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

@@ -121,7 +121,7 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
   by
   letI := I.adic_topology
   have := I.has_basis_nhds_zero_adic.map fun y => x + y
-  rwa [map_add_left_nhds_zero x] at this 
+  rwa [map_add_left_nhds_zero x] at this
 #align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adic
 -/
 
@@ -186,7 +186,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
   by
   constructor
   · intro H
-    change _ = _ at H 
+    change _ = _ at H
     rw [H]
     letI := J.adic_topology
     constructor

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

@@ -60,7 +60,7 @@ theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n •
   { inter := by
       suffices ∀ i j : ℕ, ∃ k, I ^ k ≤ I ^ i ∧ I ^ k ≤ I ^ j by simpa
       intro i j
-      exact ⟨max i j, pow_le_pow (le_max_left i j), pow_le_pow (le_max_right i j)⟩
+      exact ⟨max i j, pow_le_pow_right (le_max_left i j), pow_le_pow_right (le_max_right i j)⟩
     leftMul := by
       suffices ∀ (a : R) (i : ℕ), ∃ j : ℕ, a • I ^ j ≤ I ^ i by simpa
       intro r n

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

@@ -236,7 +236,7 @@ theorem is_bot_adic_iff {A : Type _} [CommRing A] [TopologicalSpace A] [Topologi
   rw [isAdic_iff]
   constructor
   · rintro ⟨h, h'⟩
-    rw [discreteTopology_iff_open_singleton_zero]
+    rw [discreteTopology_iff_isOpen_singleton_zero]
     simpa using h 1
   · intros
     constructor

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 -/
-import Mathbin.RingTheory.Ideal.Operations
-import Mathbin.Topology.Algebra.Nonarchimedean.Bases
-import Mathbin.Topology.UniformSpace.Completion
-import Mathbin.Topology.Algebra.UniformRing
+import RingTheory.Ideal.Operations
+import Topology.Algebra.Nonarchimedean.Bases
+import Topology.UniformSpace.Completion
+import Topology.Algebra.UniformRing
 
 #align_import topology.algebra.nonarchimedean.adic_topology from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module topology.algebra.nonarchimedean.adic_topology
-! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Ideal.Operations
 import Mathbin.Topology.Algebra.Nonarchimedean.Bases
 import Mathbin.Topology.UniformSpace.Completion
 import Mathbin.Topology.Algebra.UniformRing
 
+#align_import topology.algebra.nonarchimedean.adic_topology from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
+
 /-!
 # Adic topology
 

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

@@ -100,6 +100,7 @@ theorem nonarchimedean (I : Ideal R) : @NonarchimedeanRing R _ I.adicTopology :=
 #align ideal.nonarchimedean Ideal.nonarchimedean
 -/
 
+#print Ideal.hasBasis_nhds_zero_adic /-
 /-- For the `I`-adic topology, the neighborhoods of zero has basis given by the powers of `I`. -/
 theorem hasBasis_nhds_zero_adic (I : Ideal R) :
     HasBasis (@nhds R I.adicTopology (0 : R)) (fun n : ℕ => True) fun n =>
@@ -114,7 +115,9 @@ theorem hasBasis_nhds_zero_adic (I : Ideal R) :
     · rintro ⟨i, -, h⟩
       exact ⟨(I ^ i : Ideal R), ⟨i, by simp⟩, h⟩⟩
 #align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adic
+-/
 
+#print Ideal.hasBasis_nhds_adic /-
 theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
     HasBasis (@nhds R I.adicTopology x) (fun n : ℕ => True) fun n =>
       (fun y => x + y) '' (I ^ n : Ideal R) :=
@@ -123,9 +126,11 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
   have := I.has_basis_nhds_zero_adic.map fun y => x + y
   rwa [map_add_left_nhds_zero x] at this 
 #align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adic
+-/
 
 variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
 
+#print Ideal.adic_module_basis /-
 theorem adic_module_basis :
     I.RingFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=
   { inter := fun i j =>
@@ -139,6 +144,7 @@ theorem adic_module_basis :
         replace a_in : a ∈ I ^ i := by simpa [(I ^ i).mul_top] using a_in
         exact smul_mem_smul a_in mem_top⟩ }
 #align ideal.adic_module_basis Ideal.adic_module_basis
+-/
 
 #print Ideal.adicModuleTopology /-
 /-- The topology on a `R`-module `M` associated to an ideal `M`. Submodules $I^n M$,
@@ -149,6 +155,7 @@ def adicModuleTopology : TopologicalSpace M :=
 #align ideal.adic_module_topology Ideal.adicModuleTopology
 -/
 
+#print Ideal.openAddSubgroup /-
 /-- The elements of the basis of neighborhoods of zero for the `I`-adic topology
 on a `R`-module `M`, seen as open additive subgroups of `M`. -/
 def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology :=
@@ -158,6 +165,7 @@ def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology :=
       convert (I.adic_basis.to_ring_subgroups_basis.open_add_subgroup n).IsOpen
       simp }
 #align ideal.open_add_subgroup Ideal.openAddSubgroup
+-/
 
 end Ideal
 
@@ -171,6 +179,7 @@ def IsAdic [H : TopologicalSpace R] (J : Ideal R) : Prop :=
 #align is_adic IsAdic
 -/
 
+#print isAdic_iff /-
 /-- A topological ring is `J`-adic if and only if it admits the powers of `J` as a basis of
 open neighborhoods of zero. -/
 theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R} :
@@ -202,6 +211,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
         rw [mem_nhds_iff]
         refine' ⟨_, hn, H₁ n, (J ^ n).zero_mem⟩
 #align is_adic_iff isAdic_iff
+-/
 
 variable [TopologicalSpace R] [TopologicalRing R]
 

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

@@ -155,7 +155,7 @@ def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology :=
   { (I ^ n).toAddSubgroup with
     is_open' := by
       letI := I.adic_topology
-      convert(I.adic_basis.to_ring_subgroups_basis.open_add_subgroup n).IsOpen
+      convert (I.adic_basis.to_ring_subgroups_basis.open_add_subgroup n).IsOpen
       simp }
 #align ideal.open_add_subgroup Ideal.openAddSubgroup
 

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

@@ -121,7 +121,7 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
   by
   letI := I.adic_topology
   have := I.has_basis_nhds_zero_adic.map fun y => x + y
-  rwa [map_add_left_nhds_zero x] at this
+  rwa [map_add_left_nhds_zero x] at this 
 #align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adic
 
 variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
@@ -180,7 +180,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
   by
   constructor
   · intro H
-    change _ = _ at H
+    change _ = _ at H 
     rw [H]
     letI := J.adic_topology
     constructor
@@ -208,7 +208,7 @@ variable [TopologicalSpace R] [TopologicalRing R]
 #print is_ideal_adic_pow /-
 theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) : IsAdic (J ^ n) :=
   by
-  rw [isAdic_iff] at h⊢
+  rw [isAdic_iff] at h ⊢
   constructor
   · intro m; rw [← pow_mul]; apply h.left
   · intro V hV

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

@@ -54,7 +54,7 @@ variable {R : Type _} [CommRing R]
 
 open Set TopologicalAddGroup Submodule Filter
 
-open Topology Pointwise
+open scoped Topology Pointwise
 
 namespace Ideal
 

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

@@ -100,12 +100,6 @@ theorem nonarchimedean (I : Ideal R) : @NonarchimedeanRing R _ I.adicTopology :=
 #align ideal.nonarchimedean Ideal.nonarchimedean
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adicₓ'. -/
 /-- For the `I`-adic topology, the neighborhoods of zero has basis given by the powers of `I`. -/
 theorem hasBasis_nhds_zero_adic (I : Ideal R) :
     HasBasis (@nhds R I.adicTopology (0 : R)) (fun n : ℕ => True) fun n =>
@@ -121,12 +115,6 @@ theorem hasBasis_nhds_zero_adic (I : Ideal R) :
       exact ⟨(I ^ i : Ideal R), ⟨i, by simp⟩, h⟩⟩
 #align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adic
 
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-Case conversion may be inaccurate. Consider using '#align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adicₓ'. -/
 theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
     HasBasis (@nhds R I.adicTopology x) (fun n : ℕ => True) fun n =>
       (fun y => x + y) '' (I ^ n : Ideal R) :=
@@ -138,12 +126,6 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
 
 variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
 
-/- warning: ideal.adic_module_basis -> Ideal.adic_module_basis is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ideal.adic_module_basis Ideal.adic_module_basisₓ'. -/
 theorem adic_module_basis :
     I.RingFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=
   { inter := fun i j =>
@@ -167,12 +149,6 @@ def adicModuleTopology : TopologicalSpace M :=
 #align ideal.adic_module_topology Ideal.adicModuleTopology
 -/
 
-/- warning: ideal.open_add_subgroup -> Ideal.openAddSubgroup 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))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.adicTopology.{u1} R _inst_1 I))
-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))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.adicTopology.{u1} R _inst_1 I))
-Case conversion may be inaccurate. Consider using '#align ideal.open_add_subgroup Ideal.openAddSubgroupₓ'. -/
 /-- The elements of the basis of neighborhoods of zero for the `I`-adic topology
 on a `R`-module `M`, seen as open additive subgroups of `M`. -/
 def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology :=
@@ -195,12 +171,6 @@ def IsAdic [H : TopologicalSpace R] (J : Ideal R) : Prop :=
 #align is_adic IsAdic
 -/
 
-/- warning: is_adic_iff -> isAdic_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_adic_iff isAdic_iffₓ'. -/
 /-- A topological ring is `J`-adic if and only if it admits the powers of `J` as a basis of
 open neighborhoods of zero. -/
 theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R} :

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

@@ -240,16 +240,12 @@ theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) :
   by
   rw [isAdic_iff] at h⊢
   constructor
-  · intro m
-    rw [← pow_mul]
-    apply h.left
+  · intro m; rw [← pow_mul]; apply h.left
   · intro V hV
     cases' h.right V hV with m hm
     use m
     refine' Set.Subset.trans _ hm
-    cases n
-    · exfalso
-      exact Nat.not_succ_le_zero 0 hn
+    cases n; · exfalso; exact Nat.not_succ_le_zero 0 hn
     rw [← pow_mul, Nat.succ_mul]
     apply Ideal.pow_le_pow
     apply Nat.le_add_left

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.algebra.nonarchimedean.adic_topology
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.UniformRing
 /-!
 # Adic topology
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a commutative ring `R` and an ideal `I` in `R`, this file constructs the unique
 topology on `R` which is compatible with the ring structure and such that a set is a neighborhood
 of zero if and only if it contains a power of `I`. This topology is non-archimedean: every

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -137,9 +137,9 @@ variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
 
 /- warning: ideal.adic_module_basis -> Ideal.adic_module_basis 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)], RingFilterBasis.SubmodulesBasis.{0, u1, u2} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u1} R _inst_1 I) (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)))
+  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)], RingFilterBasis.SubmodulesBasis.{0, u1, u2} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u1} R _inst_1 I) (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)))
 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)], RingFilterBasis.SubmodulesBasis.{0, u2, u1} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u2} R _inst_1 I) (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)))
+  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)], RingFilterBasis.SubmodulesBasis.{0, u2, u1} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u2} R _inst_1 I) (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)))
 Case conversion may be inaccurate. Consider using '#align ideal.adic_module_basis Ideal.adic_module_basisₓ'. -/
 theorem adic_module_basis :
     I.RingFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=

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

@@ -101,7 +101,7 @@ theorem nonarchimedean (I : Ideal R) : @NonarchimedeanRing R _ I.adicTopology :=
 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))), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) (fun (n : Nat) => True) (fun (n : Nat) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (fun (n : Nat) => True) (fun (n : Nat) => SetLike.coe.{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)))) (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))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (fun (n : Nat) => True) (fun (n : Nat) => SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{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)))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n))
 Case conversion may be inaccurate. Consider using '#align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adicₓ'. -/
 /-- For the `I`-adic topology, the neighborhoods of zero has basis given by the powers of `I`. -/
 theorem hasBasis_nhds_zero_adic (I : Ideal R) :
@@ -122,7 +122,7 @@ theorem hasBasis_nhds_zero_adic (I : Ideal R) :
 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))) (x : R), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) x) (fun (n : Nat) => True) (fun (n : Nat) => Set.image.{u1, u1} R R (fun (y : R) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x y) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (x : R), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) x) (fun (n : Nat) => True) (fun (n : Nat) => Set.image.{u1, u1} R R (fun (y : R) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) (SetLike.coe.{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)))) (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)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (x : R), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) x) (fun (n : Nat) => True) (fun (n : Nat) => Set.image.{u1, u1} R R (fun (y : R) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{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)))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n)))
 Case conversion may be inaccurate. Consider using '#align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adicₓ'. -/
 theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
     HasBasis (@nhds R I.adicTopology x) (fun n : ℕ => True) fun n =>
@@ -139,7 +139,7 @@ variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R 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)], RingFilterBasis.SubmodulesBasis.{0, u1, u2} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u1} R _inst_1 I) (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)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], RingFilterBasis.SubmodulesBasis.{0, u2, u1} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u2} R _inst_1 I) (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{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 (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) Nat (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))
+  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)], RingFilterBasis.SubmodulesBasis.{0, u2, u1} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u2} R _inst_1 I) (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)))
 Case conversion may be inaccurate. Consider using '#align ideal.adic_module_basis Ideal.adic_module_basisₓ'. -/
 theorem adic_module_basis :
     I.RingFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=
@@ -168,7 +168,7 @@ def adicModuleTopology : TopologicalSpace 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))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.adicTopology.{u1} R _inst_1 I))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.adicTopology.{u1} R _inst_1 I))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.adicTopology.{u1} R _inst_1 I))
 Case conversion may be inaccurate. Consider using '#align ideal.open_add_subgroup Ideal.openAddSubgroupₓ'. -/
 /-- The elements of the basis of neighborhoods of zero for the `I`-adic topology
 on a `R`-module `M`, seen as open additive subgroups of `M`. -/
@@ -196,7 +196,7 @@ def IsAdic [H : TopologicalSpace R] (J : Ideal R) : Prop :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [top : TopologicalSpace.{u1} R] [_inst_2 : TopologicalRing.{u1} R top (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (IsAdic.{u1} R _inst_1 top J) (And (forall (n : Nat), IsOpen.{u1} R top ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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)))))))) J n))) (forall (s : Set.{u1} R), (Membership.Mem.{u1, u1} (Set.{u1} R) (Filter.{u1} R) (Filter.hasMem.{u1} R) s (nhds.{u1} R top (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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)))))))) J n)) s))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [top : TopologicalSpace.{u1} R] [_inst_2 : TopologicalRing.{u1} R top (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (IsAdic.{u1} R _inst_1 top J) (And (forall (n : Nat), IsOpen.{u1} R top (SetLike.coe.{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)))) (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)))))))) J n))) (forall (s : Set.{u1} R), (Membership.mem.{u1, u1} (Set.{u1} R) (Filter.{u1} R) (instMembershipSetFilter.{u1} R) s (nhds.{u1} R top (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (SetLike.coe.{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)))) (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)))))))) J n)) s))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [top : TopologicalSpace.{u1} R] [_inst_2 : TopologicalRing.{u1} R top (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Iff (IsAdic.{u1} R _inst_1 top J) (And (forall (n : Nat), IsOpen.{u1} R top (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{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)))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) J n))) (forall (s : Set.{u1} R), (Membership.mem.{u1, u1} (Set.{u1} R) (Filter.{u1} R) (instMembershipSetFilter.{u1} R) s (nhds.{u1} R top (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{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)))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) J n)) s))))
 Case conversion may be inaccurate. Consider using '#align is_adic_iff isAdic_iffₓ'. -/
 /-- A topological ring is `J`-adic if and only if it admits the powers of `J` as a basis of
 open neighborhoods of zero. -/

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

@@ -55,6 +55,7 @@ open Topology Pointwise
 
 namespace Ideal
 
+#print Ideal.adic_basis /-
 theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n • ⊤ : Ideal R) :=
   { inter := by
       suffices ∀ i j : ℕ, ∃ k, I ^ k ≤ I ^ i ∧ I ^ k ≤ I ^ j by simpa
@@ -73,22 +74,35 @@ theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n •
       rintro a ⟨x, b, hx, hb, rfl⟩
       exact (I ^ n).smul_mem x hb }
 #align ideal.adic_basis Ideal.adic_basis
+-/
 
+#print Ideal.ringFilterBasis /-
 /-- The adic ring filter basis associated to an ideal `I` is made of powers of `I`. -/
 def ringFilterBasis (I : Ideal R) :=
   I.adic_basis.toRing_subgroups_basis.toRingFilterBasis
 #align ideal.ring_filter_basis Ideal.ringFilterBasis
+-/
 
+#print Ideal.adicTopology /-
 /-- The adic topology associated to an ideal `I`. This topology admits powers of `I` as a basis of
 neighborhoods of zero. It is compatible with the ring structure and is non-archimedean. -/
 def adicTopology (I : Ideal R) : TopologicalSpace R :=
   (adic_basis I).topology
 #align ideal.adic_topology Ideal.adicTopology
+-/
 
+#print Ideal.nonarchimedean /-
 theorem nonarchimedean (I : Ideal R) : @NonarchimedeanRing R _ I.adicTopology :=
   I.adic_basis.toRing_subgroups_basis.nonarchimedean
 #align ideal.nonarchimedean Ideal.nonarchimedean
+-/
 
+/- warning: ideal.has_basis_nhds_zero_adic -> Ideal.hasBasis_nhds_zero_adic 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))), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) (fun (n : Nat) => True) (fun (n : Nat) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (fun (n : Nat) => True) (fun (n : Nat) => SetLike.coe.{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)))) (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))
+Case conversion may be inaccurate. Consider using '#align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adicₓ'. -/
 /-- For the `I`-adic topology, the neighborhoods of zero has basis given by the powers of `I`. -/
 theorem hasBasis_nhds_zero_adic (I : Ideal R) :
     HasBasis (@nhds R I.adicTopology (0 : R)) (fun n : ℕ => True) fun n =>
@@ -104,6 +118,12 @@ theorem hasBasis_nhds_zero_adic (I : Ideal R) :
       exact ⟨(I ^ i : Ideal R), ⟨i, by simp⟩, h⟩⟩
 #align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adic
 
+/- warning: ideal.has_basis_nhds_adic -> Ideal.hasBasis_nhds_adic 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))) (x : R), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) x) (fun (n : Nat) => True) (fun (n : Nat) => Set.image.{u1, u1} R R (fun (y : R) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x y) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (x : R), Filter.HasBasis.{u1, 1} R Nat (nhds.{u1} R (Ideal.adicTopology.{u1} R _inst_1 I) x) (fun (n : Nat) => True) (fun (n : Nat) => Set.image.{u1, u1} R R (fun (y : R) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x y) (SetLike.coe.{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)))) (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)))
+Case conversion may be inaccurate. Consider using '#align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adicₓ'. -/
 theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
     HasBasis (@nhds R I.adicTopology x) (fun n : ℕ => True) fun n =>
       (fun y => x + y) '' (I ^ n : Ideal R) :=
@@ -115,6 +135,12 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
 
 variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
 
+/- warning: ideal.adic_module_basis -> Ideal.adic_module_basis 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)], RingFilterBasis.SubmodulesBasis.{0, u1, u2} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u1} R _inst_1 I) (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)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], RingFilterBasis.SubmodulesBasis.{0, u2, u1} Nat R _inst_1 M _inst_2 _inst_3 (Ideal.ringFilterBasis.{u2} R _inst_1 I) (fun (n : Nat) => HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (instHSMul.{u2, u1} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{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 (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) Nat (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n) (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align ideal.adic_module_basis Ideal.adic_module_basisₓ'. -/
 theorem adic_module_basis :
     I.RingFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=
   { inter := fun i j =>
@@ -129,13 +155,21 @@ theorem adic_module_basis :
         exact smul_mem_smul a_in mem_top⟩ }
 #align ideal.adic_module_basis Ideal.adic_module_basis
 
+#print Ideal.adicModuleTopology /-
 /-- The topology on a `R`-module `M` associated to an ideal `M`. Submodules $I^n M$,
 written `I^n • ⊤` form a basis of neighborhoods of zero. -/
 def adicModuleTopology : TopologicalSpace M :=
   @ModuleFilterBasis.topology R M _ I.adic_basis.topology _ _
     (I.RingFilterBasis.ModuleFilterBasis (I.adic_module_basis M))
 #align ideal.adic_module_topology Ideal.adicModuleTopology
+-/
 
+/- warning: ideal.open_add_subgroup -> Ideal.openAddSubgroup 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))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.adicTopology.{u1} R _inst_1 I))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Nat -> (OpenAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.adicTopology.{u1} R _inst_1 I))
+Case conversion may be inaccurate. Consider using '#align ideal.open_add_subgroup Ideal.openAddSubgroupₓ'. -/
 /-- The elements of the basis of neighborhoods of zero for the `I`-adic topology
 on a `R`-module `M`, seen as open additive subgroups of `M`. -/
 def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology :=
@@ -150,12 +184,20 @@ end Ideal
 
 section IsAdic
 
+#print IsAdic /-
 /-- Given a topology on a ring `R` and an ideal `J`, `is_adic J` means the topology is the
 `J`-adic one. -/
 def IsAdic [H : TopologicalSpace R] (J : Ideal R) : Prop :=
   H = J.adicTopology
 #align is_adic IsAdic
+-/
 
+/- warning: is_adic_iff -> isAdic_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [top : TopologicalSpace.{u1} R] [_inst_2 : TopologicalRing.{u1} R top (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (IsAdic.{u1} R _inst_1 top J) (And (forall (n : Nat), IsOpen.{u1} R top ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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)))))))) J n))) (forall (s : Set.{u1} R), (Membership.Mem.{u1, u1} (Set.{u1} R) (Filter.{u1} R) (Filter.hasMem.{u1} R) s (nhds.{u1} R top (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (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)))))))) J n)) s))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [top : TopologicalSpace.{u1} R] [_inst_2 : TopologicalRing.{u1} R top (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (IsAdic.{u1} R _inst_1 top J) (And (forall (n : Nat), IsOpen.{u1} R top (SetLike.coe.{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)))) (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)))))))) J n))) (forall (s : Set.{u1} R), (Membership.mem.{u1, u1} (Set.{u1} R) (Filter.{u1} R) (instMembershipSetFilter.{u1} R) s (nhds.{u1} R top (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (SetLike.coe.{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)))) (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)))))))) J n)) s))))
+Case conversion may be inaccurate. Consider using '#align is_adic_iff isAdic_iffₓ'. -/
 /-- A topological ring is `J`-adic if and only if it admits the powers of `J` as a basis of
 open neighborhoods of zero. -/
 theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R} :
@@ -190,6 +232,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
 
 variable [TopologicalSpace R] [TopologicalRing R]
 
+#print is_ideal_adic_pow /-
 theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) : IsAdic (J ^ n) :=
   by
   rw [isAdic_iff] at h⊢
@@ -208,7 +251,9 @@ theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) :
     apply Ideal.pow_le_pow
     apply Nat.le_add_left
 #align is_ideal_adic_pow is_ideal_adic_pow
+-/
 
+#print is_bot_adic_iff /-
 theorem is_bot_adic_iff {A : Type _} [CommRing A] [TopologicalSpace A] [TopologicalRing A] :
     IsAdic (⊥ : Ideal A) ↔ DiscreteTopology A :=
   by
@@ -224,13 +269,16 @@ theorem is_bot_adic_iff {A : Type _} [CommRing A] [TopologicalSpace A] [Topologi
       use 1
       simp [mem_of_mem_nhds U_nhds]
 #align is_bot_adic_iff is_bot_adic_iff
+-/
 
 end IsAdic
 
+#print WithIdeal /-
 /-- The ring `R` is equipped with a preferred ideal. -/
 class WithIdeal (R : Type _) [CommRing R] where
   i : Ideal R
 #align with_ideal WithIdeal
+-/
 
 namespace WithIdeal
 
@@ -248,11 +296,13 @@ instance (priority := 100) : UniformSpace R :=
 instance (priority := 100) : UniformAddGroup R :=
   comm_topologicalAddGroup_is_uniform
 
+#print WithIdeal.topologicalSpaceModule /-
 /-- The adic topology on a `R` module coming from the ideal `with_ideal.I`.
 This cannot be an instance because `R` cannot be inferred from `M`. -/
 def topologicalSpaceModule (M : Type _) [AddCommGroup M] [Module R M] : TopologicalSpace M :=
   (i : Ideal R).adicModuleTopology M
 #align with_ideal.topological_space_module WithIdeal.topologicalSpaceModule
+-/
 
 /-
 The next examples are kept to make sure potential future refactors won't break the instance

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.algebra.nonarchimedean.adic_topology
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Ideal.Operations
 import Mathbin.Topology.Algebra.Nonarchimedean.Bases
+import Mathbin.Topology.UniformSpace.Completion
 import Mathbin.Topology.Algebra.UniformRing
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -54,7 +54,7 @@ open Topology Pointwise
 
 namespace Ideal
 
-theorem adicBasis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n • ⊤ : Ideal R) :=
+theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n • ⊤ : Ideal R) :=
   { inter := by
       suffices ∀ i j : ℕ, ∃ k, I ^ k ≤ I ^ i ∧ I ^ k ≤ I ^ j by simpa
       intro i j
@@ -71,21 +71,21 @@ theorem adicBasis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n •
       use n
       rintro a ⟨x, b, hx, hb, rfl⟩
       exact (I ^ n).smul_mem x hb }
-#align ideal.adic_basis Ideal.adicBasis
+#align ideal.adic_basis Ideal.adic_basis
 
 /-- The adic ring filter basis associated to an ideal `I` is made of powers of `I`. -/
 def ringFilterBasis (I : Ideal R) :=
-  I.adicBasis.toRing_subgroups_basis.toRingFilterBasis
+  I.adic_basis.toRing_subgroups_basis.toRingFilterBasis
 #align ideal.ring_filter_basis Ideal.ringFilterBasis
 
 /-- The adic topology associated to an ideal `I`. This topology admits powers of `I` as a basis of
 neighborhoods of zero. It is compatible with the ring structure and is non-archimedean. -/
 def adicTopology (I : Ideal R) : TopologicalSpace R :=
-  (adicBasis I).topology
+  (adic_basis I).topology
 #align ideal.adic_topology Ideal.adicTopology
 
 theorem nonarchimedean (I : Ideal R) : @NonarchimedeanRing R _ I.adicTopology :=
-  I.adicBasis.toRing_subgroups_basis.nonarchimedean
+  I.adic_basis.toRing_subgroups_basis.nonarchimedean
 #align ideal.nonarchimedean Ideal.nonarchimedean
 
 /-- For the `I`-adic topology, the neighborhoods of zero has basis given by the powers of `I`. -/
@@ -114,7 +114,7 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
 
 variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
 
-theorem adicModuleBasis :
+theorem adic_module_basis :
     I.RingFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=
   { inter := fun i j =>
       ⟨max i j,
@@ -126,13 +126,13 @@ theorem adicModuleBasis :
         by
         replace a_in : a ∈ I ^ i := by simpa [(I ^ i).mul_top] using a_in
         exact smul_mem_smul a_in mem_top⟩ }
-#align ideal.adic_module_basis Ideal.adicModuleBasis
+#align ideal.adic_module_basis Ideal.adic_module_basis
 
 /-- The topology on a `R`-module `M` associated to an ideal `M`. Submodules $I^n M$,
 written `I^n • ⊤` form a basis of neighborhoods of zero. -/
 def adicModuleTopology : TopologicalSpace M :=
-  @ModuleFilterBasis.topology R M _ I.adicBasis.topology _ _
-    (I.RingFilterBasis.ModuleFilterBasis (I.adicModuleBasis M))
+  @ModuleFilterBasis.topology R M _ I.adic_basis.topology _ _
+    (I.RingFilterBasis.ModuleFilterBasis (I.adic_module_basis M))
 #align ideal.adic_module_topology Ideal.adicModuleTopology
 
 /-- The elements of the basis of neighborhoods of zero for the `I`-adic topology
@@ -177,7 +177,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
     · apply @TopologicalRing.to_topologicalAddGroup
     · apply (RingSubgroupsBasis.toRingFilterBasis _).toAddGroupFilterBasis.isTopologicalAddGroup
     · ext s
-      letI := Ideal.adicBasis J
+      letI := Ideal.adic_basis J
       rw [J.has_basis_nhds_zero_adic.mem_iff]
       constructor <;> intro H
       · rcases H₂ s H with ⟨n, h⟩

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

@@ -175,7 +175,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
   · rintro ⟨H₁, H₂⟩
     apply TopologicalAddGroup.ext
     · apply @TopologicalRing.to_topologicalAddGroup
-    · apply (RingSubgroupsBasis.toRingFilterBasis _).toAddGroupFilterBasis.is_topological_add_group
+    · apply (RingSubgroupsBasis.toRingFilterBasis _).toAddGroupFilterBasis.isTopologicalAddGroup
     · ext s
       letI := Ideal.adicBasis J
       rw [J.has_basis_nhds_zero_adic.mem_iff]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -141,7 +141,7 @@ def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology :=
   { (I ^ n).toAddSubgroup with
     is_open' := by
       letI := I.adic_topology
-      convert (I.adic_basis.to_ring_subgroups_basis.open_add_subgroup n).IsOpen
+      convert(I.adic_basis.to_ring_subgroups_basis.open_add_subgroup n).IsOpen
       simp }
 #align ideal.open_add_subgroup Ideal.openAddSubgroup
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -245,7 +245,7 @@ instance (priority := 100) : UniformSpace R :=
   TopologicalAddGroup.toUniformSpace R
 
 instance (priority := 100) : UniformAddGroup R :=
-  topological_add_commGroup_is_uniform
+  comm_topologicalAddGroup_is_uniform
 
 /-- The adic topology on a `R` module coming from the ideal `with_ideal.I`.
 This cannot be an instance because `R` cannot be inferred from `M`. -/

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

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)

@@ -229,7 +229,6 @@ class WithIdeal (R : Type*) [CommRing R] where
 namespace WithIdeal
 
 variable (R)
-
 variable [WithIdeal R]
 
 instance (priority := 100) : TopologicalSpace R :=

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -181,7 +181,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
         exact ⟨n, trivial, h⟩
       · rcases H with ⟨n, -, hn⟩
         rw [mem_nhds_iff]
-        refine' ⟨_, hn, H₁ n, (J ^ n).zero_mem⟩
+        exact ⟨_, hn, H₁ n, (J ^ n).zero_mem⟩
 #align is_adic_iff isAdic_iff
 
 variable [TopologicalSpace R] [TopologicalRing R]

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,7 +5,6 @@ Authors: Patrick Massot
 -/
 import Mathlib.RingTheory.Ideal.Operations
 import Mathlib.Topology.Algebra.Nonarchimedean.Bases
-import Mathlib.Topology.UniformSpace.Completion
 import Mathlib.Topology.Algebra.UniformRing
 
 #align_import topology.algebra.nonarchimedean.adic_topology from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"

• Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
• Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
• Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
• Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

• ∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
• it looks a bit nicer.

@@ -70,7 +70,7 @@ theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n •
         simpa only [smul_top_eq_map, Algebra.id.map_eq_id, map_id] using this
       intro n
       use n
-      rintro a ⟨x, b, _hx, hb, rfl⟩
+      rintro a ⟨x, _hx, b, hb, rfl⟩
       exact (I ^ n).smul_mem x hb }
 #align ideal.adic_basis Ideal.adic_basis
 

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.

@@ -57,7 +57,7 @@ theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n •
       suffices ∀ i j : ℕ, ∃ k, I ^ k ≤ I ^ i ∧ I ^ k ≤ I ^ j by
         simpa only [smul_eq_mul, mul_top, Algebra.id.map_eq_id, map_id, le_inf_iff] using this
       intro i j
-      exact ⟨max i j, pow_le_pow (le_max_left i j), pow_le_pow (le_max_right i j)⟩
+      exact ⟨max i j, pow_le_pow_right (le_max_left i j), pow_le_pow_right (le_max_right i j)⟩
     leftMul := by
       suffices ∀ (a : R) (i : ℕ), ∃ j : ℕ, a • I ^ j ≤ I ^ i by
         simpa only [smul_top_eq_map, Algebra.id.map_eq_id, map_id] using this
@@ -119,8 +119,8 @@ theorem adic_module_basis :
   { inter := fun i j =>
       ⟨max i j,
         le_inf_iff.mpr
-          ⟨smul_mono_left <| pow_le_pow (le_max_left i j),
-            smul_mono_left <| pow_le_pow (le_max_right i j)⟩⟩
+          ⟨smul_mono_left <| pow_le_pow_right (le_max_left i j),
+            smul_mono_left <| pow_le_pow_right (le_max_right i j)⟩⟩
     smul := fun m i =>
       ⟨(I ^ i • ⊤ : Ideal R), ⟨i, by simp⟩, fun a a_in => by
         replace a_in : a ∈ I ^ i := by simpa [(I ^ i).mul_top] using a_in
@@ -201,7 +201,7 @@ theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) :
     · exfalso
       exact Nat.not_succ_le_zero 0 hn
     rw [← pow_mul, Nat.succ_mul]
-    apply Ideal.pow_le_pow
+    apply Ideal.pow_le_pow_right
     apply Nat.le_add_left
 #align is_ideal_adic_pow is_ideal_adic_pow
 

Mostly, this means replacing "of_open" by "of_isOpen". A few lemmas names were misleading and are corrected differently. Zulip discussion.

@@ -210,7 +210,7 @@ theorem is_bot_adic_iff {A : Type*} [CommRing A] [TopologicalSpace A] [Topologic
   rw [isAdic_iff]
   constructor
   · rintro ⟨h, _h'⟩
-    rw [discreteTopology_iff_open_singleton_zero]
+    rw [discreteTopology_iff_isOpen_singleton_zero]
     simpa using h 1
   · intros
     constructor

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

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

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -66,7 +66,7 @@ theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n •
       rintro a ⟨x, hx, rfl⟩
       exact (I ^ n).smul_mem r hx
     mul := by
-      suffices ∀ i : ℕ, ∃ j : ℕ, (I ^ j: Set R) * (I ^ j : Set R) ⊆ (I ^ i : Set R) by
+      suffices ∀ i : ℕ, ∃ j : ℕ, (↑(I ^ j) * ↑(I ^ j) : Set R) ⊆ (↑(I ^ i) : Set R) by
         simpa only [smul_top_eq_map, Algebra.id.map_eq_id, map_id] using this
       intro n
       use n
@@ -140,7 +140,7 @@ def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology := by
   letI := I.adicTopology
   refine ⟨(I ^ n).toAddSubgroup, ?_⟩
   convert (I.adic_basis.toRing_subgroups_basis.openAddSubgroup n).isOpen
-  change (I ^ n : Set R) = (I ^ n • (⊤ : Ideal R) : Set R)
+  change (↑(I ^ n) : Set R) = ↑(I ^ n • (⊤ : Ideal R))
   simp [smul_top_eq_map, Algebra.id.map_eq_id, map_id, restrictScalars_self]
 #align ideal.open_add_subgroup Ideal.openAddSubgroup
 

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

This has nice performance benefits.

@@ -44,7 +44,7 @@ to make sure it is definitionally equal to the `I`-topology on `R` seen as an `R
 -/
 
 
-variable {R : Type _} [CommRing R]
+variable {R : Type*} [CommRing R]
 
 open Set TopologicalAddGroup Submodule Filter
 
@@ -112,7 +112,7 @@ theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
   rwa [map_add_left_nhds_zero x] at this
 #align ideal.has_basis_nhds_adic Ideal.hasBasis_nhds_adic
 
-variable (I : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
+variable (I : Ideal R) (M : Type*) [AddCommGroup M] [Module R M]
 
 theorem adic_module_basis :
     I.ringFilterBasis.SubmodulesBasis fun n : ℕ => I ^ n • (⊤ : Submodule R M) :=
@@ -205,7 +205,7 @@ theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) :
     apply Nat.le_add_left
 #align is_ideal_adic_pow is_ideal_adic_pow
 
-theorem is_bot_adic_iff {A : Type _} [CommRing A] [TopologicalSpace A] [TopologicalRing A] :
+theorem is_bot_adic_iff {A : Type*} [CommRing A] [TopologicalSpace A] [TopologicalRing A] :
     IsAdic (⊥ : Ideal A) ↔ DiscreteTopology A := by
   rw [isAdic_iff]
   constructor
@@ -223,7 +223,7 @@ theorem is_bot_adic_iff {A : Type _} [CommRing A] [TopologicalSpace A] [Topologi
 end IsAdic
 
 /-- The ring `R` is equipped with a preferred ideal. -/
-class WithIdeal (R : Type _) [CommRing R] where
+class WithIdeal (R : Type*) [CommRing R] where
   i : Ideal R
 #align with_ideal WithIdeal
 
@@ -247,7 +247,7 @@ instance (priority := 100) : UniformAddGroup R :=
 
 /-- The adic topology on an `R` module coming from the ideal `WithIdeal.I`.
 This cannot be an instance because `R` cannot be inferred from `M`. -/
-def topologicalSpaceModule (M : Type _) [AddCommGroup M] [Module R M] : TopologicalSpace M :=
+def topologicalSpaceModule (M : Type*) [AddCommGroup M] [Module R M] : TopologicalSpace M :=
   (i : Ideal R).adicModuleTopology M
 #align with_ideal.topological_space_module WithIdeal.topologicalSpaceModule
 
@@ -259,13 +259,13 @@ example : NonarchimedeanRing R := by infer_instance
 
 example : TopologicalRing (UniformSpace.Completion R) := by infer_instance
 
-example (M : Type _) [AddCommGroup M] [Module R M] :
+example (M : Type*) [AddCommGroup M] [Module R M] :
     @TopologicalAddGroup M (WithIdeal.topologicalSpaceModule R M) _ := by infer_instance
 
-example (M : Type _) [AddCommGroup M] [Module R M] :
+example (M : Type*) [AddCommGroup M] [Module R M] :
     @ContinuousSMul R M _ _ (WithIdeal.topologicalSpaceModule R M) := by infer_instance
 
-example (M : Type _) [AddCommGroup M] [Module R M] :
+example (M : Type*) [AddCommGroup M] [Module R M] :
     @NonarchimedeanAddGroup M _ (WithIdeal.topologicalSpaceModule R M) :=
   SubmodulesBasis.nonarchimedean _
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module topology.algebra.nonarchimedean.adic_topology
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Ideal.Operations
 import Mathlib.Topology.Algebra.Nonarchimedean.Bases
 import Mathlib.Topology.UniformSpace.Completion
 import Mathlib.Topology.Algebra.UniformRing
 
+#align_import topology.algebra.nonarchimedean.adic_topology from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Adic topology
 

@@ -248,7 +248,7 @@ instance (priority := 100) : UniformSpace R :=
 instance (priority := 100) : UniformAddGroup R :=
   comm_topologicalAddGroup_is_uniform
 
-/-- The adic topology on a `R` module coming from the ideal `WithIdeal.I`.
+/-- The adic topology on an `R` module coming from the ideal `WithIdeal.I`.
 This cannot be an instance because `R` cannot be inferred from `M`. -/
 def topologicalSpaceModule (M : Type _) [AddCommGroup M] [Module R M] : TopologicalSpace M :=
   (i : Ideal R).adicModuleTopology M

Changes are of the form

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

@@ -191,7 +191,7 @@ theorem isAdic_iff [top : TopologicalSpace R] [TopologicalRing R] {J : Ideal R}
 variable [TopologicalSpace R] [TopologicalRing R]
 
 theorem is_ideal_adic_pow {J : Ideal R} (h : IsAdic J) {n : ℕ} (hn : 0 < n) : IsAdic (J ^ n) := by
-  rw [isAdic_iff] at h⊢
+  rw [isAdic_iff] at h ⊢
   constructor
   · intro m
     rw [← pow_mul]

Part 3 of #5001

@@ -42,7 +42,7 @@ corresponding adic topology to the type class inference system.
 ## Implementation notes
 
 The `I`-adic topology on a ring `R` has a contrived definition using `I^n • ⊤` instead of `I`
-to make sure it is definitionally equal to the `I`-topology on `R` seen as a `R`-module.
+to make sure it is definitionally equal to the `I`-topology on `R` seen as an `R`-module.
 
 -/
 
@@ -130,7 +130,7 @@ theorem adic_module_basis :
         exact smul_mem_smul a_in mem_top⟩ }
 #align ideal.adic_module_basis Ideal.adic_module_basis
 
-/-- The topology on a `R`-module `M` associated to an ideal `M`. Submodules $I^n M$,
+/-- The topology on an `R`-module `M` associated to an ideal `M`. Submodules $I^n M$,
 written `I^n • ⊤` form a basis of neighborhoods of zero. -/
 def adicModuleTopology : TopologicalSpace M :=
   @ModuleFilterBasis.topology R M _ I.adic_basis.topology _ _
@@ -138,7 +138,7 @@ def adicModuleTopology : TopologicalSpace M :=
 #align ideal.adic_module_topology Ideal.adicModuleTopology
 
 /-- The elements of the basis of neighborhoods of zero for the `I`-adic topology
-on a `R`-module `M`, seen as open additive subgroups of `M`. -/
+on an `R`-module `M`, seen as open additive subgroups of `M`. -/
 def openAddSubgroup (n : ℕ) : @OpenAddSubgroup R _ I.adicTopology := by
   letI := I.adicTopology
   refine ⟨(I ^ n).toAddSubgroup, ?_⟩

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

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

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

@@ -55,8 +55,6 @@ open Topology Pointwise
 
 namespace Ideal
 
-set_option synthInstance.maxHeartbeats 40000 in -- Porting note : added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem adic_basis (I : Ideal R) : SubmodulesRingBasis fun n : ℕ => (I ^ n • ⊤ : Ideal R) :=
   { inter := by
       suffices ∀ i j : ℕ, ∃ k, I ^ k ≤ I ^ i ∧ I ^ k ≤ I ^ j by
@@ -109,7 +107,6 @@ theorem hasBasis_nhds_zero_adic (I : Ideal R) :
       exact ⟨(I ^ i : Ideal R), ⟨i, by simp⟩, h⟩⟩
 #align ideal.has_basis_nhds_zero_adic Ideal.hasBasis_nhds_zero_adic
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem hasBasis_nhds_adic (I : Ideal R) (x : R) :
     HasBasis (@nhds R I.adicTopology x) (fun _n : ℕ => True) fun n =>
       (fun y => x + y) '' (I ^ n : Ideal R) := by
@@ -265,7 +262,6 @@ example : NonarchimedeanRing R := by infer_instance
 
 example : TopologicalRing (UniformSpace.Completion R) := by infer_instance
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 example (M : Type _) [AddCommGroup M] [Module R M] :
     @TopologicalAddGroup M (WithIdeal.topologicalSpaceModule R M) _ := by infer_instance