ring_theory.coprime.ideal ⟷ Mathlib.RingTheory.Coprime.Ideal

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Pierre-Alexandre Bazin
 -/
-import LinearAlgebra.Dfinsupp
+import LinearAlgebra.DFinsupp
 import RingTheory.Ideal.Operations
 
 #align_import ring_theory.coprime.ideal from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"

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

@@ -49,7 +49,7 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
   rw [Finset.coe_cons,
     Set.pairwise_insert_of_symmetric fun i j (h : I i ⊔ I j = ⊤) => sup_comm.trans h]
   constructor
-  · rintro ⟨μ, hμ⟩; rw [Finset.sum_cons] at hμ 
+  · rintro ⟨μ, hμ⟩; rw [Finset.sum_cons] at hμ
     refine' ⟨ih.mp ⟨Pi.single h.some ⟨μ a, _⟩ + fun i => ⟨μ i, _⟩, _⟩, fun b hb ab => _⟩
     · have := Submodule.coe_mem (μ a); rw [mem_infi] at this ⊢
       --for some reason `simp only [mem_infi]` times out
@@ -60,26 +60,26 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
     · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this ⊢
       intro j hj ij; exact this _ (Finset.subset_cons _ hj) ij
     · rw [← @if_pos _ _ h.some_spec R (μ a) 0, ← Finset.sum_pi_single', ← Finset.sum_add_distrib] at
-        hμ 
+        hμ
       convert hμ; ext i; rw [Pi.add_apply, Submodule.coe_add, Submodule.coe_mk]
       by_cases hi : i = h.some
       · rw [hi, Pi.single_eq_same, Pi.single_eq_same, Submodule.coe_mk]
       · rw [Pi.single_eq_of_ne hi, Pi.single_eq_of_ne hi, Submodule.coe_zero]
     · rw [eq_top_iff_one, Submodule.mem_sup]
-      rw [add_comm] at hμ ; refine' ⟨_, _, _, _, hμ⟩
+      rw [add_comm] at hμ; refine' ⟨_, _, _, _, hμ⟩
       · refine' sum_mem _ fun x hx => _
-        have := Submodule.coe_mem (μ x); simp only [mem_infi] at this 
+        have := Submodule.coe_mem (μ x); simp only [mem_infi] at this
         apply this _ (Finset.mem_cons_self _ _); rintro rfl; exact hat hx
-      · have := Submodule.coe_mem (μ a); simp only [mem_infi] at this 
+      · have := Submodule.coe_mem (μ a); simp only [mem_infi] at this
         exact this _ (Finset.subset_cons _ hb) ab.symm
   · rintro ⟨hs, Hb⟩
     obtain ⟨μ, hμ⟩ := ih.mpr hs
     have := sup_infi_eq_top fun b hb => Hb b hb (ne_of_mem_of_not_mem hb hat).symm
-    rw [eq_top_iff_one, Submodule.mem_sup] at this 
+    rw [eq_top_iff_one, Submodule.mem_sup] at this
     obtain ⟨u, hu, v, hv, huv⟩ := this
     refine' ⟨fun i => if hi : i = a then ⟨v, _⟩ else ⟨u * μ i, _⟩, _⟩
     · simp only [mem_infi] at hv ⊢
-      intro j hj ij; rw [Finset.mem_cons, ← hi] at hj 
+      intro j hj ij; rw [Finset.mem_cons, ← hi] at hj
       exact hv _ (hj.resolve_left ij)
     · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this ⊢
       intro j hj ij
@@ -87,7 +87,7 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
       · exact mul_mem_right _ _ hu
       · exact mul_mem_left _ _ (this _ hj ij)
     · rw [Finset.sum_cons, dif_pos rfl, add_comm]
-      rw [← mul_one u] at huv ; rw [← huv, ← hμ, Finset.mul_sum]
+      rw [← mul_one u] at huv; rw [← huv, ← hμ, Finset.mul_sum]
       congr 1; apply Finset.sum_congr rfl; intro j hj
       rw [dif_neg]; rfl
       rintro rfl; exact hat hj

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Pierre-Alexandre Bazin
 -/
-import Mathbin.LinearAlgebra.Dfinsupp
-import Mathbin.RingTheory.Ideal.Operations
+import LinearAlgebra.Dfinsupp
+import RingTheory.Ideal.Operations
 
 #align_import ring_theory.coprime.ideal from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Pierre-Alexandre Bazin
-
-! This file was ported from Lean 3 source module ring_theory.coprime.ideal
-! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Dfinsupp
 import Mathbin.RingTheory.Ideal.Operations
 
+#align_import ring_theory.coprime.ideal from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
+
 /-!
 # An additional lemma about coprime ideals
 

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

@@ -26,6 +26,7 @@ namespace Ideal
 
 variable {ι R : Type _} [CommSemiring R]
 
+#print Ideal.iSup_iInf_eq_top_iff_pairwise /-
 /-- A finite family of ideals is pairwise coprime (that is, any two of them generate the whole ring)
 iff when taking all the possible intersections of all but one of these ideals, the resulting family
 of ideals still generate the whole ring.
@@ -94,6 +95,7 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
       rw [dif_neg]; rfl
       rintro rfl; exact hat hj
 #align ideal.supr_infi_eq_top_iff_pairwise Ideal.iSup_iInf_eq_top_iff_pairwise
+-/
 
 end Ideal
 

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

@@ -51,45 +51,45 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
   rw [Finset.coe_cons,
     Set.pairwise_insert_of_symmetric fun i j (h : I i ⊔ I j = ⊤) => sup_comm.trans h]
   constructor
-  · rintro ⟨μ, hμ⟩; rw [Finset.sum_cons] at hμ
+  · rintro ⟨μ, hμ⟩; rw [Finset.sum_cons] at hμ 
     refine' ⟨ih.mp ⟨Pi.single h.some ⟨μ a, _⟩ + fun i => ⟨μ i, _⟩, _⟩, fun b hb ab => _⟩
-    · have := Submodule.coe_mem (μ a); rw [mem_infi] at this⊢
+    · have := Submodule.coe_mem (μ a); rw [mem_infi] at this ⊢
       --for some reason `simp only [mem_infi]` times out
       intro i;
-      specialize this i; rw [mem_infi, mem_infi] at this⊢
+      specialize this i; rw [mem_infi, mem_infi] at this ⊢
       intro hi _; apply this (Finset.subset_cons _ hi)
       rintro rfl; exact hat hi
-    · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this⊢
+    · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this ⊢
       intro j hj ij; exact this _ (Finset.subset_cons _ hj) ij
     · rw [← @if_pos _ _ h.some_spec R (μ a) 0, ← Finset.sum_pi_single', ← Finset.sum_add_distrib] at
-        hμ
+        hμ 
       convert hμ; ext i; rw [Pi.add_apply, Submodule.coe_add, Submodule.coe_mk]
       by_cases hi : i = h.some
       · rw [hi, Pi.single_eq_same, Pi.single_eq_same, Submodule.coe_mk]
       · rw [Pi.single_eq_of_ne hi, Pi.single_eq_of_ne hi, Submodule.coe_zero]
     · rw [eq_top_iff_one, Submodule.mem_sup]
-      rw [add_comm] at hμ; refine' ⟨_, _, _, _, hμ⟩
+      rw [add_comm] at hμ ; refine' ⟨_, _, _, _, hμ⟩
       · refine' sum_mem _ fun x hx => _
-        have := Submodule.coe_mem (μ x); simp only [mem_infi] at this
+        have := Submodule.coe_mem (μ x); simp only [mem_infi] at this 
         apply this _ (Finset.mem_cons_self _ _); rintro rfl; exact hat hx
-      · have := Submodule.coe_mem (μ a); simp only [mem_infi] at this
+      · have := Submodule.coe_mem (μ a); simp only [mem_infi] at this 
         exact this _ (Finset.subset_cons _ hb) ab.symm
   · rintro ⟨hs, Hb⟩
     obtain ⟨μ, hμ⟩ := ih.mpr hs
     have := sup_infi_eq_top fun b hb => Hb b hb (ne_of_mem_of_not_mem hb hat).symm
-    rw [eq_top_iff_one, Submodule.mem_sup] at this
+    rw [eq_top_iff_one, Submodule.mem_sup] at this 
     obtain ⟨u, hu, v, hv, huv⟩ := this
     refine' ⟨fun i => if hi : i = a then ⟨v, _⟩ else ⟨u * μ i, _⟩, _⟩
-    · simp only [mem_infi] at hv⊢
-      intro j hj ij; rw [Finset.mem_cons, ← hi] at hj
+    · simp only [mem_infi] at hv ⊢
+      intro j hj ij; rw [Finset.mem_cons, ← hi] at hj 
       exact hv _ (hj.resolve_left ij)
-    · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this⊢
+    · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this ⊢
       intro j hj ij
       rcases finset.mem_cons.mp hj with (rfl | hj)
       · exact mul_mem_right _ _ hu
       · exact mul_mem_left _ _ (this _ hj ij)
     · rw [Finset.sum_cons, dif_pos rfl, add_comm]
-      rw [← mul_one u] at huv; rw [← huv, ← hμ, Finset.mul_sum]
+      rw [← mul_one u] at huv ; rw [← huv, ← hμ, Finset.mul_sum]
       congr 1; apply Finset.sum_congr rfl; intro j hj
       rw [dif_neg]; rfl
       rintro rfl; exact hat hj

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

@@ -26,12 +26,6 @@ namespace Ideal
 
 variable {ι R : Type _} [CommSemiring R]
 
-/- warning: ideal.supr_infi_eq_top_iff_pairwise -> Ideal.iSup_iInf_eq_top_iff_pairwise is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {t : Finset.{u1} ι}, (Finset.Nonempty.{u1} ι t) -> (forall (I : ι -> (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))), Iff (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (iSup.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) ι (fun (i : ι) => iSup.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) => iInf.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) ι (fun (j : ι) => iInf.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) (fun (hj : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) => iInf.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Ne.{succ u1} ι j i) (fun (ij : Ne.{succ u1} ι j i) => I j)))))) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Set.Pairwise.{u1} ι ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) t) (fun (i : ι) (j : ι) => Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Sup.sup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SemilatticeSup.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (IdemSemiring.toSemilatticeSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.idemSemiring.{u2, u2} R _inst_1 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (I i) (I j)) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))
-but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {t : Finset.{u2} ι}, (Finset.Nonempty.{u2} ι t) -> (forall (I : ι -> (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))), Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (iSup.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) ι (fun (i : ι) => iSup.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) => iInf.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) ι (fun (j : ι) => iInf.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) (fun (hj : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) => iInf.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Ne.{succ u2} ι j i) (fun (ij : Ne.{succ u2} ι j i) => I j)))))) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.Pairwise.{u2} ι (Finset.toSet.{u2} ι t) (fun (i : ι) (j : ι) => Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Sup.sup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SemilatticeSup.toSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemCommSemiring.toSemilatticeSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R _inst_1))) (I i) (I j)) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align ideal.supr_infi_eq_top_iff_pairwise Ideal.iSup_iInf_eq_top_iff_pairwiseₓ'. -/
 /-- A finite family of ideals is pairwise coprime (that is, any two of them generate the whole ring)
 iff when taking all the possible intersections of all but one of these ideals, the resulting family
 of ideals still generate the whole ring.

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

@@ -49,7 +49,7 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
   refine' h.cons_induction _ _ <;> clear t h
   · simp only [Finset.sum_singleton, Finset.coe_singleton, Set.pairwise_singleton, iff_true_iff]
     refine' fun a => ⟨fun i => if h : i = a then ⟨1, _⟩ else 0, _⟩
-    · rw [h]
+    · rw [h];
       simp only [Finset.mem_singleton, Ne.def, iInf_iInf_eq_left, eq_self_iff_true, not_true,
         iInf_false]
     · simp only [dif_pos, dif_ctx_congr, Submodule.coe_mk, eq_self_iff_true]
@@ -57,42 +57,28 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
   rw [Finset.coe_cons,
     Set.pairwise_insert_of_symmetric fun i j (h : I i ⊔ I j = ⊤) => sup_comm.trans h]
   constructor
-  · rintro ⟨μ, hμ⟩
-    rw [Finset.sum_cons] at hμ
+  · rintro ⟨μ, hμ⟩; rw [Finset.sum_cons] at hμ
     refine' ⟨ih.mp ⟨Pi.single h.some ⟨μ a, _⟩ + fun i => ⟨μ i, _⟩, _⟩, fun b hb ab => _⟩
-    · have := Submodule.coe_mem (μ a)
-      rw [mem_infi] at this⊢
+    · have := Submodule.coe_mem (μ a); rw [mem_infi] at this⊢
       --for some reason `simp only [mem_infi]` times out
-      intro i
-      specialize this i
-      rw [mem_infi, mem_infi] at this⊢
-      intro hi _
-      apply this (Finset.subset_cons _ hi)
-      rintro rfl
-      exact hat hi
-    · have := Submodule.coe_mem (μ i)
-      simp only [mem_infi] at this⊢
-      intro j hj ij
-      exact this _ (Finset.subset_cons _ hj) ij
+      intro i;
+      specialize this i; rw [mem_infi, mem_infi] at this⊢
+      intro hi _; apply this (Finset.subset_cons _ hi)
+      rintro rfl; exact hat hi
+    · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this⊢
+      intro j hj ij; exact this _ (Finset.subset_cons _ hj) ij
     · rw [← @if_pos _ _ h.some_spec R (μ a) 0, ← Finset.sum_pi_single', ← Finset.sum_add_distrib] at
         hμ
-      convert hμ
-      ext i
-      rw [Pi.add_apply, Submodule.coe_add, Submodule.coe_mk]
+      convert hμ; ext i; rw [Pi.add_apply, Submodule.coe_add, Submodule.coe_mk]
       by_cases hi : i = h.some
       · rw [hi, Pi.single_eq_same, Pi.single_eq_same, Submodule.coe_mk]
       · rw [Pi.single_eq_of_ne hi, Pi.single_eq_of_ne hi, Submodule.coe_zero]
     · rw [eq_top_iff_one, Submodule.mem_sup]
-      rw [add_comm] at hμ
-      refine' ⟨_, _, _, _, hμ⟩
+      rw [add_comm] at hμ; refine' ⟨_, _, _, _, hμ⟩
       · refine' sum_mem _ fun x hx => _
-        have := Submodule.coe_mem (μ x)
-        simp only [mem_infi] at this
-        apply this _ (Finset.mem_cons_self _ _)
-        rintro rfl
-        exact hat hx
-      · have := Submodule.coe_mem (μ a)
-        simp only [mem_infi] at this
+        have := Submodule.coe_mem (μ x); simp only [mem_infi] at this
+        apply this _ (Finset.mem_cons_self _ _); rintro rfl; exact hat hx
+      · have := Submodule.coe_mem (μ a); simp only [mem_infi] at this
         exact this _ (Finset.subset_cons _ hb) ab.symm
   · rintro ⟨hs, Hb⟩
     obtain ⟨μ, hμ⟩ := ih.mpr hs
@@ -101,25 +87,18 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
     obtain ⟨u, hu, v, hv, huv⟩ := this
     refine' ⟨fun i => if hi : i = a then ⟨v, _⟩ else ⟨u * μ i, _⟩, _⟩
     · simp only [mem_infi] at hv⊢
-      intro j hj ij
-      rw [Finset.mem_cons, ← hi] at hj
+      intro j hj ij; rw [Finset.mem_cons, ← hi] at hj
       exact hv _ (hj.resolve_left ij)
-    · have := Submodule.coe_mem (μ i)
-      simp only [mem_infi] at this⊢
+    · have := Submodule.coe_mem (μ i); simp only [mem_infi] at this⊢
       intro j hj ij
       rcases finset.mem_cons.mp hj with (rfl | hj)
       · exact mul_mem_right _ _ hu
       · exact mul_mem_left _ _ (this _ hj ij)
     · rw [Finset.sum_cons, dif_pos rfl, add_comm]
-      rw [← mul_one u] at huv
-      rw [← huv, ← hμ, Finset.mul_sum]
-      congr 1
-      apply Finset.sum_congr rfl
-      intro j hj
-      rw [dif_neg]
-      rfl
-      rintro rfl
-      exact hat hj
+      rw [← mul_one u] at huv; rw [← huv, ← hμ, Finset.mul_sum]
+      congr 1; apply Finset.sum_congr rfl; intro j hj
+      rw [dif_neg]; rfl
+      rintro rfl; exact hat hj
 #align ideal.supr_infi_eq_top_iff_pairwise Ideal.iSup_iInf_eq_top_iff_pairwise
 
 end Ideal

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

@@ -26,12 +26,12 @@ namespace Ideal
 
 variable {ι R : Type _} [CommSemiring R]
 
-/- warning: ideal.supr_infi_eq_top_iff_pairwise -> Ideal.supᵢ_infᵢ_eq_top_iff_pairwise is a dubious translation:
+/- warning: ideal.supr_infi_eq_top_iff_pairwise -> Ideal.iSup_iInf_eq_top_iff_pairwise is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {t : Finset.{u1} ι}, (Finset.Nonempty.{u1} ι t) -> (forall (I : ι -> (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))), Iff (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (supᵢ.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) ι (fun (i : ι) => supᵢ.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) => infᵢ.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) ι (fun (j : ι) => infᵢ.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) (fun (hj : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) => infᵢ.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Ne.{succ u1} ι j i) (fun (ij : Ne.{succ u1} ι j i) => I j)))))) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Set.Pairwise.{u1} ι ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) t) (fun (i : ι) (j : ι) => Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Sup.sup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SemilatticeSup.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (IdemSemiring.toSemilatticeSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.idemSemiring.{u2, u2} R _inst_1 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (I i) (I j)) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {t : Finset.{u1} ι}, (Finset.Nonempty.{u1} ι t) -> (forall (I : ι -> (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))), Iff (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (iSup.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) ι (fun (i : ι) => iSup.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) => iInf.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) ι (fun (j : ι) => iInf.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) (fun (hj : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) => iInf.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Ne.{succ u1} ι j i) (fun (ij : Ne.{succ u1} ι j i) => I j)))))) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Set.Pairwise.{u1} ι ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) t) (fun (i : ι) (j : ι) => Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Sup.sup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SemilatticeSup.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (IdemSemiring.toSemilatticeSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.idemSemiring.{u2, u2} R _inst_1 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (I i) (I j)) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))
 but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {t : Finset.{u2} ι}, (Finset.Nonempty.{u2} ι t) -> (forall (I : ι -> (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))), Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (supᵢ.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) ι (fun (i : ι) => supᵢ.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) => infᵢ.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) ι (fun (j : ι) => infᵢ.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) (fun (hj : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) => infᵢ.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Ne.{succ u2} ι j i) (fun (ij : Ne.{succ u2} ι j i) => I j)))))) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.Pairwise.{u2} ι (Finset.toSet.{u2} ι t) (fun (i : ι) (j : ι) => Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Sup.sup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SemilatticeSup.toSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemCommSemiring.toSemilatticeSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R _inst_1))) (I i) (I j)) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align ideal.supr_infi_eq_top_iff_pairwise Ideal.supᵢ_infᵢ_eq_top_iff_pairwiseₓ'. -/
+  forall {ι : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {t : Finset.{u2} ι}, (Finset.Nonempty.{u2} ι t) -> (forall (I : ι -> (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))), Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (iSup.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) ι (fun (i : ι) => iSup.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) => iInf.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) ι (fun (j : ι) => iInf.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) (fun (hj : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) => iInf.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Ne.{succ u2} ι j i) (fun (ij : Ne.{succ u2} ι j i) => I j)))))) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.Pairwise.{u2} ι (Finset.toSet.{u2} ι t) (fun (i : ι) (j : ι) => Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Sup.sup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SemilatticeSup.toSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemCommSemiring.toSemilatticeSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R _inst_1))) (I i) (I j)) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.supr_infi_eq_top_iff_pairwise Ideal.iSup_iInf_eq_top_iff_pairwiseₓ'. -/
 /-- A finite family of ideals is pairwise coprime (that is, any two of them generate the whole ring)
 iff when taking all the possible intersections of all but one of these ideals, the resulting family
 of ideals still generate the whole ring.
@@ -40,18 +40,18 @@ For example with three ideals : `I ⊔ J = I ⊔ K = J ⊔ K = ⊤ ↔ (I ⊓ J)
 
 When ideals are all of the form `I i = R ∙ s i`, this is equivalent to the
 `exists_sum_eq_one_iff_pairwise_coprime` lemma.-/
-theorem supᵢ_infᵢ_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι → Ideal R) :
+theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι → Ideal R) :
     (⨆ i ∈ t, ⨅ (j) (hj : j ∈ t) (ij : j ≠ i), I j) = ⊤ ↔
       (t : Set ι).Pairwise fun i j => I i ⊔ I j = ⊤ :=
   by
   haveI : DecidableEq ι := Classical.decEq ι
-  rw [eq_top_iff_one, Submodule.mem_supᵢ_finset_iff_exists_sum]
+  rw [eq_top_iff_one, Submodule.mem_iSup_finset_iff_exists_sum]
   refine' h.cons_induction _ _ <;> clear t h
   · simp only [Finset.sum_singleton, Finset.coe_singleton, Set.pairwise_singleton, iff_true_iff]
     refine' fun a => ⟨fun i => if h : i = a then ⟨1, _⟩ else 0, _⟩
     · rw [h]
-      simp only [Finset.mem_singleton, Ne.def, infᵢ_infᵢ_eq_left, eq_self_iff_true, not_true,
-        infᵢ_false]
+      simp only [Finset.mem_singleton, Ne.def, iInf_iInf_eq_left, eq_self_iff_true, not_true,
+        iInf_false]
     · simp only [dif_pos, dif_ctx_congr, Submodule.coe_mk, eq_self_iff_true]
   intro a t hat h ih
   rw [Finset.coe_cons,
@@ -120,7 +120,7 @@ theorem supᵢ_infᵢ_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I :
       rfl
       rintro rfl
       exact hat hj
-#align ideal.supr_infi_eq_top_iff_pairwise Ideal.supᵢ_infᵢ_eq_top_iff_pairwise
+#align ideal.supr_infi_eq_top_iff_pairwise Ideal.iSup_iInf_eq_top_iff_pairwise
 
 end Ideal
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Pierre-Alexandre Bazin
 
 ! This file was ported from Lean 3 source module ring_theory.coprime.ideal
-! leanprover-community/mathlib commit 2bbc7e3884ba234309d2a43b19144105a753292e
+! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Ideal.Operations
 /-!
 # An additional lemma about coprime ideals
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This lemma generalises `exists_sum_eq_one_iff_pairwise_coprime` to the case of non-principal ideals.
 It is on a separate file due to import requirements.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -23,6 +23,12 @@ namespace Ideal
 
 variable {ι R : Type _} [CommSemiring R]
 
+/- warning: ideal.supr_infi_eq_top_iff_pairwise -> Ideal.supᵢ_infᵢ_eq_top_iff_pairwise is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {t : Finset.{u1} ι}, (Finset.Nonempty.{u1} ι t) -> (forall (I : ι -> (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))), Iff (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (supᵢ.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) ι (fun (i : ι) => supᵢ.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i t) => infᵢ.{u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) ι (fun (j : ι) => infᵢ.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) (fun (hj : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j t) => infᵢ.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasInf.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Ne.{succ u1} ι j i) (fun (ij : Ne.{succ u1} ι j i) => I j)))))) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Set.Pairwise.{u1} ι ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) t) (fun (i : ι) (j : ι) => Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Sup.sup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SemilatticeSup.toHasSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (IdemSemiring.toSemilatticeSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.idemSemiring.{u2, u2} R _inst_1 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (I i) (I j)) (Top.top.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.hasTop.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))
+but is expected to have type
+  forall {ι : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {t : Finset.{u2} ι}, (Finset.Nonempty.{u2} ι t) -> (forall (I : ι -> (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))), Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (supᵢ.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) ι (fun (i : ι) => supᵢ.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i t) => infᵢ.{u1, succ u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) ι (fun (j : ι) => infᵢ.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) (fun (hj : Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j t) => infᵢ.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Ne.{succ u2} ι j i) (fun (ij : Ne.{succ u2} ι j i) => I j)))))) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.Pairwise.{u2} ι (Finset.toSet.{u2} ι t) (fun (i : ι) (j : ι) => Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Sup.sup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SemilatticeSup.toSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemCommSemiring.toSemilatticeSup.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R _inst_1))) (I i) (I j)) (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.supr_infi_eq_top_iff_pairwise Ideal.supᵢ_infᵢ_eq_top_iff_pairwiseₓ'. -/
 /-- A finite family of ideals is pairwise coprime (that is, any two of them generate the whole ring)
 iff when taking all the possible intersections of all but one of these ideals, the resulting family
 of ideals still generate the whole ring.

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

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -27,7 +27,7 @@ of ideals still generate the whole ring.
 For example with three ideals : `I ⊔ J = I ⊔ K = J ⊔ K = ⊤ ↔ (I ⊓ J) ⊔ (I ⊓ K) ⊔ (J ⊓ K) = ⊤`.
 
 When ideals are all of the form `I i = R ∙ s i`, this is equivalent to the
-`exists_sum_eq_one_iff_pairwise_coprime` lemma.-/
+`exists_sum_eq_one_iff_pairwise_coprime` lemma. -/
 theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι → Ideal R) :
     (⨆ i ∈ t, ⨅ (j) (_ : j ∈ t) (_ : j ≠ i), I j) = ⊤ ↔
       (t : Set ι).Pairwise fun i j => I i ⊔ I j = ⊤ := by

Those lemmas have historically been very annoying to use in rw since all their arguments were implicit. One too many people complained about it on Zulip, so I'm changing them.

Downstream code broken by this change can fix it by adding appropriately many _s.

Also marks CauSeq.ext @[ext].

Order.BoundedOrder

• top_sup_eq
• sup_top_eq
• bot_sup_eq
• sup_bot_eq
• top_inf_eq
• inf_top_eq
• bot_inf_eq
• inf_bot_eq

Order.Lattice

• sup_idem
• sup_comm
• sup_assoc
• sup_left_idem
• sup_right_idem
• inf_idem
• inf_comm
• inf_assoc
• inf_left_idem
• inf_right_idem
• sup_inf_left
• sup_inf_right
• inf_sup_left
• inf_sup_right

Order.MinMax

• max_min_distrib_left
• max_min_distrib_right
• min_max_distrib_left
• min_max_distrib_right

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -40,7 +40,7 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
     · simp only [dif_pos, dif_ctx_congr, Submodule.coe_mk, eq_self_iff_true]
   intro a t hat h ih
   rw [Finset.coe_cons,
-    Set.pairwise_insert_of_symmetric fun i j (h : I i ⊔ I j = ⊤) => sup_comm.trans h]
+    Set.pairwise_insert_of_symmetric fun i j (h : I i ⊔ I j = ⊤) ↦ (sup_comm _ _).trans h]
   constructor
   · rintro ⟨μ, hμ⟩
     rw [Finset.sum_cons] at hμ

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

This has nice performance benefits.

@@ -18,7 +18,7 @@ It is on a separate file due to import requirements.
 
 namespace Ideal
 
-variable {ι R : Type _} [CommSemiring R]
+variable {ι R : Type*} [CommSemiring R]
 
 /-- A finite family of ideals is pairwise coprime (that is, any two of them generate the whole ring)
 iff when taking all the possible intersections of all but one of these ideals, the resulting family

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Pierre-Alexandre Bazin
-
-! This file was ported from Lean 3 source module ring_theory.coprime.ideal
-! leanprover-community/mathlib commit 2bbc7e3884ba234309d2a43b19144105a753292e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.DFinsupp
 import Mathlib.RingTheory.Ideal.Operations
 
+#align_import ring_theory.coprime.ideal from "leanprover-community/mathlib"@"2bbc7e3884ba234309d2a43b19144105a753292e"
+
 /-!
 # An additional lemma about coprime ideals
 

See #4354

@@ -8,7 +8,7 @@ Authors: Pierre-Alexandre Bazin
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.LinearAlgebra.Dfinsupp
+import Mathlib.LinearAlgebra.DFinsupp
 import Mathlib.RingTheory.Ideal.Operations
 
 /-!

Changes are of the form

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

@@ -93,12 +93,12 @@ theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι 
     rw [eq_top_iff_one, Submodule.mem_sup] at this
     obtain ⟨u, hu, v, hv, huv⟩ := this
     refine' ⟨fun i => if hi : i = a then ⟨v, _⟩ else ⟨u * μ i, _⟩, _⟩
-    · simp only [mem_iInf] at hv⊢
+    · simp only [mem_iInf] at hv ⊢
       intro j hj ij
       rw [Finset.mem_cons, ← hi] at hj
       exact hv _ (hj.resolve_left ij)
     · have := Submodule.coe_mem (μ i)
-      simp only [mem_iInf] at this⊢
+      simp only [mem_iInf] at this ⊢
       intro j hj ij
       rcases Finset.mem_cons.mp hj with (rfl | hj)
       · exact mul_mem_right _ _ hu

@@ -32,7 +32,7 @@ For example with three ideals : `I ⊔ J = I ⊔ K = J ⊔ K = ⊤ ↔ (I ⊓ J)
 When ideals are all of the form `I i = R ∙ s i`, this is equivalent to the
 `exists_sum_eq_one_iff_pairwise_coprime` lemma.-/
 theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι → Ideal R) :
-    (⨆ i ∈ t, ⨅ (j) (_hj : j ∈ t) (_ij : j ≠ i), I j) = ⊤ ↔
+    (⨆ i ∈ t, ⨅ (j) (_ : j ∈ t) (_ : j ≠ i), I j) = ⊤ ↔
       (t : Set ι).Pairwise fun i j => I i ⊔ I j = ⊤ := by
   haveI : DecidableEq ι := Classical.decEq ι
   rw [eq_top_iff_one, Submodule.mem_iSup_finset_iff_exists_sum]

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

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

@@ -31,11 +31,11 @@ For example with three ideals : `I ⊔ J = I ⊔ K = J ⊔ K = ⊤ ↔ (I ⊓ J)
 
 When ideals are all of the form `I i = R ∙ s i`, this is equivalent to the
 `exists_sum_eq_one_iff_pairwise_coprime` lemma.-/
-theorem supᵢ_infᵢ_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι → Ideal R) :
+theorem iSup_iInf_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I : ι → Ideal R) :
     (⨆ i ∈ t, ⨅ (j) (_hj : j ∈ t) (_ij : j ≠ i), I j) = ⊤ ↔
       (t : Set ι).Pairwise fun i j => I i ⊔ I j = ⊤ := by
   haveI : DecidableEq ι := Classical.decEq ι
-  rw [eq_top_iff_one, Submodule.mem_supᵢ_finset_iff_exists_sum]
+  rw [eq_top_iff_one, Submodule.mem_iSup_finset_iff_exists_sum]
   refine' h.cons_induction _ _ <;> clear t h
   · simp only [Finset.sum_singleton, Finset.coe_singleton, Set.pairwise_singleton, iff_true_iff]
     refine' fun a => ⟨fun i => if h : i = a then ⟨1, _⟩ else 0, _⟩
@@ -51,18 +51,18 @@ theorem supᵢ_infᵢ_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I :
     refine ⟨ih.mp ⟨Pi.single h.choose ⟨μ a, ?a1⟩ + fun i => ⟨μ i, ?a2⟩, ?a3⟩, fun b hb ab => ?a4⟩
     case a1 =>
       have := Submodule.coe_mem (μ a)
-      rw [mem_infᵢ] at this ⊢
-      --for some reason `simp only [mem_infᵢ]` times out
+      rw [mem_iInf] at this ⊢
+      --for some reason `simp only [mem_iInf]` times out
       intro i
       specialize this i
-      rw [mem_infᵢ, mem_infᵢ] at this ⊢
+      rw [mem_iInf, mem_iInf] at this ⊢
       intro hi _
       apply this (Finset.subset_cons _ hi)
       rintro rfl
       exact hat hi
     case a2 =>
       have := Submodule.coe_mem (μ i)
-      simp only [mem_infᵢ] at this ⊢
+      simp only [mem_iInf] at this ⊢
       intro j hj ij
       exact this _ (Finset.subset_cons _ hj) ij
     case a3 =>
@@ -80,25 +80,25 @@ theorem supᵢ_infᵢ_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I :
       refine' ⟨_, _, _, _, hμ⟩
       · refine' sum_mem _ fun x hx => _
         have := Submodule.coe_mem (μ x)
-        simp only [mem_infᵢ] at this
+        simp only [mem_iInf] at this
         apply this _ (Finset.mem_cons_self _ _)
         rintro rfl
         exact hat hx
       · have := Submodule.coe_mem (μ a)
-        simp only [mem_infᵢ] at this
+        simp only [mem_iInf] at this
         exact this _ (Finset.subset_cons _ hb) ab.symm
   · rintro ⟨hs, Hb⟩
     obtain ⟨μ, hμ⟩ := ih.mpr hs
-    have := sup_infᵢ_eq_top fun b hb => Hb b hb (ne_of_mem_of_not_mem hb hat).symm
+    have := sup_iInf_eq_top fun b hb => Hb b hb (ne_of_mem_of_not_mem hb hat).symm
     rw [eq_top_iff_one, Submodule.mem_sup] at this
     obtain ⟨u, hu, v, hv, huv⟩ := this
     refine' ⟨fun i => if hi : i = a then ⟨v, _⟩ else ⟨u * μ i, _⟩, _⟩
-    · simp only [mem_infᵢ] at hv⊢
+    · simp only [mem_iInf] at hv⊢
       intro j hj ij
       rw [Finset.mem_cons, ← hi] at hj
       exact hv _ (hj.resolve_left ij)
     · have := Submodule.coe_mem (μ i)
-      simp only [mem_infᵢ] at this⊢
+      simp only [mem_iInf] at this⊢
       intro j hj ij
       rcases Finset.mem_cons.mp hj with (rfl | hj)
       · exact mul_mem_right _ _ hu
@@ -113,6 +113,6 @@ theorem supᵢ_infᵢ_eq_top_iff_pairwise {t : Finset ι} (h : t.Nonempty) (I :
       rw [dif_neg]
       rintro rfl
       exact hat hj
-#align ideal.supr_infi_eq_top_iff_pairwise Ideal.supᵢ_infᵢ_eq_top_iff_pairwise
+#align ideal.supr_infi_eq_top_iff_pairwise Ideal.iSup_iInf_eq_top_iff_pairwise
 
 end Ideal

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>