algebra.squarefree | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

00d163e3

(last sync)

feat(ring_theory/zmod): Criterion for zmod to be a reduced ring (#16998)

I couldn't find a good place for this without adding some imports, so a new file seemed appropriate.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

Diff

@@ -255,3 +255,14 @@ begin
 end
 
 end unique_factorization_monoid
+
+namespace int
+
+@[simp] lemma squarefree_nat_abs {n : ℤ} : squarefree n.nat_abs ↔ squarefree n :=
+by simp_rw [squarefree, nat_abs_surjective.forall, ←nat_abs_mul, nat_abs_dvd_iff_dvd,
+  is_unit_iff_nat_abs_eq, nat.is_unit_iff]
+
+@[simp] lemma squarefree_coe_nat {n : ℕ} : squarefree (n : ℤ) ↔ squarefree n :=
+by rw [←squarefree_nat_abs, nat_abs_of_nat]
+
+end int

79de90f7

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

00d163e3

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -322,11 +322,11 @@ theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
 #align int.squarefree_nat_abs Int.squarefree_natAbs
 -/
 
-#print Int.squarefree_coe_nat /-
+#print Int.squarefree_natCast /-
 @[simp]
-theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
+theorem squarefree_natCast {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
   rw [← squarefree_nat_abs, nat_abs_of_nat]
-#align int.squarefree_coe_nat Int.squarefree_coe_nat
+#align int.squarefree_coe_nat Int.squarefree_natCast
 -/
 
 end Int

00d163e3

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -78,7 +78,7 @@ theorem Squarefree.ne_zero [MonoidWithZero R] [Nontrivial R] {m : R} (hm : Squar
 theorem Irreducible.squarefree [CommMonoid R] {x : R} (h : Irreducible x) : Squarefree x :=
   by
   rintro y ⟨z, hz⟩
-  rw [mul_assoc] at hz 
+  rw [mul_assoc] at hz
   rcases h.is_unit_or_is_unit hz with (hu | hu)
   · exact hu
   · apply isUnit_of_mul_isUnit_left hu
@@ -231,8 +231,8 @@ theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefr
   by
   rintro z ⟨w, rfl⟩
   specialize h 2 (z * w) ⟨w, by simp_rw [pow_two, mul_left_comm, ← mul_assoc]⟩
-  rwa [← one_mul (z * w), mul_assoc, mul_dvd_mul_iff_right, ← isUnit_iff_dvd_one] at h 
-  rw [mul_assoc, mul_ne_zero_iff] at h0 ; exact h0.2
+  rwa [← one_mul (z * w), mul_assoc, mul_dvd_mul_iff_right, ← isUnit_iff_dvd_one] at h
+  rw [mul_assoc, mul_ne_zero_iff] at h0; exact h0.2
 #align is_radical.squarefree IsRadical.squarefree
 -/
 
@@ -248,7 +248,7 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
           replace hy := ((dvd_gcd_iff x x _).2 ⟨dvd_rfl, hy⟩).trans gcd_pow_right_dvd_pow_gcd
           obtain ⟨z, hz⟩ := gcd_dvd_left x y
           nth_rw 1 [hz] at hy ⊢
-          rw [pow_two, mul_dvd_mul_iff_left h] at hy 
+          rw [pow_two, mul_dvd_mul_iff_left h] at hy
           obtain ⟨w, hw⟩ := hy
           exact (hx z ⟨w, by rwa [mul_right_comm, ← hw]⟩).mul_right_dvd.2 dvd_rfl)
 #align squarefree.is_radical Squarefree.isRadical
@@ -286,7 +286,7 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
     · have ha := irreducible_of_normalized_factor _ hmem
       rcases h a with (h | h)
       · rw [← normalize_normalized_factor _ hmem]
-        rw [multiplicity_eq_count_normalized_factors ha x0] at h 
+        rw [multiplicity_eq_count_normalized_factors ha x0] at h
         assumption_mod_cast
       · have := ha.1; contradiction
     · simp [Multiset.count_eq_zero_of_not_mem hmem]

00d163e3

bump to nightly-2024-02-14-08

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

b742255f

Diff

@@ -301,13 +301,13 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
 #align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors
 -/
 
-#print UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree /-
-theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
-    x ∣ y ^ n ↔ x ∣ y := by
+#print Squarefree.dvd_pow_iff_dvd /-
+theorem dvd_pow_iff_dvd {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) : x ∣ y ^ n ↔ x ∣ y :=
+  by
   classical
   haveI := UniqueFactorizationMonoid.toGCDMonoid R
   exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
-#align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
+#align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree Squarefree.dvd_pow_iff_dvd
 -/
 
 end UniqueFactorizationMonoid

00d163e3

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -153,6 +153,21 @@ variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 #print multiplicity.finite_prime_left /-
 theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
   classical
+  revert hb
+  refine'
+    WfDvdMonoid.induction_on_irreducible b (by contradiction) (fun u hu hu' => _)
+      fun b p hb hp ih hpb => _
+  · rw [multiplicity.finite_iff_dom, multiplicity.isUnit_right ha.not_unit hu]
+    exact PartENat.dom_natCast 0
+  · refine'
+      multiplicity.finite_mul ha
+        (multiplicity.finite_iff_dom.mpr
+          (PartENat.dom_of_le_natCast (show multiplicity a p ≤ ↑1 from _)))
+        (ih hb)
+    norm_cast
+    exact
+      ((multiplicity.squarefree_iff_multiplicity_le_one p).mp hp.squarefree a).resolve_right
+        ha.not_unit
 #align multiplicity.finite_prime_left multiplicity.finite_prime_left
 -/
 
@@ -262,7 +277,7 @@ variable [CancelCommMonoidWithZero R] [UniqueFactorizationMonoid R]
 theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) :=
   by
-  have drel : DecidableRel (Dvd.Dvd : R → R → Prop) := by classical
+  have drel : DecidableRel (Dvd.Dvd : R → R → Prop) := by classical infer_instance
   haveI := drel
   rw [multiplicity.squarefree_iff_multiplicity_le_one, Multiset.nodup_iff_count_le_one]
   haveI := nontrivial_of_ne x 0 x0
@@ -288,7 +303,10 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
 
 #print UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree /-
 theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
-    x ∣ y ^ n ↔ x ∣ y := by classical
+    x ∣ y ^ n ↔ x ∣ y := by
+  classical
+  haveI := UniqueFactorizationMonoid.toGCDMonoid R
+  exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
 #align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
 -/

00d163e3

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -153,21 +153,6 @@ variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 #print multiplicity.finite_prime_left /-
 theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
   classical
-  revert hb
-  refine'
-    WfDvdMonoid.induction_on_irreducible b (by contradiction) (fun u hu hu' => _)
-      fun b p hb hp ih hpb => _
-  · rw [multiplicity.finite_iff_dom, multiplicity.isUnit_right ha.not_unit hu]
-    exact PartENat.dom_natCast 0
-  · refine'
-      multiplicity.finite_mul ha
-        (multiplicity.finite_iff_dom.mpr
-          (PartENat.dom_of_le_natCast (show multiplicity a p ≤ ↑1 from _)))
-        (ih hb)
-    norm_cast
-    exact
-      ((multiplicity.squarefree_iff_multiplicity_le_one p).mp hp.squarefree a).resolve_right
-        ha.not_unit
 #align multiplicity.finite_prime_left multiplicity.finite_prime_left
 -/
 
@@ -277,7 +262,7 @@ variable [CancelCommMonoidWithZero R] [UniqueFactorizationMonoid R]
 theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) :=
   by
-  have drel : DecidableRel (Dvd.Dvd : R → R → Prop) := by classical infer_instance
+  have drel : DecidableRel (Dvd.Dvd : R → R → Prop) := by classical
   haveI := drel
   rw [multiplicity.squarefree_iff_multiplicity_le_one, Multiset.nodup_iff_count_le_one]
   haveI := nontrivial_of_ne x 0 x0
@@ -303,10 +288,7 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
 
 #print UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree /-
 theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
-    x ∣ y ^ n ↔ x ∣ y := by
-  classical
-  haveI := UniqueFactorizationMonoid.toGCDMonoid R
-  exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
+    x ∣ y ^ n ↔ x ∣ y := by classical
 #align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
 -/

00d163e3

bump to nightly-2023-11-05-06

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

acc3325f

Diff

@@ -139,7 +139,7 @@ theorem squarefree_iff_multiplicity_le_one (r : R) :
     Squarefree r ↔ ∀ x : R, multiplicity x r ≤ 1 ∨ IsUnit x :=
   by
   refine' forall_congr' fun a => _
-  rw [← sq, pow_dvd_iff_le_multiplicity, or_iff_not_imp_left, not_le, imp_congr _ Iff.rfl]
+  rw [← sq, pow_dvd_iff_le_multiplicity, Classical.or_iff_not_imp_left, not_le, imp_congr _ Iff.rfl]
   simpa using PartENat.add_one_le_iff_lt (PartENat.natCast_ne_top 1)
 #align multiplicity.squarefree_iff_multiplicity_le_one multiplicity.squarefree_iff_multiplicity_le_one
 -/
@@ -290,7 +290,7 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
         assumption_mod_cast
       · have := ha.1; contradiction
     · simp [Multiset.count_eq_zero_of_not_mem hmem]
-  · rw [or_iff_not_imp_right]; intro hu
+  · rw [Classical.or_iff_not_imp_right]; intro hu
     by_cases h0 : a = 0
     · simp [h0, x0]
     rcases WfDvdMonoid.exists_irreducible_factor hu h0 with ⟨b, hib, hdvd⟩

00d163e3

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -60,7 +60,7 @@ theorem squarefree_one [CommMonoid R] : Squarefree (1 : R) :=
 @[simp]
 theorem not_squarefree_zero [MonoidWithZero R] [Nontrivial R] : ¬Squarefree (0 : R) :=
   by
-  erw [not_forall]
+  erw [Classical.not_forall]
   exact ⟨0, by simp⟩
 #align not_squarefree_zero not_squarefree_zero
 -/

00d163e3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
-import Mathbin.RingTheory.UniqueFactorizationDomain
+import RingTheory.UniqueFactorizationDomain
 
 #align_import algebra.squarefree from "leanprover-community/mathlib"@"00d163e35035c3577c1c79fa53b68de17781ffc1"

00d163e3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module algebra.squarefree
-! leanprover-community/mathlib commit 00d163e35035c3577c1c79fa53b68de17781ffc1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.UniqueFactorizationDomain
 
+#align_import algebra.squarefree from "leanprover-community/mathlib"@"00d163e35035c3577c1c79fa53b68de17781ffc1"
+
 /-!
 # Squarefree elements of monoids

00d163e3

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -52,23 +52,29 @@ theorem IsUnit.squarefree [CommMonoid R] {x : R} (h : IsUnit x) : Squarefree x :
 #align is_unit.squarefree IsUnit.squarefree
 -/
 
+#print squarefree_one /-
 @[simp]
 theorem squarefree_one [CommMonoid R] : Squarefree (1 : R) :=
   isUnit_one.Squarefree
 #align squarefree_one squarefree_one
+-/
 
+#print not_squarefree_zero /-
 @[simp]
 theorem not_squarefree_zero [MonoidWithZero R] [Nontrivial R] : ¬Squarefree (0 : R) :=
   by
   erw [not_forall]
   exact ⟨0, by simp⟩
 #align not_squarefree_zero not_squarefree_zero
+-/
 
+#print Squarefree.ne_zero /-
 theorem Squarefree.ne_zero [MonoidWithZero R] [Nontrivial R] {m : R} (hm : Squarefree (m : R)) :
     m ≠ 0 := by
   rintro rfl
   exact not_squarefree_zero hm
 #align squarefree.ne_zero Squarefree.ne_zero
+-/
 
 #print Irreducible.squarefree /-
 @[simp]
@@ -89,13 +95,17 @@ theorem Prime.squarefree [CancelCommMonoidWithZero R] {x : R} (h : Prime x) : Sq
 #align prime.squarefree Prime.squarefree
 -/
 
+#print Squarefree.of_mul_left /-
 theorem Squarefree.of_mul_left [CommMonoid R] {m n : R} (hmn : Squarefree (m * n)) : Squarefree m :=
   fun p hp => hmn p (dvd_mul_of_dvd_left hp n)
 #align squarefree.of_mul_left Squarefree.of_mul_left
+-/
 
+#print Squarefree.of_mul_right /-
 theorem Squarefree.of_mul_right [CommMonoid R] {m n : R} (hmn : Squarefree (m * n)) :
     Squarefree n := fun p hp => hmn p (dvd_mul_of_dvd_right hp m)
 #align squarefree.of_mul_right Squarefree.of_mul_right
+-/
 
 #print Squarefree.squarefree_of_dvd /-
 theorem Squarefree.squarefree_of_dvd [CommMonoid R] {x y : R} (hdvd : x ∣ y) (hsq : Squarefree y) :
@@ -143,6 +153,7 @@ section CancelCommMonoidWithZero
 
 variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 
+#print multiplicity.finite_prime_left /-
 theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
   classical
   revert hb
@@ -161,6 +172,7 @@ theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity
       ((multiplicity.squarefree_iff_multiplicity_le_one p).mp hp.squarefree a).resolve_right
         ha.not_unit
 #align multiplicity.finite_prime_left multiplicity.finite_prime_left
+-/
 
 end CancelCommMonoidWithZero
 
@@ -170,6 +182,7 @@ section Irreducible
 
 variable [CommMonoidWithZero R] [WfDvdMonoid R]
 
+#print irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree /-
 theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r : R) :
     (∀ x : R, Irreducible x → ¬x * x ∣ r) ↔ (r = 0 ∧ ∀ x : R, ¬Irreducible x) ∨ Squarefree r :=
   by
@@ -192,18 +205,23 @@ theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r
   obtain ⟨j, hj₁, hj₂⟩ := WfDvdMonoid.exists_irreducible_factor i this
   exact h _ hj₁ ((mul_dvd_mul hj₂ hj₂).trans hx)
 #align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree
+-/
 
+#print squarefree_iff_irreducible_sq_not_dvd_of_ne_zero /-
 theorem squarefree_iff_irreducible_sq_not_dvd_of_ne_zero {r : R} (hr : r ≠ 0) :
     Squarefree r ↔ ∀ x : R, Irreducible x → ¬x * x ∣ r := by
   simpa [hr] using (irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree r).symm
 #align squarefree_iff_irreducible_sq_not_dvd_of_ne_zero squarefree_iff_irreducible_sq_not_dvd_of_ne_zero
+-/
 
+#print squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible /-
 theorem squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible {r : R}
     (hr : ∃ x : R, Irreducible x) : Squarefree r ↔ ∀ x : R, Irreducible x → ¬x * x ∣ r :=
   by
   rw [irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree, ← not_exists]
   simp only [hr, not_true, false_or_iff, and_false_iff]
 #align squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible
+-/
 
 end Irreducible
 
@@ -211,6 +229,7 @@ section IsRadical
 
 variable [CancelCommMonoidWithZero R]
 
+#print IsRadical.squarefree /-
 theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefree x :=
   by
   rintro z ⟨w, rfl⟩
@@ -218,6 +237,7 @@ theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefr
   rwa [← one_mul (z * w), mul_assoc, mul_dvd_mul_iff_right, ← isUnit_iff_dvd_one] at h 
   rw [mul_assoc, mul_ne_zero_iff] at h0 ; exact h0.2
 #align is_radical.squarefree IsRadical.squarefree
+-/
 
 variable [GCDMonoid R]
 
@@ -237,14 +257,18 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
 #align squarefree.is_radical Squarefree.isRadical
 -/
 
+#print isRadical_iff_squarefree_or_zero /-
 theorem isRadical_iff_squarefree_or_zero {x : R} : IsRadical x ↔ Squarefree x ∨ x = 0 :=
   ⟨fun hx => (em <| x = 0).elim Or.inr fun h => Or.inl <| hx.Squarefree h,
     Or.ndrec Squarefree.isRadical <| by rintro rfl; rw [zero_isRadical_iff]; infer_instance⟩
 #align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zero
+-/
 
+#print isRadical_iff_squarefree_of_ne_zero /-
 theorem isRadical_iff_squarefree_of_ne_zero {x : R} (h : x ≠ 0) : IsRadical x ↔ Squarefree x :=
   ⟨IsRadical.squarefree h, Squarefree.isRadical⟩
 #align is_radical_iff_squarefree_of_ne_zero isRadical_iff_squarefree_of_ne_zero
+-/
 
 end IsRadical
 
@@ -252,6 +276,7 @@ namespace UniqueFactorizationMonoid
 
 variable [CancelCommMonoidWithZero R] [UniqueFactorizationMonoid R]
 
+#print UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors /-
 theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) :=
   by
@@ -277,6 +302,7 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
     specialize h (normalize b)
     assumption_mod_cast
 #align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors
+-/
 
 #print UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree /-
 theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
@@ -291,16 +317,20 @@ end UniqueFactorizationMonoid
 
 namespace Int
 
+#print Int.squarefree_natAbs /-
 @[simp]
 theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
   simp_rw [Squarefree, nat_abs_surjective.forall, ← nat_abs_mul, nat_abs_dvd_iff_dvd,
     is_unit_iff_nat_abs_eq, Nat.isUnit_iff]
 #align int.squarefree_nat_abs Int.squarefree_natAbs
+-/
 
+#print Int.squarefree_coe_nat /-
 @[simp]
 theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
   rw [← squarefree_nat_abs, nat_abs_of_nat]
 #align int.squarefree_coe_nat Int.squarefree_coe_nat
+-/
 
 end Int

00d163e3

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -145,21 +145,21 @@ variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 
 theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
   classical
-    revert hb
-    refine'
-      WfDvdMonoid.induction_on_irreducible b (by contradiction) (fun u hu hu' => _)
-        fun b p hb hp ih hpb => _
-    · rw [multiplicity.finite_iff_dom, multiplicity.isUnit_right ha.not_unit hu]
-      exact PartENat.dom_natCast 0
-    · refine'
-        multiplicity.finite_mul ha
-          (multiplicity.finite_iff_dom.mpr
-            (PartENat.dom_of_le_natCast (show multiplicity a p ≤ ↑1 from _)))
-          (ih hb)
-      norm_cast
-      exact
-        ((multiplicity.squarefree_iff_multiplicity_le_one p).mp hp.squarefree a).resolve_right
-          ha.not_unit
+  revert hb
+  refine'
+    WfDvdMonoid.induction_on_irreducible b (by contradiction) (fun u hu hu' => _)
+      fun b p hb hp ih hpb => _
+  · rw [multiplicity.finite_iff_dom, multiplicity.isUnit_right ha.not_unit hu]
+    exact PartENat.dom_natCast 0
+  · refine'
+      multiplicity.finite_mul ha
+        (multiplicity.finite_iff_dom.mpr
+          (PartENat.dom_of_le_natCast (show multiplicity a p ≤ ↑1 from _)))
+        (ih hb)
+    norm_cast
+    exact
+      ((multiplicity.squarefree_iff_multiplicity_le_one p).mp hp.squarefree a).resolve_right
+        ha.not_unit
 #align multiplicity.finite_prime_left multiplicity.finite_prime_left
 
 end CancelCommMonoidWithZero
@@ -282,8 +282,8 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
 theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
     x ∣ y ^ n ↔ x ∣ y := by
   classical
-    haveI := UniqueFactorizationMonoid.toGCDMonoid R
-    exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
+  haveI := UniqueFactorizationMonoid.toGCDMonoid R
+  exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
 #align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
 -/

00d163e3

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -75,7 +75,7 @@ theorem Squarefree.ne_zero [MonoidWithZero R] [Nontrivial R] {m : R} (hm : Squar
 theorem Irreducible.squarefree [CommMonoid R] {x : R} (h : Irreducible x) : Squarefree x :=
   by
   rintro y ⟨z, hz⟩
-  rw [mul_assoc] at hz
+  rw [mul_assoc] at hz 
   rcases h.is_unit_or_is_unit hz with (hu | hu)
   · exact hu
   · apply isUnit_of_mul_isUnit_left hu
@@ -215,8 +215,8 @@ theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefr
   by
   rintro z ⟨w, rfl⟩
   specialize h 2 (z * w) ⟨w, by simp_rw [pow_two, mul_left_comm, ← mul_assoc]⟩
-  rwa [← one_mul (z * w), mul_assoc, mul_dvd_mul_iff_right, ← isUnit_iff_dvd_one] at h
-  rw [mul_assoc, mul_ne_zero_iff] at h0; exact h0.2
+  rwa [← one_mul (z * w), mul_assoc, mul_dvd_mul_iff_right, ← isUnit_iff_dvd_one] at h 
+  rw [mul_assoc, mul_ne_zero_iff] at h0 ; exact h0.2
 #align is_radical.squarefree IsRadical.squarefree
 
 variable [GCDMonoid R]
@@ -230,8 +230,8 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
           by_cases gcd x y = 0; · rw [h]; apply dvd_zero
           replace hy := ((dvd_gcd_iff x x _).2 ⟨dvd_rfl, hy⟩).trans gcd_pow_right_dvd_pow_gcd
           obtain ⟨z, hz⟩ := gcd_dvd_left x y
-          nth_rw 1 [hz] at hy⊢
-          rw [pow_two, mul_dvd_mul_iff_left h] at hy
+          nth_rw 1 [hz] at hy ⊢
+          rw [pow_two, mul_dvd_mul_iff_left h] at hy 
           obtain ⟨w, hw⟩ := hy
           exact (hx z ⟨w, by rwa [mul_right_comm, ← hw]⟩).mul_right_dvd.2 dvd_rfl)
 #align squarefree.is_radical Squarefree.isRadical
@@ -264,7 +264,7 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
     · have ha := irreducible_of_normalized_factor _ hmem
       rcases h a with (h | h)
       · rw [← normalize_normalized_factor _ hmem]
-        rw [multiplicity_eq_count_normalized_factors ha x0] at h
+        rw [multiplicity_eq_count_normalized_factors ha x0] at h 
         assumption_mod_cast
       · have := ha.1; contradiction
     · simp [Multiset.count_eq_zero_of_not_mem hmem]

00d163e3

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -52,23 +52,11 @@ theorem IsUnit.squarefree [CommMonoid R] {x : R} (h : IsUnit x) : Squarefree x :
 #align is_unit.squarefree IsUnit.squarefree
 -/
 
-/- warning: squarefree_one -> squarefree_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R], Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R], Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align squarefree_one squarefree_oneₓ'. -/
 @[simp]
 theorem squarefree_one [CommMonoid R] : Squarefree (1 : R) :=
   isUnit_one.Squarefree
 #align squarefree_one squarefree_one
 
-/- warning: not_squarefree_zero -> not_squarefree_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} R] [_inst_2 : Nontrivial.{u1} R], Not (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R _inst_1)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} R] [_inst_2 : Nontrivial.{u1} R], Not (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align not_squarefree_zero not_squarefree_zeroₓ'. -/
 @[simp]
 theorem not_squarefree_zero [MonoidWithZero R] [Nontrivial R] : ¬Squarefree (0 : R) :=
   by
@@ -76,12 +64,6 @@ theorem not_squarefree_zero [MonoidWithZero R] [Nontrivial R] : ¬Squarefree (0
   exact ⟨0, by simp⟩
 #align not_squarefree_zero not_squarefree_zero
 
-/- warning: squarefree.ne_zero -> Squarefree.ne_zero is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align squarefree.ne_zero Squarefree.ne_zeroₓ'. -/
 theorem Squarefree.ne_zero [MonoidWithZero R] [Nontrivial R] {m : R} (hm : Squarefree (m : R)) :
     m ≠ 0 := by
   rintro rfl
@@ -107,22 +89,10 @@ theorem Prime.squarefree [CancelCommMonoidWithZero R] {x : R} (h : Prime x) : Sq
 #align prime.squarefree Prime.squarefree
 -/
 
-/- warning: squarefree.of_mul_left -> Squarefree.of_mul_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align squarefree.of_mul_left Squarefree.of_mul_leftₓ'. -/
 theorem Squarefree.of_mul_left [CommMonoid R] {m n : R} (hmn : Squarefree (m * n)) : Squarefree m :=
   fun p hp => hmn p (dvd_mul_of_dvd_left hp n)
 #align squarefree.of_mul_left Squarefree.of_mul_left
 
-/- warning: squarefree.of_mul_right -> Squarefree.of_mul_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] {m : R} {n : R}, (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)))) m n)) -> (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) n)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] {m : R} {n : R}, (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)))) m n)) -> (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) n)
-Case conversion may be inaccurate. Consider using '#align squarefree.of_mul_right Squarefree.of_mul_rightₓ'. -/
 theorem Squarefree.of_mul_right [CommMonoid R] {m n : R} (hmn : Squarefree (m * n)) :
     Squarefree n := fun p hp => hmn p (dvd_mul_of_dvd_right hp m)
 #align squarefree.of_mul_right Squarefree.of_mul_right
@@ -173,12 +143,6 @@ section CancelCommMonoidWithZero
 
 variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 
-/- warning: multiplicity.finite_prime_left -> multiplicity.finite_prime_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)] {a : R} {b : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) a) -> (Ne.{succ u1} R b (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (multiplicity.Finite.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) a b)
-Case conversion may be inaccurate. Consider using '#align multiplicity.finite_prime_left multiplicity.finite_prime_leftₓ'. -/
 theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
   classical
     revert hb
@@ -206,12 +170,6 @@ section Irreducible
 
 variable [CommMonoidWithZero R] [WfDvdMonoid R]
 
-/- warning: irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree -> irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefreeₓ'. -/
 theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r : R) :
     (∀ x : R, Irreducible x → ¬x * x ∣ r) ↔ (r = 0 ∧ ∀ x : R, ¬Irreducible x) ∨ Squarefree r :=
   by
@@ -235,23 +193,11 @@ theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r
   exact h _ hj₁ ((mul_dvd_mul hj₂ hj₂).trans hx)
 #align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree
 
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-Case conversion may be inaccurate. Consider using '#align squarefree_iff_irreducible_sq_not_dvd_of_ne_zero squarefree_iff_irreducible_sq_not_dvd_of_ne_zeroₓ'. -/
 theorem squarefree_iff_irreducible_sq_not_dvd_of_ne_zero {r : R} (hr : r ≠ 0) :
     Squarefree r ↔ ∀ x : R, Irreducible x → ¬x * x ∣ r := by
   simpa [hr] using (irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree r).symm
 #align squarefree_iff_irreducible_sq_not_dvd_of_ne_zero squarefree_iff_irreducible_sq_not_dvd_of_ne_zero
 
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] {r : R}, (Exists.{succ u1} R (fun (x : R) => Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x)) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r) (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))))
-Case conversion may be inaccurate. Consider using '#align squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducibleₓ'. -/
 theorem squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible {r : R}
     (hr : ∃ x : R, Irreducible x) : Squarefree r ↔ ∀ x : R, Irreducible x → ¬x * x ∣ r :=
   by
@@ -265,12 +211,6 @@ section IsRadical
 
 variable [CancelCommMonoidWithZero R]
 
-/- warning: is_radical.squarefree -> IsRadical.squarefree is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) -> (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) -> (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x)
-Case conversion may be inaccurate. Consider using '#align is_radical.squarefree IsRadical.squarefreeₓ'. -/
 theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefree x :=
   by
   rintro z ⟨w, rfl⟩
@@ -297,23 +237,11 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
 #align squarefree.is_radical Squarefree.isRadical
 -/
 
-/- warning: is_radical_iff_squarefree_or_zero -> isRadical_iff_squarefree_or_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Or (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Or (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zeroₓ'. -/
 theorem isRadical_iff_squarefree_or_zero {x : R} : IsRadical x ↔ Squarefree x ∨ x = 0 :=
   ⟨fun hx => (em <| x = 0).elim Or.inr fun h => Or.inl <| hx.Squarefree h,
     Or.ndrec Squarefree.isRadical <| by rintro rfl; rw [zero_isRadical_iff]; infer_instance⟩
 #align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zero
 
-/- warning: is_radical_iff_squarefree_of_ne_zero -> isRadical_iff_squarefree_of_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x))
-Case conversion may be inaccurate. Consider using '#align is_radical_iff_squarefree_of_ne_zero isRadical_iff_squarefree_of_ne_zeroₓ'. -/
 theorem isRadical_iff_squarefree_of_ne_zero {x : R} (h : x ≠ 0) : IsRadical x ↔ Squarefree x :=
   ⟨IsRadical.squarefree h, Squarefree.isRadical⟩
 #align is_radical_iff_squarefree_of_ne_zero isRadical_iff_squarefree_of_ne_zero
@@ -324,12 +252,6 @@ namespace UniqueFactorizationMonoid
 
 variable [CancelCommMonoidWithZero R] [UniqueFactorizationMonoid R]
 
-/- warning: unique_factorization_monoid.squarefree_iff_nodup_normalized_factors -> UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : UniqueFactorizationMonoid.{u1} R _inst_1] [_inst_3 : NormalizationMonoid.{u1} R _inst_1] [_inst_4 : DecidableEq.{succ u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Multiset.Nodup.{u1} R (UniqueFactorizationMonoid.normalizedFactors.{u1} R _inst_1 (fun (a : R) (b : R) => _inst_4 a b) _inst_3 _inst_2 x)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : UniqueFactorizationMonoid.{u1} R _inst_1] [_inst_3 : NormalizationMonoid.{u1} R _inst_1] [_inst_4 : DecidableEq.{succ u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Multiset.Nodup.{u1} R (UniqueFactorizationMonoid.normalizedFactors.{u1} R _inst_1 (fun (a : R) (b : R) => _inst_4 a b) _inst_3 _inst_2 x)))
-Case conversion may be inaccurate. Consider using '#align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactorsₓ'. -/
 theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) :=
   by
@@ -369,24 +291,12 @@ end UniqueFactorizationMonoid
 
 namespace Int
 
-/- warning: int.squarefree_nat_abs -> Int.squarefree_natAbs is a dubious translation:
-lean 3 declaration is
-  forall {n : Int}, Iff (Squarefree.{0} Nat Nat.monoid (Int.natAbs n)) (Squarefree.{0} Int Int.monoid n)
-but is expected to have type
-  forall {n : Int}, Iff (Squarefree.{0} Nat Nat.monoid (Int.natAbs n)) (Squarefree.{0} Int Int.instMonoidInt n)
-Case conversion may be inaccurate. Consider using '#align int.squarefree_nat_abs Int.squarefree_natAbsₓ'. -/
 @[simp]
 theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
   simp_rw [Squarefree, nat_abs_surjective.forall, ← nat_abs_mul, nat_abs_dvd_iff_dvd,
     is_unit_iff_nat_abs_eq, Nat.isUnit_iff]
 #align int.squarefree_nat_abs Int.squarefree_natAbs
 
-/- warning: int.squarefree_coe_nat -> Int.squarefree_coe_nat is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat}, Iff (Squarefree.{0} Int Int.monoid ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) (Squarefree.{0} Nat Nat.monoid n)
-but is expected to have type
-  forall {n : Nat}, Iff (Squarefree.{0} Int Int.instMonoidInt (Nat.cast.{0} Int instNatCastInt n)) (Squarefree.{0} Nat Nat.monoid n)
-Case conversion may be inaccurate. Consider using '#align int.squarefree_coe_nat Int.squarefree_coe_natₓ'. -/
 @[simp]
 theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
   rw [← squarefree_nat_abs, nat_abs_of_nat]

00d163e3

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -287,9 +287,7 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
     And.right <|
       (dvd_gcd_iff x x y).1
         (by
-          by_cases gcd x y = 0;
-          · rw [h]
-            apply dvd_zero
+          by_cases gcd x y = 0; · rw [h]; apply dvd_zero
           replace hy := ((dvd_gcd_iff x x _).2 ⟨dvd_rfl, hy⟩).trans gcd_pow_right_dvd_pow_gcd
           obtain ⟨z, hz⟩ := gcd_dvd_left x y
           nth_rw 1 [hz] at hy⊢
@@ -307,10 +305,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zeroₓ'. -/
 theorem isRadical_iff_squarefree_or_zero {x : R} : IsRadical x ↔ Squarefree x ∨ x = 0 :=
   ⟨fun hx => (em <| x = 0).elim Or.inr fun h => Or.inl <| hx.Squarefree h,
-    Or.ndrec Squarefree.isRadical <| by
-      rintro rfl
-      rw [zero_isRadical_iff]
-      infer_instance⟩
+    Or.ndrec Squarefree.isRadical <| by rintro rfl; rw [zero_isRadical_iff]; infer_instance⟩
 #align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zero
 
 /- warning: is_radical_iff_squarefree_of_ne_zero -> isRadical_iff_squarefree_of_ne_zero is a dubious translation:
@@ -349,11 +344,9 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
       · rw [← normalize_normalized_factor _ hmem]
         rw [multiplicity_eq_count_normalized_factors ha x0] at h
         assumption_mod_cast
-      · have := ha.1
-        contradiction
+      · have := ha.1; contradiction
     · simp [Multiset.count_eq_zero_of_not_mem hmem]
-  · rw [or_iff_not_imp_right]
-    intro hu
+  · rw [or_iff_not_imp_right]; intro hu
     by_cases h0 : a = 0
     · simp [h0, x0]
     rcases WfDvdMonoid.exists_irreducible_factor hu h0 with ⟨b, hib, hdvd⟩

00d163e3

bump to nightly-2023-04-04-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

468d7cfa

Diff

@@ -376,12 +376,24 @@ end UniqueFactorizationMonoid
 
 namespace Int
 
+/- warning: int.squarefree_nat_abs -> Int.squarefree_natAbs is a dubious translation:
+lean 3 declaration is
+  forall {n : Int}, Iff (Squarefree.{0} Nat Nat.monoid (Int.natAbs n)) (Squarefree.{0} Int Int.monoid n)
+but is expected to have type
+  forall {n : Int}, Iff (Squarefree.{0} Nat Nat.monoid (Int.natAbs n)) (Squarefree.{0} Int Int.instMonoidInt n)
+Case conversion may be inaccurate. Consider using '#align int.squarefree_nat_abs Int.squarefree_natAbsₓ'. -/
 @[simp]
 theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
   simp_rw [Squarefree, nat_abs_surjective.forall, ← nat_abs_mul, nat_abs_dvd_iff_dvd,
     is_unit_iff_nat_abs_eq, Nat.isUnit_iff]
 #align int.squarefree_nat_abs Int.squarefree_natAbs
 
+/- warning: int.squarefree_coe_nat -> Int.squarefree_coe_nat is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, Iff (Squarefree.{0} Int Int.monoid ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) (Squarefree.{0} Nat Nat.monoid n)
+but is expected to have type
+  forall {n : Nat}, Iff (Squarefree.{0} Int Int.instMonoidInt (Nat.cast.{0} Int instNatCastInt n)) (Squarefree.{0} Nat Nat.monoid n)
+Case conversion may be inaccurate. Consider using '#align int.squarefree_coe_nat Int.squarefree_coe_natₓ'. -/
 @[simp]
 theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
   rw [← squarefree_nat_abs, nat_abs_of_nat]

00d163e3

bump to nightly-2023-04-04-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

2ee17135

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 
 ! This file was ported from Lean 3 source module algebra.squarefree
-! leanprover-community/mathlib commit c085f3044fe585c575e322bfab45b3633c48d820
+! leanprover-community/mathlib commit 00d163e35035c3577c1c79fa53b68de17781ffc1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -374,3 +374,18 @@ theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (
 
 end UniqueFactorizationMonoid
 
+namespace Int
+
+@[simp]
+theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
+  simp_rw [Squarefree, nat_abs_surjective.forall, ← nat_abs_mul, nat_abs_dvd_iff_dvd,
+    is_unit_iff_nat_abs_eq, Nat.isUnit_iff]
+#align int.squarefree_nat_abs Int.squarefree_natAbs
+
+@[simp]
+theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
+  rw [← squarefree_nat_abs, nat_abs_of_nat]
+#align int.squarefree_coe_nat Int.squarefree_coe_nat
+
+end Int
+

c085f304

bump to nightly-2023-03-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

9354dcbd

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 
 ! This file was ported from Lean 3 source module algebra.squarefree
-! leanprover-community/mathlib commit 79de90f7beca025f469dcda978ae655c4d985946
+! leanprover-community/mathlib commit c085f3044fe585c575e322bfab45b3633c48d820
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.RingTheory.UniqueFactorizationDomain
 
 /-!
 # Squarefree elements of monoids
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 An element of a monoid is squarefree when it is not divisible by any squares
 except the squares of units.

79de90f7

bump to nightly-2023-03-22-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8

2e6ecab9

Diff

@@ -34,22 +34,38 @@ squarefree, multiplicity
 
 variable {R : Type _}
 
+#print Squarefree /-
 /-- An element of a monoid is squarefree if the only squares that
   divide it are the squares of units. -/
 def Squarefree [Monoid R] (r : R) : Prop :=
   ∀ x : R, x * x ∣ r → IsUnit x
 #align squarefree Squarefree
+-/
 
+#print IsUnit.squarefree /-
 @[simp]
 theorem IsUnit.squarefree [CommMonoid R] {x : R} (h : IsUnit x) : Squarefree x := fun y hdvd =>
   isUnit_of_mul_isUnit_left (isUnit_of_dvd_unit hdvd h)
 #align is_unit.squarefree IsUnit.squarefree
+-/
 
+/- warning: squarefree_one -> squarefree_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R], Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R], Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align squarefree_one squarefree_oneₓ'. -/
 @[simp]
 theorem squarefree_one [CommMonoid R] : Squarefree (1 : R) :=
   isUnit_one.Squarefree
 #align squarefree_one squarefree_one
 
+/- warning: not_squarefree_zero -> not_squarefree_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} R] [_inst_2 : Nontrivial.{u1} R], Not (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} R] [_inst_2 : Nontrivial.{u1} R], Not (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R _inst_1) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align not_squarefree_zero not_squarefree_zeroₓ'. -/
 @[simp]
 theorem not_squarefree_zero [MonoidWithZero R] [Nontrivial R] : ¬Squarefree (0 : R) :=
   by
@@ -57,12 +73,19 @@ theorem not_squarefree_zero [MonoidWithZero R] [Nontrivial R] : ¬Squarefree (0
   exact ⟨0, by simp⟩
 #align not_squarefree_zero not_squarefree_zero
 
+/- warning: squarefree.ne_zero -> Squarefree.ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} R] [_inst_2 : Nontrivial.{u1} R] {m : R}, (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R _inst_1) m) -> (Ne.{succ u1} R m (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} R] [_inst_2 : Nontrivial.{u1} R] {m : R}, (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R _inst_1) m) -> (Ne.{succ u1} R m (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align squarefree.ne_zero Squarefree.ne_zeroₓ'. -/
 theorem Squarefree.ne_zero [MonoidWithZero R] [Nontrivial R] {m : R} (hm : Squarefree (m : R)) :
     m ≠ 0 := by
   rintro rfl
   exact not_squarefree_zero hm
 #align squarefree.ne_zero Squarefree.ne_zero
 
+#print Irreducible.squarefree /-
 @[simp]
 theorem Irreducible.squarefree [CommMonoid R] {x : R} (h : Irreducible x) : Squarefree x :=
   by
@@ -72,35 +95,56 @@ theorem Irreducible.squarefree [CommMonoid R] {x : R} (h : Irreducible x) : Squa
   · exact hu
   · apply isUnit_of_mul_isUnit_left hu
 #align irreducible.squarefree Irreducible.squarefree
+-/
 
+#print Prime.squarefree /-
 @[simp]
 theorem Prime.squarefree [CancelCommMonoidWithZero R] {x : R} (h : Prime x) : Squarefree x :=
   h.Irreducible.Squarefree
 #align prime.squarefree Prime.squarefree
+-/
 
+/- warning: squarefree.of_mul_left -> Squarefree.of_mul_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] {m : R} {n : R}, (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)))) m n)) -> (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) m)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] {m : R} {n : R}, (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)))) m n)) -> (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) m)
+Case conversion may be inaccurate. Consider using '#align squarefree.of_mul_left Squarefree.of_mul_leftₓ'. -/
 theorem Squarefree.of_mul_left [CommMonoid R] {m n : R} (hmn : Squarefree (m * n)) : Squarefree m :=
   fun p hp => hmn p (dvd_mul_of_dvd_left hp n)
 #align squarefree.of_mul_left Squarefree.of_mul_left
 
+/- warning: squarefree.of_mul_right -> Squarefree.of_mul_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] {m : R} {n : R}, (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)))) m n)) -> (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] {m : R} {n : R}, (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)))) m n)) -> (Squarefree.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1) n)
+Case conversion may be inaccurate. Consider using '#align squarefree.of_mul_right Squarefree.of_mul_rightₓ'. -/
 theorem Squarefree.of_mul_right [CommMonoid R] {m n : R} (hmn : Squarefree (m * n)) :
     Squarefree n := fun p hp => hmn p (dvd_mul_of_dvd_right hp m)
 #align squarefree.of_mul_right Squarefree.of_mul_right
 
+#print Squarefree.squarefree_of_dvd /-
 theorem Squarefree.squarefree_of_dvd [CommMonoid R] {x y : R} (hdvd : x ∣ y) (hsq : Squarefree y) :
     Squarefree x := fun a h => hsq _ (h.trans hdvd)
 #align squarefree.squarefree_of_dvd Squarefree.squarefree_of_dvd
+-/
 
 section SquarefreeGcdOfSquarefree
 
 variable {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α]
 
+#print Squarefree.gcd_right /-
 theorem Squarefree.gcd_right (a : α) {b : α} (hb : Squarefree b) : Squarefree (gcd a b) :=
   hb.squarefree_of_dvd (gcd_dvd_right _ _)
 #align squarefree.gcd_right Squarefree.gcd_right
+-/
 
+#print Squarefree.gcd_left /-
 theorem Squarefree.gcd_left {a : α} (b : α) (ha : Squarefree a) : Squarefree (gcd a b) :=
   ha.squarefree_of_dvd (gcd_dvd_left _ _)
 #align squarefree.gcd_left Squarefree.gcd_left
+-/
 
 end SquarefreeGcdOfSquarefree
 
@@ -110,6 +154,7 @@ section CommMonoid
 
 variable [CommMonoid R] [DecidableRel (Dvd.Dvd : R → R → Prop)]
 
+#print multiplicity.squarefree_iff_multiplicity_le_one /-
 theorem squarefree_iff_multiplicity_le_one (r : R) :
     Squarefree r ↔ ∀ x : R, multiplicity x r ≤ 1 ∨ IsUnit x :=
   by
@@ -117,6 +162,7 @@ theorem squarefree_iff_multiplicity_le_one (r : R) :
   rw [← sq, pow_dvd_iff_le_multiplicity, or_iff_not_imp_left, not_le, imp_congr _ Iff.rfl]
   simpa using PartENat.add_one_le_iff_lt (PartENat.natCast_ne_top 1)
 #align multiplicity.squarefree_iff_multiplicity_le_one multiplicity.squarefree_iff_multiplicity_le_one
+-/
 
 end CommMonoid
 
@@ -124,6 +170,12 @@ section CancelCommMonoidWithZero
 
 variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 
+/- warning: multiplicity.finite_prime_left -> multiplicity.finite_prime_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)] {a : R} {b : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) a) -> (Ne.{succ u1} R b (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (multiplicity.Finite.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) a b)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)] {a : R} {b : R}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) a) -> (Ne.{succ u1} R b (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (multiplicity.Finite.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) a b)
+Case conversion may be inaccurate. Consider using '#align multiplicity.finite_prime_left multiplicity.finite_prime_leftₓ'. -/
 theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
   classical
     revert hb
@@ -151,6 +203,12 @@ section Irreducible
 
 variable [CommMonoidWithZero R] [WfDvdMonoid R]
 
+/- warning: irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree -> irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] (r : R), Iff (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))) (Or (And (Eq.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))))))) (forall (x : R), Not (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x))) (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] (r : R), Iff (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))) (Or (And (Eq.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R _inst_1)))) (forall (x : R), Not (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x))) (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r))
+Case conversion may be inaccurate. Consider using '#align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefreeₓ'. -/
 theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r : R) :
     (∀ x : R, Irreducible x → ¬x * x ∣ r) ↔ (r = 0 ∧ ∀ x : R, ¬Irreducible x) ∨ Squarefree r :=
   by
@@ -174,11 +232,23 @@ theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r
   exact h _ hj₁ ((mul_dvd_mul hj₂ hj₂).trans hx)
 #align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree
 
+/- warning: squarefree_iff_irreducible_sq_not_dvd_of_ne_zero -> squarefree_iff_irreducible_sq_not_dvd_of_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] {r : R}, (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))))))) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r) (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] {r : R}, (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R _inst_1)))) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r) (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))))
+Case conversion may be inaccurate. Consider using '#align squarefree_iff_irreducible_sq_not_dvd_of_ne_zero squarefree_iff_irreducible_sq_not_dvd_of_ne_zeroₓ'. -/
 theorem squarefree_iff_irreducible_sq_not_dvd_of_ne_zero {r : R} (hr : r ≠ 0) :
     Squarefree r ↔ ∀ x : R, Irreducible x → ¬x * x ∣ r := by
   simpa [hr] using (irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree r).symm
 #align squarefree_iff_irreducible_sq_not_dvd_of_ne_zero squarefree_iff_irreducible_sq_not_dvd_of_ne_zero
 
+/- warning: squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible -> squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] {r : R}, (Exists.{succ u1} R (fun (x : R) => Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x)) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r) (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : WfDvdMonoid.{u1} R _inst_1] {r : R}, (Exists.{succ u1} R (fun (x : R) => Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x)) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) r) (forall (x : R), (Irreducible.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)) x) -> (Not (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))) x x) r))))
+Case conversion may be inaccurate. Consider using '#align squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducibleₓ'. -/
 theorem squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible {r : R}
     (hr : ∃ x : R, Irreducible x) : Squarefree r ↔ ∀ x : R, Irreducible x → ¬x * x ∣ r :=
   by
@@ -192,6 +262,12 @@ section IsRadical
 
 variable [CancelCommMonoidWithZero R]
 
+/- warning: is_radical.squarefree -> IsRadical.squarefree is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) -> (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) -> (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x)
+Case conversion may be inaccurate. Consider using '#align is_radical.squarefree IsRadical.squarefreeₓ'. -/
 theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefree x :=
   by
   rintro z ⟨w, rfl⟩
@@ -202,6 +278,7 @@ theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefr
 
 variable [GCDMonoid R]
 
+#print Squarefree.isRadical /-
 theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
   (isRadical_iff_pow_one_lt 2 one_lt_two).2 fun y hy =>
     And.right <|
@@ -217,7 +294,14 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
           obtain ⟨w, hw⟩ := hy
           exact (hx z ⟨w, by rwa [mul_right_comm, ← hw]⟩).mul_right_dvd.2 dvd_rfl)
 #align squarefree.is_radical Squarefree.isRadical
+-/
 
+/- warning: is_radical_iff_squarefree_or_zero -> isRadical_iff_squarefree_or_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Or (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Or (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zeroₓ'. -/
 theorem isRadical_iff_squarefree_or_zero {x : R} : IsRadical x ↔ Squarefree x ∨ x = 0 :=
   ⟨fun hx => (em <| x = 0).elim Or.inr fun h => Or.inl <| hx.Squarefree h,
     Or.ndrec Squarefree.isRadical <| by
@@ -226,6 +310,12 @@ theorem isRadical_iff_squarefree_or_zero {x : R} : IsRadical x ↔ Squarefree x
       infer_instance⟩
 #align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zero
 
+/- warning: is_radical_iff_squarefree_of_ne_zero -> isRadical_iff_squarefree_of_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : GCDMonoid.{u1} R _inst_1] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (Iff (IsRadical.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (MonoidWithZero.toSemigroupWithZero.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))) x) (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x))
+Case conversion may be inaccurate. Consider using '#align is_radical_iff_squarefree_of_ne_zero isRadical_iff_squarefree_of_ne_zeroₓ'. -/
 theorem isRadical_iff_squarefree_of_ne_zero {x : R} (h : x ≠ 0) : IsRadical x ↔ Squarefree x :=
   ⟨IsRadical.squarefree h, Squarefree.isRadical⟩
 #align is_radical_iff_squarefree_of_ne_zero isRadical_iff_squarefree_of_ne_zero
@@ -236,6 +326,12 @@ namespace UniqueFactorizationMonoid
 
 variable [CancelCommMonoidWithZero R] [UniqueFactorizationMonoid R]
 
+/- warning: unique_factorization_monoid.squarefree_iff_nodup_normalized_factors -> UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : UniqueFactorizationMonoid.{u1} R _inst_1] [_inst_3 : NormalizationMonoid.{u1} R _inst_1] [_inst_4 : DecidableEq.{succ u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))))))) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Multiset.Nodup.{u1} R (UniqueFactorizationMonoid.normalizedFactors.{u1} R _inst_1 (fun (a : R) (b : R) => _inst_4 a b) _inst_3 _inst_2 x)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] [_inst_2 : UniqueFactorizationMonoid.{u1} R _inst_1] [_inst_3 : NormalizationMonoid.{u1} R _inst_1] [_inst_4 : DecidableEq.{succ u1} R] {x : R}, (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) -> (Iff (Squarefree.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))) x) (Multiset.Nodup.{u1} R (UniqueFactorizationMonoid.normalizedFactors.{u1} R _inst_1 (fun (a : R) (b : R) => _inst_4 a b) _inst_3 _inst_2 x)))
+Case conversion may be inaccurate. Consider using '#align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactorsₓ'. -/
 theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) :=
   by
@@ -264,12 +360,14 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
     assumption_mod_cast
 #align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors
 
+#print UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree /-
 theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
     x ∣ y ^ n ↔ x ∣ y := by
   classical
     haveI := UniqueFactorizationMonoid.toGCDMonoid R
     exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
 #align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
+-/
 
 end UniqueFactorizationMonoid

79de90f7

bump to nightly-2023-03-21-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

92a91f20

Diff

@@ -267,7 +267,7 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
 theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
     x ∣ y ^ n ↔ x ∣ y := by
   classical
-    haveI := UniqueFactorizationMonoid.toGcdMonoid R
+    haveI := UniqueFactorizationMonoid.toGCDMonoid R
     exact ⟨hsq.is_radical n y, fun h => h.pow h0⟩
 #align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree

79de90f7

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -169,7 +169,7 @@ theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r
   have : x ≠ 0 := by
     rintro rfl
     apply hr
-    simpa only [zero_dvd_iff, mul_zero] using hx
+    simpa only [zero_dvd_iff, MulZeroClass.mul_zero] using hx
   obtain ⟨j, hj₁, hj₂⟩ := WfDvdMonoid.exists_irreducible_factor i this
   exact h _ hj₁ ((mul_dvd_mul hj₂ hj₂).trans hx)
 #align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree

79de90f7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

00d163e3

chore: reformat deprecation warnings on one line, if possible (#12335)

Occasionally, remove a "deprecated by" or "deprecated since", to fit the line length.

This is desirable (to me) because

it's more compact: I don't see a good reason for these declarations taking up more space than needed; as I understand it, deprecated lemmas are not supposed to be used in mathlib anyway
putting the date on the same line as the attribute makes it easier to discover un-dated deprecations; they also ease writing a tool to replace these by a machine-readable version using leanprover/lean4#3968

45346d9f

Diff

@@ -320,7 +320,6 @@ theorem squarefree_natCast {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n :=
   rw [← squarefree_natAbs, natAbs_ofNat]
 #align int.squarefree_coe_nat Int.squarefree_natCast
 
--- 2024-04-05
-@[deprecated] alias squarefree_coe_nat := squarefree_natCast
+@[deprecated] alias squarefree_coe_nat := squarefree_natCast -- 2024-04-05
 
 end Int

00d163e3

chore: split RingTheory.Nilpotent (#12184)

Mathlib.RingTheory.Nilpotent has a few very simple definitions (Mathlib.Data.Nat.Lattice is sufficient to state them), but needs some pretty heavy imports (ideals, linear algebra) towards the end. This change moves the heavier parts into a new file.

bdfbc7fa

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
+import Mathlib.RingTheory.Nilpotent.Basic
 import Mathlib.RingTheory.UniqueFactorizationDomain
 
 #align_import algebra.squarefree from "leanprover-community/mathlib"@"00d163e35035c3577c1c79fa53b68de17781ffc1"

00d163e3

chore: Rename coe_nat/coe_int/coe_rat to natCast/intCast/ratCast (#11499)

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

b2af0d13

Diff

@@ -315,8 +315,11 @@ theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
 #align int.squarefree_nat_abs Int.squarefree_natAbs
 
 @[simp]
-theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
+theorem squarefree_natCast {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
   rw [← squarefree_natAbs, natAbs_ofNat]
-#align int.squarefree_coe_nat Int.squarefree_coe_nat
+#align int.squarefree_coe_nat Int.squarefree_natCast
+
+-- 2024-04-05
+@[deprecated] alias squarefree_coe_nat := squarefree_natCast
 
 end Int

00d163e3

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -212,7 +212,7 @@ theorem pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right {k : ℕ}
   · obtain ⟨x', rfl⟩ := hxp
     have hx' : ¬ p ∣ x' := fun contra ↦ hp.not_unit <| hx p (mul_dvd_mul_left p contra)
     replace h : p ^ k ∣ x' * y := by
-      rw [pow_succ, mul_assoc] at h
+      rw [pow_succ', mul_assoc] at h
       exact (mul_dvd_mul_iff_left hp.ne_zero).mp h
     exact hp.pow_dvd_of_dvd_mul_left _ hx' h
   · exact (pow_dvd_pow _ k.le_succ).trans (hp.pow_dvd_of_dvd_mul_left _ hxp h)
@@ -274,7 +274,7 @@ lemma _root_.exists_squarefree_dvd_pow_of_ne_zero {x : R} (hx : x ≠ 0) :
     · exact ⟨p, 1, hp.squarefree, dvd_mul_right p z, by simp [isUnit_of_dvd_one (pow_zero y ▸ hy')]⟩
     by_cases hp' : p ∣ y
     · exact ⟨y, n + 1, hy, dvd_mul_of_dvd_right hyx _,
-        mul_comm p z ▸ pow_succ' y n ▸ mul_dvd_mul hy' hp'⟩
+        mul_comm p z ▸ pow_succ y n ▸ mul_dvd_mul hy' hp'⟩
     · suffices Squarefree (p * y) from ⟨p * y, n, this,
         mul_dvd_mul_left p hyx, mul_pow p y n ▸ mul_dvd_mul (dvd_pow_self p hn.ne') hy'⟩
       exact squarefree_mul_iff.mpr ⟨hp.isRelPrime_iff_not_dvd.mpr hp', hp.squarefree, hy⟩

00d163e3

chore(Squarefree): drop a DecidableEq assumption (#11427)

Use classical instead

d47822ad

Diff

@@ -279,9 +279,9 @@ lemma _root_.exists_squarefree_dvd_pow_of_ne_zero {x : R} (hx : x ≠ 0) :
         mul_dvd_mul_left p hyx, mul_pow p y n ▸ mul_dvd_mul (dvd_pow_self p hn.ne') hy'⟩
       exact squarefree_mul_iff.mpr ⟨hp.isRelPrime_iff_not_dvd.mpr hp', hp.squarefree, hy⟩
 
-theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
+theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) := by
-  have drel : DecidableRel (Dvd.dvd : R → R → Prop) := by classical infer_instance
+  classical
   rw [multiplicity.squarefree_iff_multiplicity_le_one, Multiset.nodup_iff_count_le_one]
   haveI := nontrivial_of_ne x 0 x0
   constructor <;> intro h a
@@ -296,13 +296,12 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
     · simp [Multiset.count_eq_zero_of_not_mem hmem]
   · rw [or_iff_not_imp_right]
     intro hu
-    by_cases h0 : a = 0
-    · simp [h0, x0]
+    rcases eq_or_ne a 0 with rfl | h0
+    · simp [x0]
     rcases WfDvdMonoid.exists_irreducible_factor hu h0 with ⟨b, hib, hdvd⟩
     apply le_trans (multiplicity.multiplicity_le_multiplicity_of_dvd_left hdvd)
     rw [multiplicity_eq_count_normalizedFactors hib x0]
-    specialize h (normalize b)
-    assumption_mod_cast
+    exact_mod_cast h (normalize b)
 #align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors
 
 end UniqueFactorizationMonoid

00d163e3

chore: move Mathlib to v4.7.0-rc1 (#11162)

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

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

fa48894a

Diff

@@ -120,6 +120,7 @@ theorem squarefree_iff_multiplicity_le_one (r : R) :
     Squarefree r ↔ ∀ x : R, multiplicity x r ≤ 1 ∨ IsUnit x := by
   refine' forall_congr' fun a => _
   rw [← sq, pow_dvd_iff_le_multiplicity, or_iff_not_imp_left, not_le, imp_congr _ Iff.rfl]
+  norm_cast
   rw [← one_add_one_eq_two]
   simpa using PartENat.add_one_le_iff_lt (PartENat.natCast_ne_top 1)
 #align multiplicity.squarefree_iff_multiplicity_le_one multiplicity.squarefree_iff_multiplicity_le_one

00d163e3

feat(RingTheory/UniqueFactorizationDomain): add WfDvdMonoid.max_power_factor['] and multiplicity.finite_of_not_isUnit (#11066)

makes UniqueFactorizationMonoid.max_power_factor obsolete
makes the proof of multiplicity.finite_prime_left trivial
relax the condition of exists_reduced_fraction'

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

c7394bfb

Diff

@@ -130,23 +130,8 @@ section CancelCommMonoidWithZero
 
 variable [CancelCommMonoidWithZero R] [WfDvdMonoid R]
 
-theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b := by
-  classical
-    revert hb
-    refine'
-      WfDvdMonoid.induction_on_irreducible b (fun c => c.irrefl.elim) (fun u hu _ => _)
-        fun b p hb hp ih _ => _
-    · rw [multiplicity.finite_iff_dom, multiplicity.isUnit_right ha.not_unit hu]
-      exact PartENat.dom_natCast 0
-    · refine'
-        multiplicity.finite_mul ha
-          (multiplicity.finite_iff_dom.mpr
-            (PartENat.dom_of_le_natCast (show multiplicity a p ≤ ↑1 from _)))
-          (ih hb)
-      norm_cast
-      exact
-        ((multiplicity.squarefree_iff_multiplicity_le_one p).mp hp.squarefree a).resolve_right
-          ha.not_unit
+theorem finite_prime_left {a b : R} (ha : Prime a) (hb : b ≠ 0) : multiplicity.Finite a b :=
+  finite_of_not_isUnit ha.not_unit hb
 #align multiplicity.finite_prime_left multiplicity.finite_prime_left
 
 end CancelCommMonoidWithZero

00d163e3

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -45,7 +45,7 @@ theorem IsUnit.squarefree [CommMonoid R] {x : R} (h : IsUnit x) : Squarefree x :
   isUnit_of_mul_isUnit_left (isUnit_of_dvd_unit hdvd h)
 #align is_unit.squarefree IsUnit.squarefree
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem squarefree_one [CommMonoid R] : Squarefree (1 : R) :=
   isUnit_one.squarefree
 #align squarefree_one squarefree_one

00d163e3

feat: introduce IsRelPrime and DecompositionMonoid and refactor (#10327)

Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.
Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.
Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.
Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.
Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.
Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

b569e065

Diff

@@ -37,6 +37,9 @@ def Squarefree [Monoid R] (r : R) : Prop :=
   ∀ x : R, x * x ∣ r → IsUnit x
 #align squarefree Squarefree
 
+theorem IsRelPrime.of_squarefree_mul [CommMonoid R] {m n : R} (h : Squarefree (m * n)) :
+    IsRelPrime m n := fun c hca hcb ↦ h c (mul_dvd_mul hca hcb)
+
 @[simp]
 theorem IsUnit.squarefree [CommMonoid R] {x : R} (h : IsUnit x) : Squarefree x := fun _ hdvd =>
   isUnit_of_mul_isUnit_left (isUnit_of_dvd_unit hdvd h)
@@ -154,26 +157,23 @@ section Irreducible
 
 variable [CommMonoidWithZero R] [WfDvdMonoid R]
 
+theorem squarefree_iff_no_irreducibles {x : R} (hx₀ : x ≠ 0) :
+    Squarefree x ↔ ∀ p, Irreducible p → ¬ (p * p ∣ x) := by
+  refine ⟨fun h p hp hp' ↦ hp.not_unit (h p hp'), fun h d hd ↦ by_contra fun hdu ↦ ?_⟩
+  have hd₀ : d ≠ 0 := ne_zero_of_dvd_ne_zero (ne_zero_of_dvd_ne_zero hx₀ hd) (dvd_mul_left d d)
+  obtain ⟨p, irr, dvd⟩ := WfDvdMonoid.exists_irreducible_factor hdu hd₀
+  exact h p irr ((mul_dvd_mul dvd dvd).trans hd)
+
 theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r : R) :
     (∀ x : R, Irreducible x → ¬x * x ∣ r) ↔ (r = 0 ∧ ∀ x : R, ¬Irreducible x) ∨ Squarefree r := by
-  symm
-  constructor
+  refine ⟨fun h ↦ ?_, ?_⟩
+  · rcases eq_or_ne r 0 with (rfl | hr)
+    · exact .inl (by simpa using h)
+    · exact .inr ((squarefree_iff_no_irreducibles hr).mpr h)
   · rintro (⟨rfl, h⟩ | h)
     · simpa using h
     intro x hx t
     exact hx.not_unit (h x t)
-  intro h
-  rcases eq_or_ne r 0 with (rfl | hr)
-  · exact Or.inl (by simpa using h)
-  right
-  intro x hx
-  by_contra i
-  have : x ≠ 0 := by
-    rintro rfl
-    apply hr
-    simpa only [zero_dvd_iff, mul_zero] using hx
-  obtain ⟨j, hj₁, hj₂⟩ := WfDvdMonoid.exists_irreducible_factor i this
-  exact h _ hj₁ ((mul_dvd_mul hj₂ hj₂).trans hx)
 #align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree
 
 theorem squarefree_iff_irreducible_sq_not_dvd_of_ne_zero {r : R} (hr : r ≠ 0) :
@@ -191,42 +191,84 @@ end Irreducible
 
 section IsRadical
 
-variable [CancelCommMonoidWithZero R]
+section
+variable [CommMonoidWithZero R] [DecompositionMonoid R]
+
+theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
+  (isRadical_iff_pow_one_lt 2 one_lt_two).2 fun y hy ↦ by
+    obtain ⟨a, b, ha, hb, rfl⟩ := exists_dvd_and_dvd_of_dvd_mul (sq y ▸ hy)
+    exact (IsRelPrime.of_squarefree_mul hx).mul_dvd ha hb
+#align squarefree.is_radical Squarefree.isRadical
+
+theorem Squarefree.dvd_pow_iff_dvd {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
+    x ∣ y ^ n ↔ x ∣ y := ⟨hsq.isRadical n y, (·.pow h0)⟩
+#align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree Squarefree.dvd_pow_iff_dvd
+@[deprecated]
+alias UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree := Squarefree.dvd_pow_iff_dvd
+
+end
+
+variable [CancelCommMonoidWithZero R] {x y p d : R}
 
-theorem IsRadical.squarefree {x : R} (h0 : x ≠ 0) (h : IsRadical x) : Squarefree x := by
+theorem IsRadical.squarefree (h0 : x ≠ 0) (h : IsRadical x) : Squarefree x := by
   rintro z ⟨w, rfl⟩
   specialize h 2 (z * w) ⟨w, by simp_rw [pow_two, mul_left_comm, ← mul_assoc]⟩
   rwa [← one_mul (z * w), mul_assoc, mul_dvd_mul_iff_right, ← isUnit_iff_dvd_one] at h
   rw [mul_assoc, mul_ne_zero_iff] at h0; exact h0.2
 #align is_radical.squarefree IsRadical.squarefree
 
-variable [GCDMonoid R]
-
-theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
-  (isRadical_iff_pow_one_lt 2 one_lt_two).2 fun y hy =>
-    And.right <|
-      (dvd_gcd_iff x x y).1
-        (by
-          by_cases h : gcd x y = 0
-          · rw [h]
-            apply dvd_zero
-          replace hy := ((dvd_gcd_iff x x _).2 ⟨dvd_rfl, hy⟩).trans gcd_pow_right_dvd_pow_gcd
-          obtain ⟨z, hz⟩ := gcd_dvd_left x y
-          nth_rw 1 [hz] at hy ⊢
-          rw [pow_two, mul_dvd_mul_iff_left h] at hy
-          obtain ⟨w, hw⟩ := hy
-          exact (hx z ⟨w, by rwa [mul_right_comm, ← hw]⟩).mul_right_dvd.2 dvd_rfl)
-#align squarefree.is_radical Squarefree.isRadical
-
-theorem isRadical_iff_squarefree_or_zero {x : R} : IsRadical x ↔ Squarefree x ∨ x = 0 :=
-  ⟨fun hx => (em <| x = 0).elim Or.inr fun h => Or.inl <| hx.squarefree h,
+namespace Squarefree
+
+theorem pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right {k : ℕ}
+    (hx : Squarefree x) (hp : Prime p) (h : p ^ (k + 1) ∣ x * y) :
+    p ^ k ∣ y := by
+  by_cases hxp : p ∣ x
+  · obtain ⟨x', rfl⟩ := hxp
+    have hx' : ¬ p ∣ x' := fun contra ↦ hp.not_unit <| hx p (mul_dvd_mul_left p contra)
+    replace h : p ^ k ∣ x' * y := by
+      rw [pow_succ, mul_assoc] at h
+      exact (mul_dvd_mul_iff_left hp.ne_zero).mp h
+    exact hp.pow_dvd_of_dvd_mul_left _ hx' h
+  · exact (pow_dvd_pow _ k.le_succ).trans (hp.pow_dvd_of_dvd_mul_left _ hxp h)
+
+theorem pow_dvd_of_squarefree_of_pow_succ_dvd_mul_left {k : ℕ}
+    (hy : Squarefree y) (hp : Prime p) (h : p ^ (k + 1) ∣ x * y) :
+    p ^ k ∣ x := by
+  rw [mul_comm] at h
+  exact pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right hy hp h
+
+variable [DecompositionMonoid R]
+
+theorem dvd_of_squarefree_of_mul_dvd_mul_right (hx : Squarefree x) (h : d * d ∣ x * y) : d ∣ y := by
+  nontriviality R
+  obtain ⟨a, b, ha, hb, eq⟩ := exists_dvd_and_dvd_of_dvd_mul h
+  replace ha : Squarefree a := hx.squarefree_of_dvd ha
+  obtain ⟨c, hc⟩ : a ∣ d := ha.isRadical 2 d ⟨b, by rw [sq, eq]⟩
+  rw [hc, mul_assoc, (mul_right_injective₀ ha.ne_zero).eq_iff] at eq
+  exact dvd_trans ⟨c, by rw [hc, ← eq, mul_comm]⟩ hb
+
+theorem dvd_of_squarefree_of_mul_dvd_mul_left (hy : Squarefree y) (h : d * d ∣ x * y) : d ∣ x :=
+  dvd_of_squarefree_of_mul_dvd_mul_right hy (mul_comm x y ▸ h)
+
+end Squarefree
+
+variable [DecompositionMonoid R]
+
+/-- `x * y` is square-free iff `x` and `y` have no common factors and are themselves square-free. -/
+theorem squarefree_mul_iff : Squarefree (x * y) ↔ IsRelPrime x y ∧ Squarefree x ∧ Squarefree y :=
+  ⟨fun h ↦ ⟨IsRelPrime.of_squarefree_mul h, h.of_mul_left, h.of_mul_right⟩,
+    fun ⟨hp, sqx, sqy⟩ _ dvd ↦ hp (sqy.dvd_of_squarefree_of_mul_dvd_mul_left dvd)
+      (sqx.dvd_of_squarefree_of_mul_dvd_mul_right dvd)⟩
+
+theorem isRadical_iff_squarefree_or_zero : IsRadical x ↔ Squarefree x ∨ x = 0 :=
+  ⟨fun hx ↦ (em <| x = 0).elim .inr fun h ↦ .inl <| hx.squarefree h,
     Or.rec Squarefree.isRadical <| by
       rintro rfl
       rw [zero_isRadical_iff]
       infer_instance⟩
 #align is_radical_iff_squarefree_or_zero isRadical_iff_squarefree_or_zero
 
-theorem isRadical_iff_squarefree_of_ne_zero {x : R} (h : x ≠ 0) : IsRadical x ↔ Squarefree x :=
+theorem isRadical_iff_squarefree_of_ne_zero (h : x ≠ 0) : IsRadical x ↔ Squarefree x :=
   ⟨IsRadical.squarefree h, Squarefree.isRadical⟩
 #align is_radical_iff_squarefree_of_ne_zero isRadical_iff_squarefree_of_ne_zero
 
@@ -236,6 +278,21 @@ namespace UniqueFactorizationMonoid
 
 variable [CancelCommMonoidWithZero R] [UniqueFactorizationMonoid R]
 
+lemma _root_.exists_squarefree_dvd_pow_of_ne_zero {x : R} (hx : x ≠ 0) :
+    ∃ (y : R) (n : ℕ), Squarefree y ∧ y ∣ x ∧ x ∣ y ^ n := by
+  induction' x using WfDvdMonoid.induction_on_irreducible with u hu z p hz hp ih
+  · contradiction
+  · exact ⟨1, 0, squarefree_one, one_dvd u, hu.dvd⟩
+  · obtain ⟨y, n, hy, hyx, hy'⟩ := ih hz
+    rcases n.eq_zero_or_pos with rfl | hn
+    · exact ⟨p, 1, hp.squarefree, dvd_mul_right p z, by simp [isUnit_of_dvd_one (pow_zero y ▸ hy')]⟩
+    by_cases hp' : p ∣ y
+    · exact ⟨y, n + 1, hy, dvd_mul_of_dvd_right hyx _,
+        mul_comm p z ▸ pow_succ' y n ▸ mul_dvd_mul hy' hp'⟩
+    · suffices Squarefree (p * y) from ⟨p * y, n, this,
+        mul_dvd_mul_left p hyx, mul_pow p y n ▸ mul_dvd_mul (dvd_pow_self p hn.ne') hy'⟩
+      exact squarefree_mul_iff.mpr ⟨hp.isRelPrime_iff_not_dvd.mpr hp', hp.squarefree, hy⟩
+
 theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [DecidableEq R] {x : R}
     (x0 : x ≠ 0) : Squarefree x ↔ Multiset.Nodup (normalizedFactors x) := by
   have drel : DecidableRel (Dvd.dvd : R → R → Prop) := by classical infer_instance
@@ -262,13 +319,6 @@ theorem squarefree_iff_nodup_normalizedFactors [NormalizationMonoid R] [Decidabl
     assumption_mod_cast
 #align unique_factorization_monoid.squarefree_iff_nodup_normalized_factors UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors
 
-theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (h0 : n ≠ 0) :
-    x ∣ y ^ n ↔ x ∣ y := by
-  classical
-    haveI := UniqueFactorizationMonoid.toGCDMonoid R
-    exact ⟨hsq.isRadical n y, fun h => h.pow h0⟩
-#align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
-
 end UniqueFactorizationMonoid
 
 namespace Int

00d163e3

feat: a polynomial over a perfect field is separable iff it is square-free (#10170)

Yet another small step toward Jordan-Chevalley-Dunford.

This was far more work than expected, partly because of missing API for Squarefree, and partly because the definition IsCoprime is the wrong concept for unique factorization domains.

aec68874

Diff

@@ -85,6 +85,14 @@ theorem Squarefree.squarefree_of_dvd [CommMonoid R] {x y : R} (hdvd : x ∣ y) (
     Squarefree x := fun _ h => hsq _ (h.trans hdvd)
 #align squarefree.squarefree_of_dvd Squarefree.squarefree_of_dvd
 
+theorem Squarefree.eq_zero_or_one_of_pow_of_not_isUnit [CommMonoid R] {x : R} {n : ℕ}
+    (h : Squarefree (x ^ n)) (h' : ¬ IsUnit x) :
+    n = 0 ∨ n = 1 := by
+  contrapose! h'
+  replace h' : 2 ≤ n := by omega
+  have : x * x ∣ x ^ n := by rw [← sq]; exact pow_dvd_pow x h'
+  exact h.squarefree_of_dvd this x (refl _)
+
 section SquarefreeGcdOfSquarefree
 
 variable {α : Type*} [CancelCommMonoidWithZero α] [GCDMonoid α]

00d163e3

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -109,7 +109,7 @@ theorem squarefree_iff_multiplicity_le_one (r : R) :
     Squarefree r ↔ ∀ x : R, multiplicity x r ≤ 1 ∨ IsUnit x := by
   refine' forall_congr' fun a => _
   rw [← sq, pow_dvd_iff_le_multiplicity, or_iff_not_imp_left, not_le, imp_congr _ Iff.rfl]
-  rw [←one_add_one_eq_two]
+  rw [← one_add_one_eq_two]
   simpa using PartENat.add_one_le_iff_lt (PartENat.natCast_ne_top 1)
 #align multiplicity.squarefree_iff_multiplicity_le_one multiplicity.squarefree_iff_multiplicity_le_one

00d163e3

chore: add missing hypothesis names to by_cases (#8533)

I've also got a change to make this required, but I'd like to land this first.

2009db69

Diff

@@ -199,7 +199,7 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
     And.right <|
       (dvd_gcd_iff x x y).1
         (by
-          by_cases gcd x y = 0
+          by_cases h : gcd x y = 0
           · rw [h]
             apply dvd_zero
           replace hy := ((dvd_gcd_iff x x _).2 ⟨dvd_rfl, hy⟩).trans gcd_pow_right_dvd_pow_gcd

00d163e3

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -163,7 +163,7 @@ theorem irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree (r
   have : x ≠ 0 := by
     rintro rfl
     apply hr
-    simpa only [zero_dvd_iff, MulZeroClass.mul_zero] using hx
+    simpa only [zero_dvd_iff, mul_zero] using hx
   obtain ⟨j, hj₁, hj₂⟩ := WfDvdMonoid.exists_irreducible_factor i this
   exact h _ hj₁ ((mul_dvd_mul hj₂ hj₂).trans hx)
 #align irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree

00d163e3

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -29,7 +29,7 @@ squarefree, multiplicity
 -/
 
 
-variable {R : Type _}
+variable {R : Type*}
 
 /-- An element of a monoid is squarefree if the only squares that
   divide it are the squares of units. -/
@@ -87,7 +87,7 @@ theorem Squarefree.squarefree_of_dvd [CommMonoid R] {x y : R} (hdvd : x ∣ y) (
 
 section SquarefreeGcdOfSquarefree
 
-variable {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α]
+variable {α : Type*} [CancelCommMonoidWithZero α] [GCDMonoid α]
 
 theorem Squarefree.gcd_right (a : α) {b : α} (hb : Squarefree b) : Squarefree (gcd a b) :=
   hb.squarefree_of_dvd (gcd_dvd_right _ _)

00d163e3

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module algebra.squarefree
-! leanprover-community/mathlib commit 00d163e35035c3577c1c79fa53b68de17781ffc1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.UniqueFactorizationDomain
 
+#align_import algebra.squarefree from "leanprover-community/mathlib"@"00d163e35035c3577c1c79fa53b68de17781ffc1"
+
 /-!
 # Squarefree elements of monoids
 An element of a monoid is squarefree when it is not divisible by any squares

00d163e3

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

Changes are of the form

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

2a870323

Diff

@@ -207,7 +207,7 @@ theorem Squarefree.isRadical {x : R} (hx : Squarefree x) : IsRadical x :=
             apply dvd_zero
           replace hy := ((dvd_gcd_iff x x _).2 ⟨dvd_rfl, hy⟩).trans gcd_pow_right_dvd_pow_gcd
           obtain ⟨z, hz⟩ := gcd_dvd_left x y
-          nth_rw 1 [hz] at hy⊢
+          nth_rw 1 [hz] at hy ⊢
           rw [pow_two, mul_dvd_mul_iff_left h] at hy
           obtain ⟨w, hw⟩ := hy
           exact (hx z ⟨w, by rwa [mul_right_comm, ← hw]⟩).mul_right_dvd.2 dvd_rfl)

00d163e3

feat: port RingTheory.ZMod (#3257)

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

f6c95f52

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 
 ! This file was ported from Lean 3 source module algebra.squarefree
-! leanprover-community/mathlib commit 79de90f7beca025f469dcda978ae655c4d985946
+! leanprover-community/mathlib commit 00d163e35035c3577c1c79fa53b68de17781ffc1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -265,3 +265,18 @@ theorem dvd_pow_iff_dvd_of_squarefree {x y : R} {n : ℕ} (hsq : Squarefree x) (
 #align unique_factorization_monoid.dvd_pow_iff_dvd_of_squarefree UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree
 
 end UniqueFactorizationMonoid
+
+namespace Int
+
+@[simp]
+theorem squarefree_natAbs {n : ℤ} : Squarefree n.natAbs ↔ Squarefree n := by
+  simp_rw [Squarefree, natAbs_surjective.forall, ← natAbs_mul, natAbs_dvd_natAbs,
+    isUnit_iff_natAbs_eq, Nat.isUnit_iff]
+#align int.squarefree_nat_abs Int.squarefree_natAbs
+
+@[simp]
+theorem squarefree_coe_nat {n : ℕ} : Squarefree (n : ℤ) ↔ Squarefree n := by
+  rw [← squarefree_natAbs, natAbs_ofNat]
+#align int.squarefree_coe_nat Int.squarefree_coe_nat
+
+end Int

79de90f7

feat: port Algebra.Squarefree (#3018)

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

98e7a89e

`algebra.squarefree` ⟷ `Mathlib.Algebra.Squarefree.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 469

algebra.squarefree ⟷ Mathlib.Algebra.Squarefree.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 469

`algebra.squarefree` ⟷ `Mathlib.Algebra.Squarefree.Basic`