data.nat.order.lemmas | 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

e8638a0f

(last sync)

feat(algebra/divisibility/basic): Dot notation aliases (#18698)

A few convenience shortcuts for dvd along with some simple nat lemmas. Also

Drop neg_dvd_of_dvd/dvd_of_neg_dvd/dvd_neg_of_dvd/dvd_of_dvd_neg in favor of the aforementioned shortcuts.
Remove explicit arguments to dvd_neg/neg_dvd.
Drop int.of_nat_dvd_of_dvd_nat_abs/int.dvd_nat_abs_of_of_nat_dvd because they are the two directions of int.coe_nat_dvd_left.
Move group_with_zero.to_cancel_monoid_with_zero from algebra.group_with_zero.units.basic back to algebra.group_with_zero.basic. It was erroneously moved during the Great Splits.

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 -/
 import data.nat.order.basic
+import data.nat.units
 import data.set.basic
 import algebra.ring.divisibility
 import algebra.group_with_zero.divisibility

47a1a733

feat(data/{int,nat}/modeq): a/c ≡ b/c mod m/c → a ≡ b mod m (#18666)

Also prove -a ≡ -b [ZMOD n] ↔ a ≡ b [ZMOD n], a ≡ b [ZMOD -n] ↔ a ≡ b [ZMOD n], generalise int.modeq.mul_left'/int.modeq.mul_right', and rename

int.gcd_pos_of_non_zero_left → int.gcd_pos_of_ne_zero_left
int.gcd_pos_of_non_zero_right → int.gcd_pos_of_ne_zero_right
eq_iff_modeq_int, char_p.int_coe_eq_int_coe_iff → char_p.int_cast_eq_int_cast (they were duplicates)

Diff

@@ -21,7 +21,7 @@ mathlib4. After `data.rat.order` has been ported, please feel free to reorganize
 
 universes u v
 
-variables {m n k : ℕ}
+variables {a b m n k : ℕ}
 namespace nat
 
 /-! ### Sets -/
@@ -183,6 +183,13 @@ lemma eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
 nat.eq_zero_of_dvd_of_div_eq_zero w
   ((nat.div_eq_zero_iff (lt_of_le_of_lt (zero_le b) h)).elim_right h)
 
+lemma le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
+begin
+  rintro ⟨a, rfl⟩ ⟨b, rfl⟩,
+  rw ←mul_add_one at h,
+  exact mul_le_mul_left' (lt_succ_iff.1 $ lt_of_mul_lt_mul_left h bot_le) _,
+end
+
 @[simp] lemma mod_div_self (m n : ℕ) : m % n / n = 0 :=
 begin
   cases n,

2258b40d

(no changes)

2e0975f6

refactor(algebra/group/defs): use is_left_cancel_mul etc (#17884)

The Lean 4 version is here: leanprover-community/mathlib4#945.

Diff

@@ -61,7 +61,7 @@ end
 
 protected lemma div_eq_zero_iff {a b : ℕ} (hb : 0 < b) : a / b = 0 ↔ a < b :=
 ⟨λ h, by rw [← mod_add_div a b, h, mul_zero, add_zero]; exact mod_lt _ hb,
-  λ h, by rw [← mul_right_inj' hb.ne', ← @add_left_cancel_iff _ _ (a % b), mod_add_div,
+  λ h, by rw [← mul_right_inj' hb.ne', ← @add_left_cancel_iff _ _ _ (a % b), mod_add_div,
     mod_eq_of_lt h, mul_zero, add_zero]⟩
 
 protected lemma div_eq_zero {a b : ℕ} (hb : a < b) : a / b = 0 :=

10b4e499

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

e8638a0f

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights r
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 -/
-import Data.Nat.Order.Basic
+import Algebra.Order.Group.Nat
 import Data.Nat.Units
 import Data.Set.Basic
 import Algebra.Ring.Divisibility.Basic

e8638a0f

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -6,7 +6,7 @@ Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 import Data.Nat.Order.Basic
 import Data.Nat.Units
 import Data.Set.Basic
-import Algebra.Ring.Divisibility
+import Algebra.Ring.Divisibility.Basic
 import Algebra.GroupWithZero.Divisibility
 
 #align_import data.nat.order.lemmas from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"

e8638a0f

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -255,7 +255,7 @@ theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
 theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
   by
   rintro ⟨a, rfl⟩ ⟨b, rfl⟩
-  rw [← mul_add_one] at h 
+  rw [← mul_add_one] at h
   exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
 #align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
 -/

e8638a0f

bump to nightly-2023-10-21-06

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

a2dc86f8

Diff

@@ -92,10 +92,12 @@ protected theorem div_eq_zero_iff {a b : ℕ} (hb : 0 < b) : a / b = 0 ↔ a < b
 #align nat.div_eq_zero_iff Nat.div_eq_zero_iff
 -/
 
-#print Nat.div_eq_zero /-
-protected theorem div_eq_zero {a b : ℕ} (hb : a < b) : a / b = 0 :=
+/- warning: nat.div_eq_zero clashes with nat.div_eq_of_lt -> Nat.div_eq_of_lt
+Case conversion may be inaccurate. Consider using '#align nat.div_eq_zero Nat.div_eq_of_ltₓ'. -/
+#print Nat.div_eq_of_lt /-
+protected theorem div_eq_of_lt {a b : ℕ} (hb : a < b) : a / b = 0 :=
   (Nat.div_eq_zero_iff <| (zero_le a).trans_lt hb).mpr hb
-#align nat.div_eq_zero Nat.div_eq_zero
+#align nat.div_eq_zero Nat.div_eq_of_lt
 -/
 
 /-! ### `mod`, `dvd` -/
@@ -264,7 +266,7 @@ theorem mod_div_self (m n : ℕ) : m % n / n = 0 :=
   by
   cases n
   · exact (m % 0).div_zero
-  · exact Nat.div_eq_zero (m.mod_lt n.succ_pos)
+  · exact Nat.div_eq_of_lt (m.mod_lt n.succ_pos)
 #align nat.mod_div_self Nat.mod_div_self
 -/

e8638a0f

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights r
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 -/
-import Mathbin.Data.Nat.Order.Basic
-import Mathbin.Data.Nat.Units
-import Mathbin.Data.Set.Basic
-import Mathbin.Algebra.Ring.Divisibility
-import Mathbin.Algebra.GroupWithZero.Divisibility
+import Data.Nat.Order.Basic
+import Data.Nat.Units
+import Data.Set.Basic
+import Algebra.Ring.Divisibility
+import Algebra.GroupWithZero.Divisibility
 
 #align_import data.nat.order.lemmas from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"

e8638a0f

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Nat.Order.Basic
 import Mathbin.Data.Nat.Units
@@ -14,6 +9,8 @@ import Mathbin.Data.Set.Basic
 import Mathbin.Algebra.Ring.Divisibility
 import Mathbin.Algebra.GroupWithZero.Divisibility
 
+#align_import data.nat.order.lemmas from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Further lemmas about the natural numbers

e8638a0f

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -49,10 +49,12 @@ instance Subtype.semilatticeSup (s : Set ℕ) : SemilatticeSup s :=
 #align nat.subtype.semilattice_sup Nat.Subtype.semilatticeSup
 -/
 
+#print Nat.Subtype.coe_bot /-
 theorem Subtype.coe_bot {s : Set ℕ} [DecidablePred (· ∈ s)] [h : Nonempty s] :
     ((⊥ : s) : ℕ) = Nat.find (nonempty_subtype.1 h) :=
   rfl
 #align nat.subtype.coe_bot Nat.Subtype.coe_bot
+-/
 
 #print Nat.set_eq_univ /-
 theorem set_eq_univ {S : Set ℕ} : S = Set.univ ↔ 0 ∈ S ∧ ∀ k : ℕ, k ∈ S → k + 1 ∈ S :=
@@ -143,6 +145,7 @@ theorem dvd_sub' {k m n : ℕ} (h₁ : k ∣ m) (h₂ : k ∣ n) : k ∣ m - n :
 #align nat.dvd_sub' Nat.dvd_sub'
 -/
 
+#print Nat.succ_div /-
 theorem succ_div : ∀ a b : ℕ, (a + 1) / b = a / b + if b ∣ a + 1 then 1 else 0
   | a, 0 => by simp
   | 0, 1 => by simp
@@ -171,6 +174,7 @@ theorem succ_div : ∀ a b : ℕ, (a + 1) / b = a / b + if b ∣ a + 1 then 1 el
         hb_le_a1 (le_of_succ_le_succ (le_of_dvd (succ_pos _) h))
       simp [hba, hb_le_a1, hb_dvd_a]
 #align nat.succ_div Nat.succ_div
+-/
 
 #print Nat.succ_div_of_dvd /-
 theorem succ_div_of_dvd {a b : ℕ} (hba : b ∣ a + 1) : (a + 1) / b = a / b + 1 := by

e8638a0f

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -252,7 +252,7 @@ theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
 theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
   by
   rintro ⟨a, rfl⟩ ⟨b, rfl⟩
-  rw [← mul_add_one] at h
+  rw [← mul_add_one] at h 
   exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
 #align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
 -/

e8638a0f

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -49,12 +49,6 @@ instance Subtype.semilatticeSup (s : Set ℕ) : SemilatticeSup s :=
 #align nat.subtype.semilattice_sup Nat.Subtype.semilatticeSup
 -/
 
-/- warning: nat.subtype.coe_bot -> Nat.Subtype.coe_bot is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Nat} [_inst_1 : DecidablePred.{1} Nat (fun (_x : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) _x s)] [h : Nonempty.{1} (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s)], Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s) Nat (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s) Nat (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s) Nat (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s) Nat (coeSubtype.{1} Nat (fun (x : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) x s))))) (Bot.bot.{0} (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s) (OrderBot.toHasBot.{0} (coeSort.{1, 2} (Set.{0} Nat) Type (Set.hasCoeToSort.{0} Nat) s) (Subtype.hasLe.{0} Nat Nat.hasLe (fun (x : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) x s)) (Nat.Subtype.orderBot s (fun (a : Nat) => _inst_1 a) h)))) (Nat.find (fun (n : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) n s) (fun (a : Nat) => _inst_1 a) (Iff.mp (Nonempty.{1} (Subtype.{1} Nat (fun (x : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) x s))) (Exists.{1} Nat (fun (a : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) a s)) (nonempty_subtype.{1} Nat (fun (x : Nat) => Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) x s)) h))
-but is expected to have type
-  forall {s : Set.{0} Nat} [_inst_1 : DecidablePred.{1} Nat (fun (_x : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) _x s)] [h : Nonempty.{1} (Set.Elem.{0} Nat s)], Eq.{1} Nat (Subtype.val.{1} Nat (fun (x : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) x s) (Bot.bot.{0} (Set.Elem.{0} Nat s) (OrderBot.toBot.{0} (Set.Elem.{0} Nat s) (Subtype.le.{0} Nat instLENat (fun (x : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) x s)) (Nat.Subtype.orderBot s (fun (a : Nat) => _inst_1 a) h)))) (Nat.find (fun (n : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) n s) (fun (a : Nat) => _inst_1 a) (Iff.mp (Nonempty.{1} (Subtype.{1} Nat (fun (x : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) x s))) (Exists.{1} Nat (fun (a : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) a s)) (nonempty_subtype.{1} Nat (fun (x : Nat) => Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) x s)) h))
-Case conversion may be inaccurate. Consider using '#align nat.subtype.coe_bot Nat.Subtype.coe_botₓ'. -/
 theorem Subtype.coe_bot {s : Set ℕ} [DecidablePred (· ∈ s)] [h : Nonempty s] :
     ((⊥ : s) : ℕ) = Nat.find (nonempty_subtype.1 h) :=
   rfl
@@ -149,12 +143,6 @@ theorem dvd_sub' {k m n : ℕ} (h₁ : k ∣ m) (h₂ : k ∣ n) : k ∣ m - n :
 #align nat.dvd_sub' Nat.dvd_sub'
 -/
 
-/- warning: nat.succ_div -> Nat.succ_div is a dubious translation:
-lean 3 declaration is
-  forall (a : Nat) (b : Nat), Eq.{1} Nat (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) b) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) a b) (ite.{1} Nat (Dvd.Dvd.{0} Nat Nat.hasDvd b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Nat.decidableDvd b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
-but is expected to have type
-  forall (a : Nat) (b : Nat), Eq.{1} Nat (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) b) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) a b) (ite.{1} Nat (Dvd.dvd.{0} Nat Nat.instDvdNat b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Nat.decidable_dvd b (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
-Case conversion may be inaccurate. Consider using '#align nat.succ_div Nat.succ_divₓ'. -/
 theorem succ_div : ∀ a b : ℕ, (a + 1) / b = a / b + if b ∣ a + 1 then 1 else 0
   | a, 0 => by simp
   | 0, 1 => by simp

e8638a0f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -86,8 +86,7 @@ theorem div_eq_iff_eq_of_dvd_dvd {n x y : ℕ} (hn : n ≠ 0) (hx : x ∣ n) (hy
     apply Nat.eq_mul_of_div_eq_left (dvd_mul_of_dvd_left hy x)
     rw [eq_comm, mul_comm, Nat.mul_div_assoc _ hy]
     exact Nat.eq_mul_of_div_eq_right hx h
-  · intro h
-    rw [h]
+  · intro h; rw [h]
 #align nat.div_eq_iff_eq_of_dvd_dvd Nat.div_eq_iff_eq_of_dvd_dvd
 -/
 
@@ -118,10 +117,8 @@ protected theorem dvd_one {n : ℕ} : n ∣ 1 ↔ n = 1 :=
 
 #print Nat.not_two_dvd_bit1 /-
 @[simp]
-protected theorem not_two_dvd_bit1 (n : ℕ) : ¬2 ∣ bit1 n :=
-  by
-  rw [bit1, Nat.dvd_add_right two_dvd_bit0, Nat.dvd_one]
-  cc
+protected theorem not_two_dvd_bit1 (n : ℕ) : ¬2 ∣ bit1 n := by
+  rw [bit1, Nat.dvd_add_right two_dvd_bit0, Nat.dvd_one]; cc
 #align nat.not_two_dvd_bit1 Nat.not_two_dvd_bit1
 -/
 
@@ -316,10 +313,8 @@ theorem dvd_left_injective : Function.Injective ((· ∣ ·) : ℕ → ℕ → P
 -/
 
 #print Nat.div_lt_div_of_lt_of_dvd /-
-theorem div_lt_div_of_lt_of_dvd {a b d : ℕ} (hdb : d ∣ b) (h : a < b) : a / d < b / d :=
-  by
-  rw [Nat.lt_div_iff_mul_lt hdb]
-  exact lt_of_le_of_lt (mul_div_le a d) h
+theorem div_lt_div_of_lt_of_dvd {a b d : ℕ} (hdb : d ∣ b) (h : a < b) : a / d < b / d := by
+  rw [Nat.lt_div_iff_mul_lt hdb]; exact lt_of_le_of_lt (mul_div_le a d) h
 #align nat.div_lt_div_of_lt_of_dvd Nat.div_lt_div_of_lt_of_dvd
 -/

e8638a0f

bump to nightly-2023-04-06-20

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

86c1d414

Diff

@@ -263,12 +263,14 @@ theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
 #align nat.eq_zero_of_dvd_of_lt Nat.eq_zero_of_dvd_of_lt
 -/
 
+#print Nat.le_of_lt_add_of_dvd /-
 theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
   by
   rintro ⟨a, rfl⟩ ⟨b, rfl⟩
   rw [← mul_add_one] at h
   exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
 #align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
+-/
 
 #print Nat.mod_div_self /-
 @[simp]

e8638a0f

bump to nightly-2023-04-06-02

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

89485060

Diff

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Nat.Order.Basic
+import Mathbin.Data.Nat.Units
 import Mathbin.Data.Set.Basic
 import Mathbin.Algebra.Ring.Divisibility
 import Mathbin.Algebra.GroupWithZero.Divisibility

47a1a733

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: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
+! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -27,7 +27,7 @@ mathlib4. After `data.rat.order` has been ported, please feel free to reorganize
 
 universe u v
 
-variable {m n k : ℕ}
+variable {a b m n k : ℕ}
 
 namespace Nat
 
@@ -262,6 +262,13 @@ theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
 #align nat.eq_zero_of_dvd_of_lt Nat.eq_zero_of_dvd_of_lt
 -/
 
+theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
+  by
+  rintro ⟨a, rfl⟩ ⟨b, rfl⟩
+  rw [← mul_add_one] at h
+  exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
+#align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
+
 #print Nat.mod_div_self /-
 @[simp]
 theorem mod_div_self (m n : ℕ) : m % n / n = 0 :=

448144f7

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -92,9 +92,10 @@ theorem div_eq_iff_eq_of_dvd_dvd {n x y : ℕ} (hn : n ≠ 0) (hx : x ∣ n) (hy
 
 #print Nat.div_eq_zero_iff /-
 protected theorem div_eq_zero_iff {a b : ℕ} (hb : 0 < b) : a / b = 0 ↔ a < b :=
-  ⟨fun h => by rw [← mod_add_div a b, h, mul_zero, add_zero] <;> exact mod_lt _ hb, fun h => by
+  ⟨fun h => by rw [← mod_add_div a b, h, MulZeroClass.mul_zero, add_zero] <;> exact mod_lt _ hb,
+    fun h => by
     rw [← mul_right_inj' hb.ne', ← @add_left_cancel_iff _ _ _ (a % b), mod_add_div, mod_eq_of_lt h,
-      mul_zero, add_zero]⟩
+      MulZeroClass.mul_zero, add_zero]⟩
 #align nat.div_eq_zero_iff Nat.div_eq_zero_iff
 -/

448144f7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e8638a0f

chore: Split Data.{Nat,Int}{.Order}.Basic in group vs ring instances (#11924)

Scatter the content of Data.Nat.Basic across:

Data.Nat.Defs for the lemmas having no dependencies
Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before pre_11924

After post_11924

47062a71

Diff

@@ -3,18 +3,15 @@ Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights r
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 -/
-import Mathlib.Data.Nat.Order.Basic
-import Mathlib.Data.Nat.Units
+import Mathlib.Data.Nat.Defs
 import Mathlib.Data.Set.Basic
-import Mathlib.Algebra.Ring.Divisibility.Basic
-import Mathlib.Algebra.GroupWithZero.Divisibility
 
 #align_import data.nat.order.lemmas from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
 
 /-!
 # Further lemmas about the natural numbers
 
-The distinction between this file and `Mathlib.Data.Nat.Order.Basic` is not particularly clear.
+The distinction between this file and `Mathlib.Algebra.Order.Ring.Nat` is not particularly clear.
 They are separated for now to minimize the porting requirements for tactics during the transition to
 mathlib4. After `Mathlib.Data.Rat.Order` has been ported,
 please feel free to reorganize these two files.
@@ -48,204 +45,4 @@ theorem set_eq_univ {S : Set ℕ} : S = Set.univ ↔ 0 ∈ S ∧ ∀ k : ℕ, k
   ⟨by rintro rfl; simp, fun ⟨h0, hs⟩ => Set.eq_univ_of_forall (set_induction h0 hs)⟩
 #align nat.set_eq_univ Nat.set_eq_univ
 
-/-! ### `div` -/
-
-protected theorem lt_div_iff_mul_lt {n d : ℕ} (hnd : d ∣ n) (a : ℕ) : a < n / d ↔ d * a < n := by
-  rcases d.eq_zero_or_pos with (rfl | hd0); · simp [zero_dvd_iff.mp hnd]
-  rw [← mul_lt_mul_left hd0, ← Nat.eq_mul_of_div_eq_right hnd rfl]
-#align nat.lt_div_iff_mul_lt Nat.lt_div_iff_mul_lt
-
--- Porting note (#10756): new lemma
-theorem mul_div_eq_iff_dvd {n d : ℕ} : d * (n / d) = n ↔ d ∣ n :=
-  calc
-    d * (n / d) = n ↔ d * (n / d) = d * (n / d) + (n % d) := by rw [div_add_mod]
-    _ ↔ d ∣ n := by rw [self_eq_add_right, dvd_iff_mod_eq_zero]
-
--- Porting note (#10756): new lemma
-theorem mul_div_lt_iff_not_dvd {n d : ℕ} : d * (n / d) < n ↔ ¬(d ∣ n) :=
-  (mul_div_le _ _).lt_iff_ne.trans mul_div_eq_iff_dvd.not
-
-theorem div_eq_iff_eq_of_dvd_dvd {n x y : ℕ} (hn : n ≠ 0) (hx : x ∣ n) (hy : y ∣ n) :
-    n / x = n / y ↔ x = y := by
-  constructor
-  · intro h
-    rw [← mul_right_inj' hn]
-    apply Nat.eq_mul_of_div_eq_left (dvd_mul_of_dvd_left hy x)
-    rw [eq_comm, mul_comm, Nat.mul_div_assoc _ hy]
-    exact Nat.eq_mul_of_div_eq_right hx h
-  · intro h
-    rw [h]
-#align nat.div_eq_iff_eq_of_dvd_dvd Nat.div_eq_iff_eq_of_dvd_dvd
-
-protected theorem div_eq_zero_iff {a b : ℕ} (hb : 0 < b) : a / b = 0 ↔ a < b :=
-  ⟨fun h => by rw [← mod_add_div a b, h, mul_zero, add_zero]; exact mod_lt _ hb, fun h => by
-    rw [← mul_right_inj' hb.ne', ← @add_left_cancel_iff _ _ _ (a % b), mod_add_div, mod_eq_of_lt h,
-      mul_zero, add_zero]⟩
-#align nat.div_eq_zero_iff Nat.div_eq_zero_iff
-
-protected lemma div_ne_zero_iff (hb : b ≠ 0) : a / b ≠ 0 ↔ b ≤ a := by
-  rw [ne_eq, Nat.div_eq_zero_iff hb.bot_lt, not_lt]
-
-protected lemma div_pos_iff (hb : b ≠ 0) : 0 < a / b ↔ b ≤ a := by
-  rw [pos_iff_ne_zero, Nat.div_ne_zero_iff hb]
-
-#align nat.div_eq_zero Nat.div_eq_of_lt
-
-/-! ### `mod`, `dvd` -/
-
-set_option linter.deprecated false in
-@[simp]
-protected theorem not_two_dvd_bit1 (n : ℕ) : ¬2 ∣ bit1 n := by
-  rw [bit1, Nat.dvd_add_right two_dvd_bit0, Nat.dvd_one]
-  -- Porting note: was `cc`
-  decide
-#align nat.not_two_dvd_bit1 Nat.not_two_dvd_bit1
-
-/-- A natural number `m` divides the sum `m + n` if and only if `m` divides `n`.-/
-@[simp]
-protected theorem dvd_add_self_left {m n : ℕ} : m ∣ m + n ↔ m ∣ n :=
-  Nat.dvd_add_right (dvd_refl m)
-#align nat.dvd_add_self_left Nat.dvd_add_self_left
-
-/-- A natural number `m` divides the sum `n + m` if and only if `m` divides `n`.-/
-@[simp]
-protected theorem dvd_add_self_right {m n : ℕ} : m ∣ n + m ↔ m ∣ n :=
-  Nat.dvd_add_left (dvd_refl m)
-#align nat.dvd_add_self_right Nat.dvd_add_self_right
-
--- TODO: update `Nat.dvd_sub` in core
-theorem dvd_sub' {k m n : ℕ} (h₁ : k ∣ m) (h₂ : k ∣ n) : k ∣ m - n := by
-  rcases le_total n m with H | H
-  · exact dvd_sub H h₁ h₂
-  · rw [tsub_eq_zero_iff_le.mpr H]
-    exact dvd_zero k
-#align nat.dvd_sub' Nat.dvd_sub'
-
-theorem succ_div : ∀ a b : ℕ, (a + 1) / b = a / b + if b ∣ a + 1 then 1 else 0
-  | a, 0 => by simp
-  | 0, 1 => by simp
-  | 0, b + 2 => by
-    have hb2 : b + 2 > 1 := by simp
-    simp [ne_of_gt hb2, div_eq_of_lt hb2]
-  | a + 1, b + 1 => by
-    rw [Nat.div_eq]
-    conv_rhs => rw [Nat.div_eq]
-    by_cases hb_eq_a : b = a + 1
-    · simp [hb_eq_a, le_refl]
-    by_cases hb_le_a1 : b ≤ a + 1
-    · have hb_le_a : b ≤ a := le_of_lt_succ (lt_of_le_of_ne hb_le_a1 hb_eq_a)
-      have h₁ : 0 < b + 1 ∧ b + 1 ≤ a + 1 + 1 := ⟨succ_pos _, (add_le_add_iff_right _).2 hb_le_a1⟩
-      have h₂ : 0 < b + 1 ∧ b + 1 ≤ a + 1 := ⟨succ_pos _, (add_le_add_iff_right _).2 hb_le_a⟩
-      have dvd_iff : b + 1 ∣ a - b + 1 ↔ b + 1 ∣ a + 1 + 1 := by
-        rw [Nat.dvd_add_iff_left (dvd_refl (b + 1)), ← add_tsub_add_eq_tsub_right a 1 b,
-          add_comm (_ - _), add_assoc, tsub_add_cancel_of_le (succ_le_succ hb_le_a), add_comm 1]
-      have wf : a - b < a + 1 := lt_succ_of_le tsub_le_self
-      rw [if_pos h₁, if_pos h₂, @add_tsub_add_eq_tsub_right, ← tsub_add_eq_add_tsub hb_le_a,
-        have := wf
-        succ_div (a - b),
-        @add_tsub_add_eq_tsub_right]
-      simp [dvd_iff, succ_eq_add_one, add_comm 1, add_assoc]
-    · have hba : ¬b ≤ a := not_le_of_gt (lt_trans (lt_succ_self a) (lt_of_not_ge hb_le_a1))
-      have hb_dvd_a : ¬b + 1 ∣ a + 2 := fun h =>
-        hb_le_a1 (le_of_succ_le_succ (le_of_dvd (succ_pos _) h))
-      simp [hba, hb_le_a1, hb_dvd_a]
-#align nat.succ_div Nat.succ_div
-
-theorem succ_div_of_dvd {a b : ℕ} (hba : b ∣ a + 1) : (a + 1) / b = a / b + 1 := by
-  rw [succ_div, if_pos hba]
-#align nat.succ_div_of_dvd Nat.succ_div_of_dvd
-
-theorem succ_div_of_not_dvd {a b : ℕ} (hba : ¬b ∣ a + 1) : (a + 1) / b = a / b := by
-  rw [succ_div, if_neg hba, add_zero]
-#align nat.succ_div_of_not_dvd Nat.succ_div_of_not_dvd
-
-theorem dvd_iff_div_mul_eq (n d : ℕ) : d ∣ n ↔ n / d * d = n :=
-  ⟨fun h => Nat.div_mul_cancel h, fun h => Dvd.intro_left (n / d) h⟩
-#align nat.dvd_iff_div_mul_eq Nat.dvd_iff_div_mul_eq
-
-theorem dvd_iff_le_div_mul (n d : ℕ) : d ∣ n ↔ n ≤ n / d * d :=
-  ((dvd_iff_div_mul_eq _ _).trans le_antisymm_iff).trans (and_iff_right (div_mul_le_self n d))
-#align nat.dvd_iff_le_div_mul Nat.dvd_iff_le_div_mul
-
-theorem dvd_iff_dvd_dvd (n d : ℕ) : d ∣ n ↔ ∀ k : ℕ, k ∣ d → k ∣ n :=
-  ⟨fun h _ hkd => dvd_trans hkd h, fun h => h _ dvd_rfl⟩
-#align nat.dvd_iff_dvd_dvd Nat.dvd_iff_dvd_dvd
-
-theorem dvd_div_of_mul_dvd {a b c : ℕ} (h : a * b ∣ c) : b ∣ c / a :=
-  if ha : a = 0 then by simp [ha]
-  else
-    have ha : 0 < a := Nat.pos_of_ne_zero ha
-    have h1 : ∃ d, c = a * b * d := h
-    let ⟨d, hd⟩ := h1
-    have h2 : c / a = b * d := Nat.div_eq_of_eq_mul_right ha (by simpa [mul_assoc] using hd)
-    show ∃ d, c / a = b * d from ⟨d, h2⟩
-#align nat.dvd_div_of_mul_dvd Nat.dvd_div_of_mul_dvd
-
-@[simp]
-theorem dvd_div_iff {a b c : ℕ} (hbc : c ∣ b) : a ∣ b / c ↔ c * a ∣ b :=
-  ⟨fun h => mul_dvd_of_dvd_div hbc h, fun h => dvd_div_of_mul_dvd h⟩
-#align nat.dvd_div_iff Nat.dvd_div_iff
-
-@[simp]
-theorem div_div_div_eq_div {a b c : ℕ} (dvd : b ∣ a) (dvd2 : a ∣ c) : c / (a / b) / b = c / a :=
-  match a, b, c with
-  | 0, _, _ => by simp
-  | a + 1, 0, _ => by simp at dvd
-  | a + 1, c + 1, _ => by
-    have a_split : a + 1 ≠ 0 := succ_ne_zero a
-    have c_split : c + 1 ≠ 0 := succ_ne_zero c
-    rcases dvd2 with ⟨k, rfl⟩
-    rcases dvd with ⟨k2, pr⟩
-    have k2_nonzero : k2 ≠ 0 := fun k2_zero => by simp [k2_zero] at pr
-    rw [Nat.mul_div_cancel_left k (Nat.pos_of_ne_zero a_split), pr,
-      Nat.mul_div_cancel_left k2 (Nat.pos_of_ne_zero c_split), Nat.mul_comm ((c + 1) * k2) k, ←
-      Nat.mul_assoc k (c + 1) k2, Nat.mul_div_cancel _ (Nat.pos_of_ne_zero k2_nonzero),
-      Nat.mul_div_cancel _ (Nat.pos_of_ne_zero c_split)]
-#align nat.div_div_div_eq_div Nat.div_div_div_eq_div
-
-/-- If a small natural number is divisible by a larger natural number,
-the small number is zero. -/
-theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
-  Nat.eq_zero_of_dvd_of_div_eq_zero w
-    ((Nat.div_eq_zero_iff (lt_of_le_of_lt (zero_le b) h)).mpr h)
-#align nat.eq_zero_of_dvd_of_lt Nat.eq_zero_of_dvd_of_lt
-
-theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b := by
-  rintro ⟨a, rfl⟩ ⟨b, rfl⟩
-  -- Porting note: Needed to give an explicit argument to `mul_add_one`
-  rw [← mul_add_one n] at h
-  exact mul_le_mul_left' (Nat.lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
-#align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
-
-#align nat.mod_div_self Nat.mod_div_self
-
-/-- `n` is not divisible by `a` iff it is between `a * k` and `a * (k + 1)` for some `k`. -/
-theorem not_dvd_iff_between_consec_multiples (n : ℕ) {a : ℕ} (ha : 0 < a) :
-    (∃ k : ℕ, a * k < n ∧ n < a * (k + 1)) ↔ ¬a ∣ n := by
-  refine'
-    ⟨fun ⟨k, hk1, hk2⟩ => not_dvd_of_between_consec_multiples hk1 hk2, fun han =>
-      ⟨n / a, ⟨lt_of_le_of_ne (mul_div_le n a) _, lt_mul_div_succ _ ha⟩⟩⟩
-  exact mt (Dvd.intro (n / a)) han
-#align nat.not_dvd_iff_between_consec_multiples Nat.not_dvd_iff_between_consec_multiples
-
-/-- Two natural numbers are equal if and only if they have the same multiples. -/
-theorem dvd_right_iff_eq {m n : ℕ} : (∀ a : ℕ, m ∣ a ↔ n ∣ a) ↔ m = n :=
-  ⟨fun h => dvd_antisymm ((h _).mpr dvd_rfl) ((h _).mp dvd_rfl), fun h n => by rw [h]⟩
-#align nat.dvd_right_iff_eq Nat.dvd_right_iff_eq
-
-/-- Two natural numbers are equal if and only if they have the same divisors. -/
-theorem dvd_left_iff_eq {m n : ℕ} : (∀ a : ℕ, a ∣ m ↔ a ∣ n) ↔ m = n :=
-  ⟨fun h => dvd_antisymm ((h _).mp dvd_rfl) ((h _).mpr dvd_rfl), fun h n => by rw [h]⟩
-#align nat.dvd_left_iff_eq Nat.dvd_left_iff_eq
-
-/-- `dvd` is injective in the left argument -/
-theorem dvd_left_injective : Function.Injective ((· ∣ ·) : ℕ → ℕ → Prop) := fun _ _ h =>
-  dvd_right_iff_eq.mp fun a => iff_of_eq (congr_fun h a)
-#align nat.dvd_left_injective Nat.dvd_left_injective
-
-theorem div_lt_div_of_lt_of_dvd {a b d : ℕ} (hdb : d ∣ b) (h : a < b) : a / d < b / d := by
-  rw [Nat.lt_div_iff_mul_lt hdb]
-  exact lt_of_le_of_lt (mul_div_le a d) h
-#align nat.div_lt_div_of_lt_of_dvd Nat.div_lt_div_of_lt_of_dvd
-
 end Nat

e8638a0f

chore(Order): add missing inst prefix to instance names (#11238)

This is not exhaustive; it largely does not rename instances that relate to algebra, and only focuses on the "core" order files.

4d23d2cb

Diff

@@ -36,7 +36,7 @@ instance Subtype.orderBot (s : Set ℕ) [DecidablePred (· ∈ s)] [h : Nonempty
 #align nat.subtype.order_bot Nat.Subtype.orderBot
 
 instance Subtype.semilatticeSup (s : Set ℕ) : SemilatticeSup s :=
-  { Subtype.linearOrder s, LinearOrder.toLattice with }
+  { Subtype.instLinearOrder s, LinearOrder.toLattice with }
 #align nat.subtype.semilattice_sup Nat.Subtype.semilatticeSup
 
 theorem Subtype.coe_bot {s : Set ℕ} [DecidablePred (· ∈ s)] [h : Nonempty s] :

e8638a0f

chore: classify new lemma porting notes (#11217)

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

"new lemma"
"added lemma"

68df7d0d

Diff

@@ -55,13 +55,13 @@ protected theorem lt_div_iff_mul_lt {n d : ℕ} (hnd : d ∣ n) (a : ℕ) : a <
   rw [← mul_lt_mul_left hd0, ← Nat.eq_mul_of_div_eq_right hnd rfl]
 #align nat.lt_div_iff_mul_lt Nat.lt_div_iff_mul_lt
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem mul_div_eq_iff_dvd {n d : ℕ} : d * (n / d) = n ↔ d ∣ n :=
   calc
     d * (n / d) = n ↔ d * (n / d) = d * (n / d) + (n % d) := by rw [div_add_mod]
     _ ↔ d ∣ n := by rw [self_eq_add_right, dvd_iff_mod_eq_zero]
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem mul_div_lt_iff_not_dvd {n d : ℕ} : d * (n / d) < n ↔ ¬(d ∣ n) :=
   (mul_div_le _ _).lt_iff_ne.trans mul_div_eq_iff_dvd.not

e8638a0f

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -55,13 +55,13 @@ protected theorem lt_div_iff_mul_lt {n d : ℕ} (hnd : d ∣ n) (a : ℕ) : a <
   rw [← mul_lt_mul_left hd0, ← Nat.eq_mul_of_div_eq_right hnd rfl]
 #align nat.lt_div_iff_mul_lt Nat.lt_div_iff_mul_lt
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem mul_div_eq_iff_dvd {n d : ℕ} : d * (n / d) = n ↔ d ∣ n :=
   calc
     d * (n / d) = n ↔ d * (n / d) = d * (n / d) + (n % d) := by rw [div_add_mod]
     _ ↔ d ∣ n := by rw [self_eq_add_right, dvd_iff_mod_eq_zero]
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem mul_div_lt_iff_not_dvd {n d : ℕ} : d * (n / d) < n ↔ ¬(d ∣ n) :=
   (mul_div_le _ _).lt_iff_ne.trans mul_div_eq_iff_dvd.not
 
@@ -212,7 +212,7 @@ theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
 
 theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b := by
   rintro ⟨a, rfl⟩ ⟨b, rfl⟩
-  -- porting note: Needed to give an explicit argument to `mul_add_one`
+  -- Porting note: Needed to give an explicit argument to `mul_add_one`
   rw [← mul_add_one n] at h
   exact mul_le_mul_left' (Nat.lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
 #align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd

e8638a0f

chore: bump dependencies (#10315)

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

ba9f2e5b

Diff

@@ -214,7 +214,7 @@ theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
   rintro ⟨a, rfl⟩ ⟨b, rfl⟩
   -- porting note: Needed to give an explicit argument to `mul_add_one`
   rw [← mul_add_one n] at h
-  exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
+  exact mul_le_mul_left' (Nat.lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
 #align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
 
 #align nat.mod_div_self Nat.mod_div_self

e8638a0f

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -115,7 +115,7 @@ protected theorem dvd_add_self_right {m n : ℕ} : m ∣ n + m ↔ m ∣ n :=
 
 -- TODO: update `Nat.dvd_sub` in core
 theorem dvd_sub' {k m n : ℕ} (h₁ : k ∣ m) (h₂ : k ∣ n) : k ∣ m - n := by
-  cases' le_total n m with H H
+  rcases le_total n m with H | H
   · exact dvd_sub H h₁ h₂
   · rw [tsub_eq_zero_iff_le.mpr H]
     exact dvd_zero k

e8638a0f

feat(Data/Fin): add lemmas (#8974)

move Nat.dvd_one to Data.Nat.Basic; it should go to Std4;
rename Fin.ofNat_eq_val to Fin.ofNat''_eq_cast;
add @[simp] lemmas Fin.val_nat_cast, Fin.nat_cast_self, and Fin.nat_cast_eq_zero;
add @[simp] to Fin.cast_nat_eq_last and ZMod.val_nat_cast;
add binomial_apply_last, as the LHS of binomial_apply_self is no longer in simp normal form.

a45fd777

Diff

@@ -93,12 +93,6 @@ protected lemma div_pos_iff (hb : b ≠ 0) : 0 < a / b ↔ b ≤ a := by
 
 /-! ### `mod`, `dvd` -/
 
-
-@[simp]
-protected theorem dvd_one {n : ℕ} : n ∣ 1 ↔ n = 1 :=
-  ⟨eq_one_of_dvd_one, fun e => e.symm ▸ dvd_rfl⟩
-#align nat.dvd_one Nat.dvd_one
-
 set_option linter.deprecated false in
 @[simp]
 protected theorem not_two_dvd_bit1 (n : ℕ) : ¬2 ∣ bit1 n := by

e8638a0f

chore: bump Std, changes for leanprover/std4#366 (#8700)

Notably leanprover/std4#366 changed the definition of testBit (to something equivalent) when upstreaming it, which broke a handful of proofs.

Other conflicting changes in Std, resolved for now by priming the mathlib name:

Std.BitVec.adc: the type was changed from BitVec (n + 1) to Bool × BitVec w
Nat.mul_add_mod: the type was changed from (a * b + c) % b = c % b to (b * a + c) % b = c % b

Zulip thread

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Alex Keizer <alex@keizer.dev> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

1c6d0cef

Diff

@@ -223,11 +223,6 @@ theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
   exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
 #align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
 
-@[simp]
-theorem mod_div_self (m n : ℕ) : m % n / n = 0 := by
-  cases n
-  · exact (m % 0).div_zero
-  · case succ n => exact Nat.div_eq_of_lt (m.mod_lt n.succ_pos)
 #align nat.mod_div_self Nat.mod_div_self
 
 /-- `n` is not divisible by `a` iff it is between `a * k` and `a * (k + 1)` for some `k`. -/

e8638a0f

feat: Squarefree lemmas for Nat (#8323)

029b3d78

Diff

@@ -83,6 +83,12 @@ protected theorem div_eq_zero_iff {a b : ℕ} (hb : 0 < b) : a / b = 0 ↔ a < b
       mul_zero, add_zero]⟩
 #align nat.div_eq_zero_iff Nat.div_eq_zero_iff
 
+protected lemma div_ne_zero_iff (hb : b ≠ 0) : a / b ≠ 0 ↔ b ≤ a := by
+  rw [ne_eq, Nat.div_eq_zero_iff hb.bot_lt, not_lt]
+
+protected lemma div_pos_iff (hb : b ≠ 0) : 0 < a / b ↔ b ≤ a := by
+  rw [pos_iff_ne_zero, Nat.div_ne_zero_iff hb]
+
 #align nat.div_eq_zero Nat.div_eq_of_lt
 
 /-! ### `mod`, `dvd` -/

e8638a0f

chore: cleanup of Data.Nat.Bitwise (#7763)

We would like to move much of the content of this file up to Std, as projects working on SMT automation need them.

This is a preliminary cleanup to reduce imports in preparation for upstreaming.

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

a3e0e089

Diff

@@ -83,9 +83,7 @@ protected theorem div_eq_zero_iff {a b : ℕ} (hb : 0 < b) : a / b = 0 ↔ a < b
       mul_zero, add_zero]⟩
 #align nat.div_eq_zero_iff Nat.div_eq_zero_iff
 
-protected theorem div_eq_zero {a b : ℕ} (hb : a < b) : a / b = 0 :=
-  (Nat.div_eq_zero_iff <| (zero_le a).trans_lt hb).mpr hb
-#align nat.div_eq_zero Nat.div_eq_zero
+#align nat.div_eq_zero Nat.div_eq_of_lt
 
 /-! ### `mod`, `dvd` -/
 
@@ -223,7 +221,7 @@ theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b :=
 theorem mod_div_self (m n : ℕ) : m % n / n = 0 := by
   cases n
   · exact (m % 0).div_zero
-  · case succ n => exact Nat.div_eq_zero (m.mod_lt n.succ_pos)
+  · case succ n => exact Nat.div_eq_of_lt (m.mod_lt n.succ_pos)
 #align nat.mod_div_self Nat.mod_div_self
 
 /-- `n` is not divisible by `a` iff it is between `a * k` and `a * (k + 1)` for some `k`. -/

e8638a0f

feat: lemmas about divisibility, mostly related to nilpotency (#7355)

bf1ceb82

Diff

@@ -6,7 +6,7 @@ Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 import Mathlib.Data.Nat.Order.Basic
 import Mathlib.Data.Nat.Units
 import Mathlib.Data.Set.Basic
-import Mathlib.Algebra.Ring.Divisibility
+import Mathlib.Algebra.Ring.Divisibility.Basic
 import Mathlib.Algebra.GroupWithZero.Divisibility
 
 #align_import data.nat.order.lemmas from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"

e8638a0f

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

@@ -2,11 +2,6 @@
 Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Nat.Order.Basic
 import Mathlib.Data.Nat.Units
@@ -14,6 +9,8 @@ import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Ring.Divisibility
 import Mathlib.Algebra.GroupWithZero.Divisibility
 
+#align_import data.nat.order.lemmas from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Further lemmas about the natural numbers

e8638a0f

feat: port NumberTheory.SumFourSquares (#4604)

eb95d896

Diff

@@ -53,12 +53,21 @@ theorem set_eq_univ {S : Set ℕ} : S = Set.univ ↔ 0 ∈ S ∧ ∀ k : ℕ, k
 
 /-! ### `div` -/
 
-
 protected theorem lt_div_iff_mul_lt {n d : ℕ} (hnd : d ∣ n) (a : ℕ) : a < n / d ↔ d * a < n := by
   rcases d.eq_zero_or_pos with (rfl | hd0); · simp [zero_dvd_iff.mp hnd]
   rw [← mul_lt_mul_left hd0, ← Nat.eq_mul_of_div_eq_right hnd rfl]
 #align nat.lt_div_iff_mul_lt Nat.lt_div_iff_mul_lt
 
+-- porting note: new lemma
+theorem mul_div_eq_iff_dvd {n d : ℕ} : d * (n / d) = n ↔ d ∣ n :=
+  calc
+    d * (n / d) = n ↔ d * (n / d) = d * (n / d) + (n % d) := by rw [div_add_mod]
+    _ ↔ d ∣ n := by rw [self_eq_add_right, dvd_iff_mod_eq_zero]
+
+-- porting note: new lemma
+theorem mul_div_lt_iff_not_dvd {n d : ℕ} : d * (n / d) < n ↔ ¬(d ∣ n) :=
+  (mul_div_le _ _).lt_iff_ne.trans mul_div_eq_iff_dvd.not
+
 theorem div_eq_iff_eq_of_dvd_dvd {n x y : ℕ} (hn : n ≠ 0) (hx : x ∣ n) (hy : y ∣ n) :
     n / x = n / y ↔ x = y := by
   constructor

e8638a0f

feat: Dot notation aliases (#3303)

Match https://github.com/leanprover-community/mathlib/pull/18698 and a bit of https://github.com/leanprover-community/mathlib/pull/18785.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

4fa401fa

Diff

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Nat.Order.Basic
+import Mathlib.Data.Nat.Units
 import Mathlib.Data.Set.Basic
 import Mathlib.Algebra.Ring.Divisibility
 import Mathlib.Algebra.GroupWithZero.Divisibility

47a1a733

feat: a/c ≡ b/c mod m/c → a ≡ b mod m (#3259)

https://github.com/leanprover-community/mathlib/pull/18119, https://github.com/leanprover-community/mathlib/pull/18666.

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

9d339228

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit 2258b40dacd2942571c8ce136215350c702dc78f
+! leanprover-community/mathlib commit 47a1a73351de8dd6c8d3d32b569c8e434b03ca47
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -25,7 +25,7 @@ please feel free to reorganize these two files.
 
 universe u v
 
-variable {m n k : ℕ}
+variable {a b m n k : ℕ}
 
 namespace Nat
 
@@ -205,6 +205,13 @@ theorem eq_zero_of_dvd_of_lt {a b : ℕ} (w : a ∣ b) (h : b < a) : b = 0 :=
     ((Nat.div_eq_zero_iff (lt_of_le_of_lt (zero_le b) h)).mpr h)
 #align nat.eq_zero_of_dvd_of_lt Nat.eq_zero_of_dvd_of_lt
 
+theorem le_of_lt_add_of_dvd (h : a < b + n) : n ∣ a → n ∣ b → a ≤ b := by
+  rintro ⟨a, rfl⟩ ⟨b, rfl⟩
+  -- porting note: Needed to give an explicit argument to `mul_add_one`
+  rw [← mul_add_one n] at h
+  exact mul_le_mul_left' (lt_succ_iff.1 <| lt_of_mul_lt_mul_left h bot_le) _
+#align nat.le_of_lt_add_of_dvd Nat.le_of_lt_add_of_dvd
+
 @[simp]
 theorem mod_div_self (m n : ℕ) : m % n / n = 0 := by
   cases n

2258b40d

chore: bump to leanprover/lean4:nightly-2023-02-10 (#2188)

5bbbc25c

Diff

@@ -135,10 +135,10 @@ theorem succ_div : ∀ a b : ℕ, (a + 1) / b = a / b + if b ∣ a + 1 then 1 el
         rw [Nat.dvd_add_iff_left (dvd_refl (b + 1)), ← add_tsub_add_eq_tsub_right a 1 b,
           add_comm (_ - _), add_assoc, tsub_add_cancel_of_le (succ_le_succ hb_le_a), add_comm 1]
       have wf : a - b < a + 1 := lt_succ_of_le tsub_le_self
-      rw [if_pos h₁, if_pos h₂, add_tsub_add_eq_tsub_right, ← tsub_add_eq_add_tsub hb_le_a,
+      rw [if_pos h₁, if_pos h₂, @add_tsub_add_eq_tsub_right, ← tsub_add_eq_add_tsub hb_le_a,
         have := wf
         succ_div (a - b),
-        add_tsub_add_eq_tsub_right]
+        @add_tsub_add_eq_tsub_right]
       simp [dvd_iff, succ_eq_add_one, add_comm 1, add_assoc]
     · have hba : ¬b ≤ a := not_le_of_gt (lt_trans (lt_succ_self a) (lt_of_not_ge hb_le_a1))
       have hb_dvd_a : ¬b + 1 ∣ a + 2 := fun h =>

2258b40d

chore: fix more casing errors per naming scheme (#1232)

I've avoided anything under Tactic or test.

In correcting the names, I found Option.isNone_iff_eq_none duplicated between Std and Mathlib, so the Mathlib one has been removed.

Co-authored-by: Reid Barton <rwbarton@gmail.com>

31a56f75

Diff

@@ -108,7 +108,7 @@ protected theorem dvd_add_self_right {m n : ℕ} : m ∣ n + m ↔ m ∣ n :=
   Nat.dvd_add_left (dvd_refl m)
 #align nat.dvd_add_self_right Nat.dvd_add_self_right
 
--- TODO: update `nat.dvd_sub` in core
+-- TODO: update `Nat.dvd_sub` in core
 theorem dvd_sub' {k m n : ℕ} (h₁ : k ∣ m) (h₂ : k ∣ n) : k ∣ m - n := by
   cases' le_total n m with H H
   · exact dvd_sub H h₁ h₂

2258b40d

chore: update SHA in porting header (#1306)

These files correspond to files flagged "The following files have been modified since the commit at which they were verified." by port_status.py but are in sync with mathlib3, so we can update the hash.

I only updated the easy ones, the others need a closer inspection.

Co-authored-by: Reid Barton <rwbarton@gmail.com>

cac405f4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.order.lemmas
-! leanprover-community/mathlib commit 10b4e499f43088dd3bb7b5796184ad5216648ab1
+! leanprover-community/mathlib commit 2258b40dacd2942571c8ce136215350c702dc78f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

10b4e499

chore: add source headers to ported theory files (#1094)

The script used to do this is included. The yaml file was obtained from https://raw.githubusercontent.com/wiki/leanprover-community/mathlib/mathlib4-port-status.md

f168625e

Diff

@@ -2,6 +2,11 @@
 Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
+
+! This file was ported from Lean 3 source module data.nat.order.lemmas
+! leanprover-community/mathlib commit 10b4e499f43088dd3bb7b5796184ad5216648ab1
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
 -/
 import Mathlib.Data.Nat.Order.Basic
 import Mathlib.Data.Set.Basic

`data.nat.order.lemmas` ⟷ `Mathlib.Data.Nat.Order.Lemmas`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 1 + 83

data.nat.order.lemmas ⟷ Mathlib.Data.Nat.Order.Lemmas

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 1 + 83

`data.nat.order.lemmas` ⟷ `Mathlib.Data.Nat.Order.Lemmas`