_comp_of -> Hausdorffification.lift_comp_of is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_ofₓ'. -/
 theorem lift_comp_of (f : M →ₗ[R] N) : (lift I f).comp (of I M) = f :=
   LinearMap.ext fun _ => rfl
 #align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_of
 
 /- warning: Hausdorffification.lift_eq -> Hausdorffification.lift_eq is a dubious translation:
-lean 3 declaration is
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_inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5), (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5) (LinearMap.comp.{u1, u1, u1, u2, u2, u3} R R R M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R 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-but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u1}} [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [h : IsHausdorff.{u3, u1} R _inst_1 I N _inst_4 _inst_5] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5), (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (LinearMap.comp.{u3, u3, u3, u2, u2, u1} R R R M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R 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u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3)) f) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R 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_inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) g (Hausdorffification.lift.{u3, u2, u1} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_eq Hausdorffification.lift_eqₓ'. -/
 /-- Uniqueness of lift. -/
 theorem lift_eq (f : M →ₗ[R] N) (g : Hausdorffification I M →ₗ[R] N) (hg : g.comp (of I M) = f) :

1b0a28e1

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -212,7 +212,7 @@ variable {I M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {C : (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> Prop} (x : Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3), (forall (x : M), C (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => M -> (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.of.{u1, u2} R _inst_1 I M _inst_2 _inst_3) x)) -> (C x)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {C : (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> Prop} (x : Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3), (forall (x : M), C (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Hausdorffification.of.{u2, u1} R _inst_1 I M _inst_2 _inst_3) x)) -> (C x)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {C : (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> Prop} (x : Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3), (forall (x : M), C (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Hausdorffification.of.{u2, u1} R _inst_1 I M _inst_2 _inst_3) x)) -> (C x)
 Case conversion may be inaccurate. Consider using '#align Hausdorffification.induction_on Hausdorffification.induction_onₓ'. -/
 @[elab_as_elim]
 theorem induction_on {C : Hausdorffification I M → Prop} (x : Hausdorffification I M)
@@ -256,7 +256,7 @@ def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u3}} [_inst_4 : AddCommGroup.{u3} N] [_inst_5 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4)] [h : IsHausdorff.{u1, u3} R _inst_1 I N _inst_4 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5) (x : M), Eq.{succ u3} N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) => (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.lift.{u1, u2, u3} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => M -> (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.of.{u1, u2} R _inst_1 I M _inst_2 _inst_3) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f x)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u1}} [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [h : IsHausdorff.{u3, u1} R _inst_1 I N _inst_4 _inst_5] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => N) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) a) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (fun (_x : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.lift.{u3, u2, u1} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f x)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u1}} [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [h : IsHausdorff.{u3, u1} R _inst_1 I N _inst_4 _inst_5] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => N) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) a) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (fun (_x : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.lift.{u3, u2, u1} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f x)
 Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_of Hausdorffification.lift_ofₓ'. -/
 theorem lift_of (f : M →ₗ[R] N) (x : M) : lift I f (of I M x) = f x :=
   rfl

1b0a28e1

bump to nightly-2023-05-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

5dfda1a5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module linear_algebra.adic_completion
-! leanprover-community/mathlib commit 2bbc7e3884ba234309d2a43b19144105a753292e
+! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.JacobsonIdeal
 /-!
 # Completion of a module with respect to an ideal.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the notions of Hausdorff, precomplete, and complete for an `R`-module `M`
 with respect to an ideal `I`:

2bbc7e38

bump to nightly-2023-05-20-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

cb56d47a

Diff

@@ -39,11 +39,14 @@ variable (M : Type _) [AddCommGroup M] [Module R M]
 
 variable {N : Type _} [AddCommGroup N] [Module R N]
 
+#print IsHausdorff /-
 /-- A module `M` is Hausdorff with respect to an ideal `I` if `⋂ I^n M = 0`. -/
 class IsHausdorff : Prop where
   haus' : ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0
 #align is_Hausdorff IsHausdorff
+-/
 
+#print IsPrecomplete /-
 /-- A module `M` is precomplete with respect to an ideal `I` if every Cauchy sequence converges. -/
 class IsPrecomplete : Prop where
   prec' :
@@ -51,29 +54,56 @@ class IsPrecomplete : Prop where
       (∀ {m n}, m ≤ n → f m ≡ f n [SMOD (I ^ m • ⊤ : Submodule R M)]) →
         ∃ L : M, ∀ n, f n ≡ L [SMOD (I ^ n • ⊤ : Submodule R M)]
 #align is_precomplete IsPrecomplete
+-/
 
+#print IsAdicComplete /-
 /-- A module `M` is `I`-adically complete if it is Hausdorff and precomplete. -/
 class IsAdicComplete extends IsHausdorff I M, IsPrecomplete I M : Prop
 #align is_adic_complete IsAdicComplete
+-/
 
 variable {I M}
 
+/- warning: is_Hausdorff.haus -> IsHausdorff.haus is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_Hausdorff.haus IsHausdorff.hausₓ'. -/
 theorem IsHausdorff.haus (h : IsHausdorff I M) :
     ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0 :=
   IsHausdorff.haus'
 #align is_Hausdorff.haus IsHausdorff.haus
 
+/- warning: is_Hausdorff_iff -> isHausdorff_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_Hausdorff_iff isHausdorff_iffₓ'. -/
 theorem isHausdorff_iff :
     IsHausdorff I M ↔ ∀ x : M, (∀ n : ℕ, x ≡ 0 [SMOD (I ^ n • ⊤ : Submodule R M)]) → x = 0 :=
   ⟨IsHausdorff.haus, fun h => ⟨h⟩⟩
 #align is_Hausdorff_iff isHausdorff_iff
 
+/- warning: is_precomplete.prec -> IsPrecomplete.prec is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsPrecomplete.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (forall {f : Nat -> M}, (forall {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (SModEq.{u2, u1} R (CommRing.toRing.{u2} R _inst_1) M _inst_2 _inst_3 (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, 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(Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (f n) L)))
+Case conversion may be inaccurate. Consider using '#align is_precomplete.prec IsPrecomplete.precₓ'. -/
 theorem IsPrecomplete.prec (h : IsPrecomplete I M) {f : ℕ → M} :
     (∀ {m n}, m ≤ n → f m ≡ f n [SMOD (I ^ m • ⊤ : Submodule R M)]) →
       ∃ L : M, ∀ n, f n ≡ L [SMOD (I ^ n • ⊤ : Submodule R M)] :=
   IsPrecomplete.prec' _
 #align is_precomplete.prec IsPrecomplete.prec
 
+/- warning: is_precomplete_iff -> isPrecomplete_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], Iff (IsPrecomplete.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (forall (f : Nat -> M), (forall {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (SModEq.{u1, u2} R (CommRing.toRing.{u1} R _inst_1) M _inst_2 _inst_3 (SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I m) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (f m) (f n))) -> (Exists.{succ u2} M (fun (L : M) => forall (n : Nat), SModEq.{u1, u2} R (CommRing.toRing.{u1} R _inst_1) M _inst_2 _inst_3 (SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (f n) L)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (IsPrecomplete.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (forall (f : Nat -> M), (forall {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (SModEq.{u2, u1} R (CommRing.toRing.{u2} R _inst_1) M _inst_2 _inst_3 (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, 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R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (f n) L)))
+Case conversion may be inaccurate. Consider using '#align is_precomplete_iff isPrecomplete_iffₓ'. -/
 theorem isPrecomplete_iff :
     IsPrecomplete I M ↔
       ∀ f : ℕ → M,
@@ -84,12 +114,15 @@ theorem isPrecomplete_iff :
 
 variable (I M)
 
+#print Hausdorffification /-
 /-- The Hausdorffification of a module with respect to an ideal. -/
 @[reducible]
 def Hausdorffification : Type _ :=
   M ⧸ (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M)
 #align Hausdorffification Hausdorffification
+-/
 
+#print adicCompletion /-
 /-- The completion of a module with respect to an ideal. This is not necessarily Hausdorff.
 In fact, this is only complete if the ideal is finitely generated. -/
 def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule R M))
@@ -108,15 +141,28 @@ def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule
     rw [Pi.add_apply, Pi.add_apply, LinearMap.map_add, hf hmn, hg hmn]
   smul_mem' c f hf m n hmn := by rw [Pi.smul_apply, Pi.smul_apply, LinearMap.map_smul, hf hmn]
 #align adic_completion adicCompletion
+-/
 
 namespace IsHausdorff
 
+/- warning: is_Hausdorff.bot -> IsHausdorff.bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsHausdorff.{u1, u2} R _inst_1 (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) M _inst_2 _inst_3
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsHausdorff.{u1, u2} R _inst_1 (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M _inst_2 _inst_3
+Case conversion may be inaccurate. Consider using '#align is_Hausdorff.bot IsHausdorff.botₓ'. -/
 instance bot : IsHausdorff (⊥ : Ideal R) M :=
   ⟨fun x hx => by simpa only [pow_one ⊥, bot_smul, SModEq.bot] using hx 1⟩
 #align is_Hausdorff.bot IsHausdorff.bot
 
 variable {M}
 
+/- warning: is_Hausdorff.subsingleton -> IsHausdorff.subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsHausdorff.{u1, u2} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) M _inst_2 _inst_3) -> (Subsingleton.{succ u2} M)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsHausdorff.{u2, u1} R _inst_1 (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instTopSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M _inst_2 _inst_3) -> (Subsingleton.{succ u1} M)
+Case conversion may be inaccurate. Consider using '#align is_Hausdorff.subsingleton IsHausdorff.subsingletonₓ'. -/
 protected theorem subsingleton (h : IsHausdorff (⊤ : Ideal R) M) : Subsingleton M :=
   ⟨fun x y =>
     eq_of_sub_eq_zero <|
@@ -127,12 +173,20 @@ protected theorem subsingleton (h : IsHausdorff (⊤ : Ideal R) M) : Subsingleto
 
 variable (M)
 
+#print IsHausdorff.of_subsingleton /-
 instance (priority := 100) of_subsingleton [Subsingleton M] : IsHausdorff I M :=
   ⟨fun x _ => Subsingleton.elim _ _⟩
 #align is_Hausdorff.of_subsingleton IsHausdorff.of_subsingleton
+-/
 
 variable {I M}
 
+/- warning: is_Hausdorff.infi_pow_smul -> IsHausdorff.iInf_pow_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsHausdorff.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsHausdorff.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (Bot.bot.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align is_Hausdorff.infi_pow_smul IsHausdorff.iInf_pow_smulₓ'. -/
 theorem iInf_pow_smul (h : IsHausdorff I M) : (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) = ⊥ :=
   eq_bot_iff.2 fun x hx =>
     (mem_bot _).2 <| h.haus x fun n => SModEq.zero.2 <| (mem_iInf fun n : ℕ => I ^ n • ⊤).1 hx n
@@ -142,13 +196,21 @@ end IsHausdorff
 
 namespace Hausdorffification
 
+#print Hausdorffification.of /-
 /-- The canonical linear map to the Hausdorffification. -/
 def of : M →ₗ[R] Hausdorffification I M :=
   mkQ _
 #align Hausdorffification.of Hausdorffification.of
+-/
 
 variable {I M}
 
+/- warning: Hausdorffification.induction_on -> Hausdorffification.induction_on is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {C : (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> Prop} (x : Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3), (forall (x : M), C (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => M -> (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.of.{u1, u2} R _inst_1 I M _inst_2 _inst_3) x)) -> (C x)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {C : (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> Prop} (x : Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3), (forall (x : M), C (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (Hausdorffification.{u2, u1} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 (iInf.{u1, 1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} 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+Case conversion may be inaccurate. Consider using '#align Hausdorffification.induction_on Hausdorffification.induction_onₓ'. -/
 @[elab_as_elim]
 theorem induction_on {C : Hausdorffification I M → Prop} (x : Hausdorffification I M)
     (ih : ∀ x, C (of I M x)) : C x :=
@@ -172,6 +234,7 @@ variable {M} [h : IsHausdorff I N]
 
 include h
 
+#print Hausdorffification.lift /-
 /-- universal property of Hausdorffification: any linear map to a Hausdorff module extends to a
 unique map from the Hausdorffification. -/
 def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
@@ -184,15 +247,34 @@ def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
             rw [map_smul'']
             exact smul_mono le_rfl le_top
 #align Hausdorffification.lift Hausdorffification.lift
+-/
 
+/- warning: Hausdorffification.lift_of -> Hausdorffification.lift_of is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R 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(CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) => (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.lift.{u1, u2, u3} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => M -> (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Hausdorffification.of.{u1, u2} R _inst_1 I M _inst_2 _inst_3) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f x)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u1}} [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [h : IsHausdorff.{u3, u1} R _inst_1 I N _inst_4 _inst_5] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) a) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u2} R R M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) 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_inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (fun (_x : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Hausdorffification.lift.{u3, u2, u1} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) _inst_3 (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) M (fun (_x : M) => (fun 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+Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_of Hausdorffification.lift_ofₓ'. -/
 theorem lift_of (f : M →ₗ[R] N) (x : M) : lift I f (of I M x) = f x :=
   rfl
 #align Hausdorffification.lift_of Hausdorffification.lift_of
 
+/- warning: Hausdorffification.lift_comp_of -> Hausdorffification.lift_comp_of is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_ofₓ'. -/
 theorem lift_comp_of (f : M →ₗ[R] N) : (lift I f).comp (of I M) = f :=
   LinearMap.ext fun _ => rfl
 #align Hausdorffification.lift_comp_of Hausdorffification.lift_comp_of
 
+/- warning: Hausdorffification.lift_eq -> Hausdorffification.lift_eq is a dubious translation:
+lean 3 declaration is
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(Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) g (Hausdorffification.of.{u1, u2} R _inst_1 I M _inst_2 _inst_3)) f) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_4) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => SMul.smul.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5) g (Hausdorffification.lift.{u1, u2, u3} R _inst_1 I M _inst_2 _inst_3 N _inst_4 _inst_5 h f))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u1}} [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [h : IsHausdorff.{u3, u1} R _inst_1 I N _inst_4 _inst_5] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) N (AddCommGroup.toAddCommMonoid.{u2} (Hausdorffification.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 (iInf.{u2, 1} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instInfSetSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Nat (fun (n : Nat) => HSMul.hSMul.{u3, u2, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (instHSMul.{u3, u2} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HPow.hPow.{u3, 0, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instHPow.{u3, 0} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) Nat (Monoid.Pow.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toMonoidWithZero.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemSemiring.toSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Submodule.idemSemiring.{u3, u3} R (CommRing.toCommSemiring.{u3} R _inst_1) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) I n) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomCompTriple.ids.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) g (Hausdorffification.of.{u3, u2} R _inst_1 I M _inst_2 _inst_3)) f) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R 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+Case conversion may be inaccurate. Consider using '#align Hausdorffification.lift_eq Hausdorffification.lift_eqₓ'. -/
 /-- Uniqueness of lift. -/
 theorem lift_eq (f : M →ₗ[R] N) (g : Hausdorffification I M →ₗ[R] N) (hg : g.comp (of I M) = f) :
     g = lift I f :=
@@ -203,6 +285,12 @@ end Hausdorffification
 
 namespace IsPrecomplete
 
+/- warning: is_precomplete.bot -> IsPrecomplete.bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsPrecomplete.{u1, u2} R _inst_1 (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) M _inst_2 _inst_3
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsPrecomplete.{u1, u2} R _inst_1 (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M _inst_2 _inst_3
+Case conversion may be inaccurate. Consider using '#align is_precomplete.bot IsPrecomplete.botₓ'. -/
 instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   by
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
@@ -212,6 +300,12 @@ instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   rw [pow_one, bot_smul, SModEq.bot] at hf; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
 
+/- warning: is_precomplete.top -> IsPrecomplete.top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsPrecomplete.{u1, u2} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) M _inst_2 _inst_3
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsPrecomplete.{u1, u2} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M _inst_2 _inst_3
+Case conversion may be inaccurate. Consider using '#align is_precomplete.top IsPrecomplete.topₓ'. -/
 instance top : IsPrecomplete (⊤ : Ideal R) M :=
   ⟨fun f hf =>
     ⟨0, fun n => by
@@ -219,14 +313,17 @@ instance top : IsPrecomplete (⊤ : Ideal R) M :=
       exact SModEq.top⟩⟩
 #align is_precomplete.top IsPrecomplete.top
 
+#print IsPrecomplete.of_subsingleton /-
 instance (priority := 100) of_subsingleton [Subsingleton M] : IsPrecomplete I M :=
   ⟨fun f hf => ⟨0, fun n => by rw [Subsingleton.elim (f n) 0]⟩⟩
 #align is_precomplete.of_subsingleton IsPrecomplete.of_subsingleton
+-/
 
 end IsPrecomplete
 
 namespace adicCompletion
 
+#print adicCompletion.of /-
 /-- The canonical linear map to the completion. -/
 def of : M →ₗ[R] adicCompletion I M
     where
@@ -234,12 +331,16 @@ def of : M →ₗ[R] adicCompletion I M
   map_add' x y := rfl
   map_smul' c x := rfl
 #align adic_completion.of adicCompletion.of
+-/
 
+#print adicCompletion.of_apply /-
 @[simp]
 theorem of_apply (x : M) (n : ℕ) : (of I M x).1 n = mkQ _ x :=
   rfl
 #align adic_completion.of_apply adicCompletion.of_apply
+-/
 
+#print adicCompletion.eval /-
 /-- Linearly evaluating a sequence in the completion at a given input. -/
 def eval (n : ℕ) : adicCompletion I M →ₗ[R] M ⧸ (I ^ n • ⊤ : Submodule R M)
     where
@@ -247,37 +348,50 @@ def eval (n : ℕ) : adicCompletion I M →ₗ[R] M ⧸ (I ^ n • ⊤ : Submodu
   map_add' f g := rfl
   map_smul' c f := rfl
 #align adic_completion.eval adicCompletion.eval
+-/
 
+#print adicCompletion.coe_eval /-
 @[simp]
 theorem coe_eval (n : ℕ) :
     (eval I M n : adicCompletion I M → M ⧸ (I ^ n • ⊤ : Submodule R M)) = fun f => f.1 n :=
   rfl
 #align adic_completion.coe_eval adicCompletion.coe_eval
+-/
 
+#print adicCompletion.eval_apply /-
 theorem eval_apply (n : ℕ) (f : adicCompletion I M) : eval I M n f = f.1 n :=
   rfl
 #align adic_completion.eval_apply adicCompletion.eval_apply
+-/
 
+#print adicCompletion.eval_of /-
 theorem eval_of (n : ℕ) (x : M) : eval I M n (of I M x) = mkQ _ x :=
   rfl
 #align adic_completion.eval_of adicCompletion.eval_of
+-/
 
+#print adicCompletion.eval_comp_of /-
 @[simp]
 theorem eval_comp_of (n : ℕ) : (eval I M n).comp (of I M) = mkQ _ :=
   rfl
 #align adic_completion.eval_comp_of adicCompletion.eval_comp_of
+-/
 
+#print adicCompletion.range_eval /-
 @[simp]
 theorem range_eval (n : ℕ) : (eval I M n).range = ⊤ :=
   LinearMap.range_eq_top.2 fun x => Quotient.inductionOn' x fun x => ⟨of I M x, rfl⟩
 #align adic_completion.range_eval adicCompletion.range_eval
+-/
 
 variable {I M}
 
+#print adicCompletion.ext /-
 @[ext]
 theorem ext {x y : adicCompletion I M} (h : ∀ n, eval I M n x = eval I M n y) : x = y :=
   Subtype.eq <| funext h
 #align adic_completion.ext adicCompletion.ext
+-/
 
 variable (I M)
 
@@ -294,20 +408,40 @@ end adicCompletion
 
 namespace IsAdicComplete
 
+/- warning: is_adic_complete.bot -> IsAdicComplete.bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsAdicComplete.{u1, u2} R _inst_1 (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) M _inst_2 _inst_3
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], IsAdicComplete.{u1, u2} R _inst_1 (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M _inst_2 _inst_3
+Case conversion may be inaccurate. Consider using '#align is_adic_complete.bot IsAdicComplete.botₓ'. -/
 instance bot : IsAdicComplete (⊥ : Ideal R) M where
 #align is_adic_complete.bot IsAdicComplete.bot
 
+/- warning: is_adic_complete.subsingleton -> IsAdicComplete.subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAdicComplete.{u1, u2} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) M _inst_2 _inst_3) -> (Subsingleton.{succ u2} M)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAdicComplete.{u2, u1} R _inst_1 (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instTopSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M _inst_2 _inst_3) -> (Subsingleton.{succ u1} M)
+Case conversion may be inaccurate. Consider using '#align is_adic_complete.subsingleton IsAdicComplete.subsingletonₓ'. -/
 protected theorem subsingleton (h : IsAdicComplete (⊤ : Ideal R) M) : Subsingleton M :=
   h.1.Subsingleton
 #align is_adic_complete.subsingleton IsAdicComplete.subsingleton
 
+#print IsAdicComplete.of_subsingleton /-
 instance (priority := 100) of_subsingleton [Subsingleton M] : IsAdicComplete I M where
 #align is_adic_complete.of_subsingleton IsAdicComplete.of_subsingleton
+-/
 
 open BigOperators
 
 open Finset
 
+/- warning: is_adic_complete.le_jacobson_bot -> IsAdicComplete.le_jacobson_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_6 : IsAdicComplete.{u1, u1} R _inst_1 I R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))], LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) I (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) [_inst_6 : IsAdicComplete.{u1, u1} R _inst_1 I R (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))], LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align is_adic_complete.le_jacobson_bot IsAdicComplete.le_jacobson_botₓ'. -/
 theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
   by
   intro x hx

2bbc7e38

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -133,10 +133,10 @@ instance (priority := 100) of_subsingleton [Subsingleton M] : IsHausdorff I M :=
 
 variable {I M}
 
-theorem infᵢ_pow_smul (h : IsHausdorff I M) : (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) = ⊥ :=
+theorem iInf_pow_smul (h : IsHausdorff I M) : (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) = ⊥ :=
   eq_bot_iff.2 fun x hx =>
-    (mem_bot _).2 <| h.haus x fun n => SModEq.zero.2 <| (mem_infᵢ fun n : ℕ => I ^ n • ⊤).1 hx n
-#align is_Hausdorff.infi_pow_smul IsHausdorff.infᵢ_pow_smul
+    (mem_bot _).2 <| h.haus x fun n => SModEq.zero.2 <| (mem_iInf fun n : ℕ => I ^ n • ⊤).1 hx n
+#align is_Hausdorff.infi_pow_smul IsHausdorff.iInf_pow_smul
 
 end IsHausdorff
 
@@ -161,10 +161,10 @@ instance : IsHausdorff I (Hausdorffification I M) :=
   ⟨fun x =>
     Quotient.inductionOn' x fun x hx =>
       (Quotient.mk_eq_zero _).2 <|
-        (mem_infᵢ _).2 fun n =>
+        (mem_iInf _).2 fun n =>
           by
           have := comap_map_mkq (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) (I ^ n • ⊤)
-          simp only [sup_of_le_right (infᵢ_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this
+          simp only [sup_of_le_right (iInf_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this
           rw [← this, map_smul'', mem_comap, Submodule.map_top, range_mkq, ← SModEq.zero];
           exact hx n⟩
 
@@ -177,9 +177,9 @@ unique map from the Hausdorffification. -/
 def lift (f : M →ₗ[R] N) : Hausdorffification I M →ₗ[R] N :=
   liftQ _ f <|
     map_le_iff_le_comap.1 <|
-      h.infᵢ_pow_smul ▸
-        le_infᵢ fun n =>
-          le_trans (map_mono <| infᵢ_le _ n) <|
+      h.iInf_pow_smul ▸
+        le_iInf fun n =>
+          le_trans (map_mono <| iInf_le _ n) <|
             by
             rw [map_smul'']
             exact smul_mono le_rfl le_top

2bbc7e38

bump to nightly-2023-03-13-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

66e1e587

Diff

@@ -112,7 +112,7 @@ def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule
 namespace IsHausdorff
 
 instance bot : IsHausdorff (⊥ : Ideal R) M :=
-  ⟨fun x hx => by simpa only [pow_one ⊥, bot_smul, Smodeq.bot] using hx 1⟩
+  ⟨fun x hx => by simpa only [pow_one ⊥, bot_smul, SModEq.bot] using hx 1⟩
 #align is_Hausdorff.bot IsHausdorff.bot
 
 variable {M}
@@ -122,7 +122,7 @@ protected theorem subsingleton (h : IsHausdorff (⊤ : Ideal R) M) : Subsingleto
     eq_of_sub_eq_zero <|
       h.haus (x - y) fun n => by
         rw [Ideal.top_pow, top_smul]
-        exact Smodeq.top⟩
+        exact SModEq.top⟩
 #align is_Hausdorff.subsingleton IsHausdorff.subsingleton
 
 variable (M)
@@ -135,7 +135,7 @@ variable {I M}
 
 theorem infᵢ_pow_smul (h : IsHausdorff I M) : (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) = ⊥ :=
   eq_bot_iff.2 fun x hx =>
-    (mem_bot _).2 <| h.haus x fun n => Smodeq.zero.2 <| (mem_infᵢ fun n : ℕ => I ^ n • ⊤).1 hx n
+    (mem_bot _).2 <| h.haus x fun n => SModEq.zero.2 <| (mem_infᵢ fun n : ℕ => I ^ n • ⊤).1 hx n
 #align is_Hausdorff.infi_pow_smul IsHausdorff.infᵢ_pow_smul
 
 end IsHausdorff
@@ -165,7 +165,7 @@ instance : IsHausdorff I (Hausdorffification I M) :=
           by
           have := comap_map_mkq (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M) (I ^ n • ⊤)
           simp only [sup_of_le_right (infᵢ_le (fun n => (I ^ n • ⊤ : Submodule R M)) n)] at this
-          rw [← this, map_smul'', mem_comap, Submodule.map_top, range_mkq, ← Smodeq.zero];
+          rw [← this, map_smul'', mem_comap, Submodule.map_top, range_mkq, ← SModEq.zero];
           exact hx n⟩
 
 variable {M} [h : IsHausdorff I N]
@@ -207,16 +207,16 @@ instance bot : IsPrecomplete (⊥ : Ideal R) M :=
   by
   refine' ⟨fun f hf => ⟨f 1, fun n => _⟩⟩; cases n
   · rw [pow_zero, Ideal.one_eq_top, top_smul]
-    exact Smodeq.top
+    exact SModEq.top
   specialize hf (Nat.le_add_left 1 n)
-  rw [pow_one, bot_smul, Smodeq.bot] at hf; rw [hf]
+  rw [pow_one, bot_smul, SModEq.bot] at hf; rw [hf]
 #align is_precomplete.bot IsPrecomplete.bot
 
 instance top : IsPrecomplete (⊤ : Ideal R) M :=
   ⟨fun f hf =>
     ⟨0, fun n => by
       rw [Ideal.top_pow, top_smul]
-      exact Smodeq.top⟩⟩
+      exact SModEq.top⟩⟩
 #align is_precomplete.top IsPrecomplete.top
 
 instance (priority := 100) of_subsingleton [Subsingleton M] : IsPrecomplete I M :=
@@ -284,10 +284,10 @@ variable (I M)
 instance : IsHausdorff I (adicCompletion I M) :=
   ⟨fun x hx =>
     ext fun n =>
-      smul_induction_on (Smodeq.zero.1 <| hx n)
+      smul_induction_on (SModEq.zero.1 <| hx n)
         (fun r hr x _ =>
           ((eval I M n).map_smul r x).symm ▸
-            Quotient.inductionOn' (eval I M n x) fun x => Smodeq.zero.2 <| smul_mem_smul hr mem_top)
+            Quotient.inductionOn' (eval I M n x) fun x => SModEq.zero.2 <| smul_mem_smul hr mem_top)
         fun _ _ ih1 ih2 => by rw [LinearMap.map_add, ih1, ih2, LinearMap.map_zero, add_zero]⟩
 
 end adicCompletion
@@ -318,7 +318,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
   have hf : ∀ m n, m ≤ n → f m ≡ f n [SMOD I ^ m • (⊤ : Submodule R R)] :=
     by
     intro m n h
-    simp only [f, Algebra.id.smul_eq_mul, Ideal.mul_top, Smodeq.sub_mem]
+    simp only [f, Algebra.id.smul_eq_mul, Ideal.mul_top, SModEq.sub_mem]
     rw [← add_tsub_cancel_of_le h, Finset.sum_range_add, ← sub_sub, sub_self, zero_sub, neg_mem_iff]
     apply Submodule.sum_mem
     intro n hn
@@ -331,7 +331,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
     apply IsHausdorff.haus (to_is_Hausdorff : IsHausdorff I R)
     intro n
     specialize hL n
-    rw [Smodeq.sub_mem, Algebra.id.smul_eq_mul, Ideal.mul_top] at hL⊢
+    rw [SModEq.sub_mem, Algebra.id.smul_eq_mul, Ideal.mul_top] at hL⊢
     rw [sub_zero]
     suffices (1 - x * y) * f n - 1 ∈ I ^ n
       by

2bbc7e38

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

2bbc7e38

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -31,9 +31,7 @@ with respect to an ideal `I`:
 open Submodule
 
 variable {R : Type*} [CommRing R] (I : Ideal R)
-
 variable (M : Type*) [AddCommGroup M] [Module R M]
-
 variable {N : Type*} [AddCommGroup N] [Module R N]
 
 /-- A module `M` is Hausdorff with respect to an ideal `I` if `⋂ I^n M = 0`. -/

2bbc7e38

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -289,7 +289,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
   let f : ℕ → R := fun n => ∑ i in range n, (x * y) ^ i
   have hf : ∀ m n, m ≤ n → f m ≡ f n [SMOD I ^ m • (⊤ : Submodule R R)] := by
     intro m n h
-    simp only [Algebra.id.smul_eq_mul, Ideal.mul_top, SModEq.sub_mem]
+    simp only [f, Algebra.id.smul_eq_mul, Ideal.mul_top, SModEq.sub_mem]
     rw [← add_tsub_cancel_of_le h, Finset.sum_range_add, ← sub_sub, sub_self, zero_sub,
       @neg_mem_iff]
     apply Submodule.sum_mem

2bbc7e38

chore: Rename pow monotonicity lemmas (#9095)

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

`Algebra.GroupPower.Order`

pow_mono → pow_right_mono
pow_le_pow → pow_le_pow_right
pow_le_pow_of_le_left → pow_le_pow_left
pow_lt_pow_of_lt_left → pow_lt_pow_left
strictMonoOn_pow → pow_left_strictMonoOn
pow_strictMono_right → pow_right_strictMono
pow_lt_pow → pow_lt_pow_right
pow_lt_pow_iff → pow_lt_pow_iff_right
pow_le_pow_iff → pow_le_pow_iff_right
self_lt_pow → lt_self_pow
strictAnti_pow → pow_right_strictAnti
pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
le_of_pow_le_pow → le_of_pow_le_pow_left
pow_lt_pow₀ → pow_lt_pow_right₀

`Algebra.GroupPower.CovariantClass`

pow_le_pow_of_le_left' → pow_le_pow_left'
nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
pow_lt_pow' → pow_lt_pow_right'
nsmul_lt_nsmul → nsmul_lt_nsmul_left
pow_strictMono_left → pow_right_strictMono'
nsmul_strictMono_right → nsmul_left_strictMono
StrictMono.pow_right' → StrictMono.pow_const
StrictMono.nsmul_left → StrictMono.const_nsmul
pow_strictMono_right' → pow_left_strictMono
nsmul_strictMono_left → nsmul_right_strictMono
Monotone.pow_right → Monotone.pow_const
Monotone.nsmul_left → Monotone.const_nsmul
lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
pow_le_pow' → pow_le_pow_right'
nsmul_le_nsmul → nsmul_le_nsmul_left
pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow' → le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
pow_le_pow_iff' → pow_le_pow_iff_right'
nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
pow_lt_pow_iff' → pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

`Data.Nat.Pow`

Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

self_le_pow was a duplicate of le_self_pow.
Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
Nat.pow_right_strictMono is defeq to pow_right_strictMono.
Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

A bunch of proofs have been golfed.
Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
A few Nat lemmas have been protected.
One docstring has been fixed.

d61c95e1

Diff

@@ -90,7 +90,7 @@ In fact, this is only complete if the ideal is finitely generated. -/
 def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule R M)) where
   carrier := { f | ∀ {m n} (h : m ≤ n), liftQ _ (mkQ _) (by
       rw [ker_mkQ]
-      exact smul_mono (Ideal.pow_le_pow h) le_rfl)
+      exact smul_mono (Ideal.pow_le_pow_right h) le_rfl)
     (f n) = f m }
   zero_mem' hmn := by rw [Pi.zero_apply, Pi.zero_apply, LinearMap.map_zero]
   add_mem' hf hg m n hmn := by

2bbc7e38

chore: removing unneeded maxHeartbeats (#7761)

Due to recent changes in core we can reduce or remove many set_option maxHeartbeats statements.

I have tried to be careful to not leave anything too close to the line, so don't be surprised if some of these can still be reduced further.

This reduces us from 96 maxHeartbeats statements to 44. (There are 10 false positives in meta or testing code.)

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

ae7ec61a

Diff

@@ -212,7 +212,6 @@ def of : M →ₗ[R] adicCompletion I M where
   map_smul' _ _ := rfl
 #align adic_completion.of adicCompletion.of
 
-set_option maxHeartbeats 300000 in
 @[simp]
 theorem of_apply (x : M) (n : ℕ) : (of I M x).1 n = mkQ _ x :=
   rfl
@@ -235,7 +234,6 @@ theorem eval_apply (n : ℕ) (f : adicCompletion I M) : eval I M n f = f.1 n :=
   rfl
 #align adic_completion.eval_apply adicCompletion.eval_apply
 
-set_option maxHeartbeats 300000 in
 theorem eval_of (n : ℕ) (x : M) : eval I M n (of I M x) = mkQ _ x :=
   rfl
 #align adic_completion.eval_of adicCompletion.eval_of

2bbc7e38

chore: update/remove heart beat bumps (#6860)

We clean up heart beat bumps after #6474.

c95f05bd

Diff

@@ -85,7 +85,6 @@ def Hausdorffification : Type _ :=
   M ⧸ (⨅ n : ℕ, I ^ n • ⊤ : Submodule R M)
 #align Hausdorffification Hausdorffification
 
-set_option maxHeartbeats 700000 in
 /-- The completion of a module with respect to an ideal. This is not necessarily Hausdorff.
 In fact, this is only complete if the ideal is finitely generated. -/
 def adicCompletion : Submodule R (∀ n : ℕ, M ⧸ (I ^ n • ⊤ : Submodule R M)) where
@@ -213,7 +212,7 @@ def of : M →ₗ[R] adicCompletion I M where
   map_smul' _ _ := rfl
 #align adic_completion.of adicCompletion.of
 
-set_option maxHeartbeats 700000 in
+set_option maxHeartbeats 300000 in
 @[simp]
 theorem of_apply (x : M) (n : ℕ) : (of I M x).1 n = mkQ _ x :=
   rfl
@@ -236,7 +235,7 @@ theorem eval_apply (n : ℕ) (f : adicCompletion I M) : eval I M n f = f.1 n :=
   rfl
 #align adic_completion.eval_apply adicCompletion.eval_apply
 
-set_option maxHeartbeats 700000 in
+set_option maxHeartbeats 300000 in
 theorem eval_of (n : ℕ) (x : M) : eval I M n (of I M x) = mkQ _ x :=
   rfl
 #align adic_completion.eval_of adicCompletion.eval_of

2bbc7e38

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -30,11 +30,11 @@ with respect to an ideal `I`:
 
 open Submodule
 
-variable {R : Type _} [CommRing R] (I : Ideal R)
+variable {R : Type*} [CommRing R] (I : Ideal R)
 
-variable (M : Type _) [AddCommGroup M] [Module R M]
+variable (M : Type*) [AddCommGroup M] [Module R M]
 
-variable {N : Type _} [AddCommGroup N] [Module R N]
+variable {N : Type*} [AddCommGroup N] [Module R N]
 
 /-- A module `M` is Hausdorff with respect to an ideal `I` if `⋂ I^n M = 0`. -/
 class IsHausdorff : Prop where

2bbc7e38

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module linear_algebra.adic_completion
-! leanprover-community/mathlib commit 2bbc7e3884ba234309d2a43b19144105a753292e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GeomSum
 import Mathlib.LinearAlgebra.SModEq
 import Mathlib.RingTheory.JacobsonIdeal
 
+#align_import linear_algebra.adic_completion from "leanprover-community/mathlib"@"2bbc7e3884ba234309d2a43b19144105a753292e"
+
 /-!
 # Completion of a module with respect to an ideal.

2bbc7e38

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -309,7 +309,7 @@ theorem le_jacobson_bot [IsAdicComplete I R] : I ≤ (⊥ : Ideal R).jacobson :=
     apply IsHausdorff.haus (toIsHausdorff : IsHausdorff I R)
     intro n
     specialize hL n
-    rw [SModEq.sub_mem, Algebra.id.smul_eq_mul, Ideal.mul_top] at hL⊢
+    rw [SModEq.sub_mem, Algebra.id.smul_eq_mul, Ideal.mul_top] at hL ⊢
     rw [sub_zero]
     suffices (1 - x * y) * f n - 1 ∈ I ^ n by
       convert Ideal.sub_mem _ this (Ideal.mul_mem_left _ (1 + -(x * y)) hL) using 1

2bbc7e38

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -24,7 +24,7 @@ with respect to an ideal `I`:
 - `IsPrecomplete I M`: this says that every Cauchy sequence converges.
 - `IsAdicComplete I M`: this says that `M` is Hausdorff and precomplete.
 - `Hausdorffification I M`: this is the universal Hausdorff module with a map from `M`.
-- `adicCcompletion I M`: if `I` is finitely generated, then this is the universal complete module
+- `adicCompletion I M`: if `I` is finitely generated, then this is the universal complete module
   (TODO) with a map from `M`. This map is injective iff `M` is Hausdorff and surjective iff `M` is
   precomplete.

2bbc7e38

feat: port LinearAlgebra.AdicCompletion (#4133)

7c8c9643

`linear_algebra.adic_completion` ⟷ `Mathlib.LinearAlgebra.AdicCompletion`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`

Lemmas added

Lemmas removed

Other changes

Dependencies 8 + 542

linear_algebra.adic_completion ⟷ Mathlib.LinearAlgebra.AdicCompletion

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Algebra.GroupPower.Order

Algebra.GroupPower.CovariantClass

Data.Nat.Pow

Lemmas added

Lemmas removed

Other changes

Dependencies 8 + 542

`linear_algebra.adic_completion` ⟷ `Mathlib.LinearAlgebra.AdicCompletion`

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`