group_theory.archimedean | 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

f93c1193

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

a11f9106

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Heather Macbeth, Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth, Patrick Massot
 -/
-import Mathbin.Algebra.Order.Archimedean
-import Mathbin.GroupTheory.Subgroup.Basic
+import Algebra.Order.Archimedean
+import GroupTheory.Subgroup.Basic
 
 #align_import group_theory.archimedean from "leanprover-community/mathlib"@"a11f9106a169dd302a285019e5165f8ab32ff433"

a11f9106

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Heather Macbeth, Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth, Patrick Massot
-
-! This file was ported from Lean 3 source module group_theory.archimedean
-! leanprover-community/mathlib commit a11f9106a169dd302a285019e5165f8ab32ff433
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Archimedean
 import Mathbin.GroupTheory.Subgroup.Basic
 
+#align_import group_theory.archimedean from "leanprover-community/mathlib"@"a11f9106a169dd302a285019e5165f8ab32ff433"
+
 /-!
 # Archimedean groups

a11f9106

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -42,6 +42,7 @@ variable {G : Type _} [LinearOrderedAddCommGroup G] [Archimedean G]
 
 open LinearOrderedAddCommGroup
 
+#print AddSubgroup.cyclic_of_min /-
 /-- Given a subgroup `H` of a decidable linearly ordered archimedean abelian group `G`, if there
 exists a minimal element `a` of `H ∩ G_{>0}` then `H` is generated by `a`. -/
 theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
@@ -62,7 +63,9 @@ theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
     contradiction
   simp [sub_eq_zero.mp h_zero, AddSubgroup.mem_closure_singleton]
 #align add_subgroup.cyclic_of_min AddSubgroup.cyclic_of_min
+-/
 
+#print Int.subgroup_cyclic /-
 /-- Every subgroup of `ℤ` is cyclic. -/
 theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closure {a} :=
   by
@@ -81,4 +84,5 @@ theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closu
   obtain ⟨a, ha, ha'⟩ := Int.exists_least_of_bdd ⟨(0 : ℤ), h_bdd⟩ ⟨g₁, g₁_in, g₁_pos⟩
   exact ⟨a, AddSubgroup.cyclic_of_min ⟨ha, ha'⟩⟩
 #align int.subgroup_cyclic Int.subgroup_cyclic
+-/

a11f9106

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -45,7 +45,7 @@ open LinearOrderedAddCommGroup
 /-- Given a subgroup `H` of a decidable linearly ordered archimedean abelian group `G`, if there
 exists a minimal element `a` of `H ∩ G_{>0}` then `H` is generated by `a`. -/
 theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
-    (ha : IsLeast { g : G | g ∈ H ∧ 0 < g } a) : H = AddSubgroup.closure {a} :=
+    (ha : IsLeast {g : G | g ∈ H ∧ 0 < g} a) : H = AddSubgroup.closure {a} :=
   by
   obtain ⟨⟨a_in, a_pos⟩, a_min⟩ := ha
   refine' le_antisymm _ (H.closure_le.mpr <| by simp [a_in])
@@ -70,7 +70,7 @@ theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closu
   · use 0
     rw [h]
     exact add_subgroup.closure_singleton_zero.symm
-  let s := { g : ℤ | g ∈ H ∧ 0 < g }
+  let s := {g : ℤ | g ∈ H ∧ 0 < g}
   have h_bdd : ∀ g ∈ s, (0 : ℤ) ≤ g := fun _ h => le_of_lt h.2
   obtain ⟨g₀, g₀_in, g₀_ne⟩ := h
   obtain ⟨g₁, g₁_in, g₁_pos⟩ : ∃ g₁ : ℤ, g₁ ∈ H ∧ 0 < g₁ :=

a11f9106

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -42,12 +42,6 @@ variable {G : Type _} [LinearOrderedAddCommGroup G] [Archimedean G]
 
 open LinearOrderedAddCommGroup
 
-/- warning: add_subgroup.cyclic_of_min -> AddSubgroup.cyclic_of_min is a dubious translation:
-lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} G] [_inst_2 : Archimedean.{u1} G (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} G (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))] {H : AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))} {a : G}, (IsLeast.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (setOf.{u1} G (fun (g : G) => And (Membership.Mem.{u1, u1} G (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) G (AddSubgroup.setLike.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))) g H) (LT.lt.{u1} G (Preorder.toHasLt.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (OfNat.ofNat.{u1} G 0 (OfNat.mk.{u1} G 0 (Zero.zero.{u1} G (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (SubNegMonoid.toAddMonoid.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))))))))) g))) a) -> (Eq.{succ u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) H (AddSubgroup.closure.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (Singleton.singleton.{u1, u1} G (Set.{u1} G) (Set.hasSingleton.{u1} G) a)))
-but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} G] [_inst_2 : Archimedean.{u1} G (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} G (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} G (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} G _inst_1)))] {H : AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))} {a : G}, (IsLeast.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (setOf.{u1} G (fun (g : G) => And (Membership.mem.{u1, u1} G (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) G (AddSubgroup.instSetLikeAddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))) g H) (LT.lt.{u1} G (Preorder.toLT.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (OfNat.ofNat.{u1} G 0 (Zero.toOfNat0.{u1} G (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))))))) g))) a) -> (Eq.{succ u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) H (AddSubgroup.closure.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (Singleton.singleton.{u1, u1} G (Set.{u1} G) (Set.instSingletonSet.{u1} G) a)))
-Case conversion may be inaccurate. Consider using '#align add_subgroup.cyclic_of_min AddSubgroup.cyclic_of_minₓ'. -/
 /-- Given a subgroup `H` of a decidable linearly ordered archimedean abelian group `G`, if there
 exists a minimal element `a` of `H ∩ G_{>0}` then `H` is generated by `a`. -/
 theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
@@ -69,12 +63,6 @@ theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
   simp [sub_eq_zero.mp h_zero, AddSubgroup.mem_closure_singleton]
 #align add_subgroup.cyclic_of_min AddSubgroup.cyclic_of_min
 
-/- warning: int.subgroup_cyclic -> Int.subgroup_cyclic is a dubious translation:
-lean 3 declaration is
-  forall (H : AddSubgroup.{0} Int Int.addGroup), Exists.{1} Int (fun (a : Int) => Eq.{1} (AddSubgroup.{0} Int Int.addGroup) H (AddSubgroup.closure.{0} Int Int.addGroup (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) a)))
-but is expected to have type
-  forall (H : AddSubgroup.{0} Int Int.instAddGroupInt), Exists.{1} Int (fun (a : Int) => Eq.{1} (AddSubgroup.{0} Int Int.instAddGroupInt) H (AddSubgroup.closure.{0} Int Int.instAddGroupInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) a)))
-Case conversion may be inaccurate. Consider using '#align int.subgroup_cyclic Int.subgroup_cyclicₓ'. -/
 /-- Every subgroup of `ℤ` is cyclic. -/
 theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closure {a} :=
   by

a11f9106

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -44,7 +44,7 @@ open LinearOrderedAddCommGroup
 
 /- warning: add_subgroup.cyclic_of_min -> AddSubgroup.cyclic_of_min is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} G] [_inst_2 : Archimedean.{u1} G (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} G (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))] {H : AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))} {a : G}, (IsLeast.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (setOf.{u1} G (fun (g : G) => And (Membership.Mem.{u1, u1} G (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) G (AddSubgroup.setLike.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))) g H) (LT.lt.{u1} G (Preorder.toLT.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (OfNat.ofNat.{u1} G 0 (OfNat.mk.{u1} G 0 (Zero.zero.{u1} G (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (SubNegMonoid.toAddMonoid.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))))))))) g))) a) -> (Eq.{succ u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) H (AddSubgroup.closure.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (Singleton.singleton.{u1, u1} G (Set.{u1} G) (Set.hasSingleton.{u1} G) a)))
+  forall {G : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} G] [_inst_2 : Archimedean.{u1} G (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} G (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))] {H : AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))} {a : G}, (IsLeast.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (setOf.{u1} G (fun (g : G) => And (Membership.Mem.{u1, u1} G (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) G (AddSubgroup.setLike.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))) g H) (LT.lt.{u1} G (Preorder.toHasLt.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (OfNat.ofNat.{u1} G 0 (OfNat.mk.{u1} G 0 (Zero.zero.{u1} G (AddZeroClass.toHasZero.{u1} G (AddMonoid.toAddZeroClass.{u1} G (SubNegMonoid.toAddMonoid.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))))))))) g))) a) -> (Eq.{succ u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) H (AddSubgroup.closure.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (Singleton.singleton.{u1, u1} G (Set.{u1} G) (Set.hasSingleton.{u1} G) a)))
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} G] [_inst_2 : Archimedean.{u1} G (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} G (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} G (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} G _inst_1)))] {H : AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))} {a : G}, (IsLeast.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (setOf.{u1} G (fun (g : G) => And (Membership.mem.{u1, u1} G (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) G (AddSubgroup.instSetLikeAddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))) g H) (LT.lt.{u1} G (Preorder.toLT.{u1} G (PartialOrder.toPreorder.{u1} G (OrderedAddCommGroup.toPartialOrder.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) (OfNat.ofNat.{u1} G 0 (Zero.toOfNat0.{u1} G (NegZeroClass.toZero.{u1} G (SubNegZeroMonoid.toNegZeroClass.{u1} G (SubtractionMonoid.toSubNegZeroMonoid.{u1} G (SubtractionCommMonoid.toSubtractionMonoid.{u1} G (AddCommGroup.toDivisionAddCommMonoid.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))))))))) g))) a) -> (Eq.{succ u1} (AddSubgroup.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1)))) H (AddSubgroup.closure.{u1} G (AddCommGroup.toAddGroup.{u1} G (OrderedAddCommGroup.toAddCommGroup.{u1} G (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} G _inst_1))) (Singleton.singleton.{u1, u1} G (Set.{u1} G) (Set.instSingletonSet.{u1} G) a)))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.cyclic_of_min AddSubgroup.cyclic_of_minₓ'. -/

a11f9106

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f93c1193

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

@@ -83,7 +83,7 @@ theorem AddSubgroup.exists_isLeast_pos {H : AddSubgroup G} (hbot : H ≠ ⊥) {a
   · refine disjoint_left.1 hd (sub_mem hxH hyH) ⟨sub_pos.2 hxy, sub_lt_iff_lt_add'.2 ?_⟩
     calc x ≤ (n + 1) • a := hxn
     _ ≤ (m + 1) • a := nsmul_le_nsmul_left h₀.le (add_le_add_right hnm _)
-    _ = m • a + a := succ_nsmul' _ _
+    _ = m • a + a := succ_nsmul _ _
     _ < y + a := add_lt_add_right hm.1 _
 
 /-- If an additive subgroup of a linear ordered additive commutative group is disjoint with the

f93c1193

chore: Rename zpow_coe_nat to zpow_natCast (#11528)

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

75dad162

Diff

@@ -66,7 +66,7 @@ theorem AddSubgroup.exists_isLeast_pos {H : AddSubgroup G} (hbot : H ≠ ⊥) {a
     lift m to ℕ
     · rw [← Int.lt_add_one_iff, ← zsmul_lt_zsmul_iff h₀, zero_zsmul]
       exact hg.trans_le hm
-    · simp only [← Nat.cast_succ, coe_nat_zsmul] at hm hm'
+    · simp only [← Nat.cast_succ, natCast_zsmul] at hm hm'
       exact ⟨m, hm', hm⟩
   have : ∃ n : ℕ, Set.Nonempty (H ∩ Ioc (n • a) ((n + 1) • a)) := by
     rcases (bot_or_exists_ne_zero H).resolve_left hbot with ⟨g, hgH, hg₀⟩

f93c1193

chore(Order/*): move SupSet, Set.sUnion etc to a new file (#10232)

d18f1d0b

Diff

@@ -5,6 +5,7 @@ Authors: Heather Macbeth, Patrick Massot
 -/
 import Mathlib.Algebra.Order.Archimedean
 import Mathlib.GroupTheory.Subgroup.Basic
+import Mathlib.Data.Set.Lattice
 
 #align_import group_theory.archimedean from "leanprover-community/mathlib"@"f93c11933efbc3c2f0299e47b8ff83e9b539cbf6"

f93c1193

chore: Rename pow monotonicity lemmas (#9095)

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

Renames

`Algebra.GroupPower.Order`

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

`Algebra.GroupPower.CovariantClass`

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

`Data.Nat.Pow`

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

Lemmas added

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

Lemmas removed

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

Other changes

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

d61c95e1

Diff

@@ -81,7 +81,7 @@ theorem AddSubgroup.exists_isLeast_pos {H : AddSubgroup G} (hbot : H ≠ ⊥) {a
   · exact hmin m hmn ⟨y, hyH, hm⟩
   · refine disjoint_left.1 hd (sub_mem hxH hyH) ⟨sub_pos.2 hxy, sub_lt_iff_lt_add'.2 ?_⟩
     calc x ≤ (n + 1) • a := hxn
-    _ ≤ (m + 1) • a := nsmul_le_nsmul h₀.le (add_le_add_right hnm _)
+    _ ≤ (m + 1) • a := nsmul_le_nsmul_left h₀.le (add_le_add_right hnm _)
     _ = m • a + a := succ_nsmul' _ _
     _ < y + a := add_lt_add_right hm.1 _

f93c1193

chore: avoid lean3 style have/suffices (#6964)

Many proofs use the "stream of consciousness" style from Lean 3, rather than have ... := or suffices ... from/by.

This PR updates a fraction of these to the preferred Lean 4 style.

I think a good goal would be to delete the "deferred" versions of have, suffices, and let at the bottom of Mathlib.Tactic.Have

(Anyone who would like to contribute more cleanup is welcome to push directly to this branch.)

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

bdc47f68

Diff

@@ -67,8 +67,8 @@ theorem AddSubgroup.exists_isLeast_pos {H : AddSubgroup G} (hbot : H ≠ ⊥) {a
       exact hg.trans_le hm
     · simp only [← Nat.cast_succ, coe_nat_zsmul] at hm hm'
       exact ⟨m, hm', hm⟩
-  have : ∃ n : ℕ, Set.Nonempty (H ∩ Ioc (n • a) ((n + 1) • a))
-  · rcases (bot_or_exists_ne_zero H).resolve_left hbot with ⟨g, hgH, hg₀⟩
+  have : ∃ n : ℕ, Set.Nonempty (H ∩ Ioc (n • a) ((n + 1) • a)) := by
+    rcases (bot_or_exists_ne_zero H).resolve_left hbot with ⟨g, hgH, hg₀⟩
     rcases hex |g| (abs_pos.2 hg₀) with ⟨n, hn⟩
     exact ⟨n, _, (@abs_mem_iff (AddSubgroup G) G _ _).2 hgH, hn⟩
   classical rcases Nat.findX this with ⟨n, ⟨x, hxH, hnx, hxn⟩, hmin⟩

f93c1193

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

@@ -32,7 +32,7 @@ subgroups of `ℝ`.
 -/
 
 open Set
-variable {G : Type _} [LinearOrderedAddCommGroup G] [Archimedean G]
+variable {G : Type*} [LinearOrderedAddCommGroup G] [Archimedean G]
 
 /-- Given a subgroup `H` of a decidable linearly ordered archimedean abelian group `G`, if there
 exists a minimal element `a` of `H ∩ G_{>0}` then `H` is generated by `a`. -/

f93c1193

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Heather Macbeth, Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth, Patrick Massot
-
-! This file was ported from Lean 3 source module group_theory.archimedean
-! leanprover-community/mathlib commit f93c11933efbc3c2f0299e47b8ff83e9b539cbf6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Order.Archimedean
 import Mathlib.GroupTheory.Subgroup.Basic
 
+#align_import group_theory.archimedean from "leanprover-community/mathlib"@"f93c11933efbc3c2f0299e47b8ff83e9b539cbf6"
+
 /-!
 # Archimedean groups

f93c1193

fix: precedence of ⁺, ⁻ and abs (#5619)

6c1021b5

Diff

@@ -72,7 +72,7 @@ theorem AddSubgroup.exists_isLeast_pos {H : AddSubgroup G} (hbot : H ≠ ⊥) {a
       exact ⟨m, hm', hm⟩
   have : ∃ n : ℕ, Set.Nonempty (H ∩ Ioc (n • a) ((n + 1) • a))
   · rcases (bot_or_exists_ne_zero H).resolve_left hbot with ⟨g, hgH, hg₀⟩
-    rcases hex (|g|) (abs_pos.2 hg₀) with ⟨n, hn⟩
+    rcases hex |g| (abs_pos.2 hg₀) with ⟨n, hn⟩
     exact ⟨n, _, (@abs_mem_iff (AddSubgroup G) G _ _).2 hgH, hn⟩
   classical rcases Nat.findX this with ⟨n, ⟨x, hxH, hnx, hxn⟩, hmin⟩
   by_contra hxmin

f93c1193

chore: strip trailing spaces in lean files (#2828)

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

6ceb5945

Diff

@@ -99,6 +99,6 @@ theorem AddSubgroup.cyclic_of_isolated_zero {H : AddSubgroup G} {a : G} (h₀ :
 /-- Every subgroup of `ℤ` is cyclic. -/
 theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closure {a} :=
   have : Ioo (0 : ℤ) 1 = ∅ := eq_empty_of_forall_not_mem fun m hm =>
-    hm.1.not_le (lt_add_one_iff.1 hm.2) 
+    hm.1.not_le (lt_add_one_iff.1 hm.2)
   AddSubgroup.cyclic_of_isolated_zero one_pos <| by simp [this]
 #align int.subgroup_cyclic Int.subgroup_cyclic

f93c1193

feat: port Topology.Instances.Real (#2633)

I generalized some lemmas from additive subgroups of the real numbers to additive subgroups of an archimedean additive group.

342815a1

Diff

@@ -34,11 +34,9 @@ The result is also used in `Topology.Instances.Real` as an ingredient in the cla
 subgroups of `ℝ`.
 -/
 
-
+open Set
 variable {G : Type _} [LinearOrderedAddCommGroup G] [Archimedean G]
 
-open LinearOrderedAddCommGroup
-
 /-- Given a subgroup `H` of a decidable linearly ordered archimedean abelian group `G`, if there
 exists a minimal element `a` of `H ∩ G_{>0}` then `H` is generated by `a`. -/
 theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
@@ -58,21 +56,49 @@ theorem AddSubgroup.cyclic_of_min {H : AddSubgroup G} {a : G}
   simp [sub_eq_zero.mp h_zero, AddSubgroup.mem_closure_singleton]
 #align add_subgroup.cyclic_of_min AddSubgroup.cyclic_of_min
 
+/-- If a nontrivial additive subgroup of a linear ordered additive commutative group is disjoint
+with the interval `Set.Ioo 0 a` for some positive `a`, then the set of positive elements of this
+group admits the least element. -/
+theorem AddSubgroup.exists_isLeast_pos {H : AddSubgroup G} (hbot : H ≠ ⊥) {a : G} (h₀ : 0 < a)
+    (hd : Disjoint (H : Set G) (Ioo 0 a)) : ∃ b, IsLeast { g : G | g ∈ H ∧ 0 < g } b := by
+  -- todo: move to a lemma?
+  have hex : ∀ g > 0, ∃ n : ℕ, g ∈ Ioc (n • a) ((n + 1) • a) := fun g hg => by
+    rcases existsUnique_add_zsmul_mem_Ico h₀ 0 (g - a) with ⟨m, ⟨hm, hm'⟩, -⟩
+    simp only [zero_add, sub_le_iff_le_add, sub_add_cancel, ← add_one_zsmul] at hm hm'
+    lift m to ℕ
+    · rw [← Int.lt_add_one_iff, ← zsmul_lt_zsmul_iff h₀, zero_zsmul]
+      exact hg.trans_le hm
+    · simp only [← Nat.cast_succ, coe_nat_zsmul] at hm hm'
+      exact ⟨m, hm', hm⟩
+  have : ∃ n : ℕ, Set.Nonempty (H ∩ Ioc (n • a) ((n + 1) • a))
+  · rcases (bot_or_exists_ne_zero H).resolve_left hbot with ⟨g, hgH, hg₀⟩
+    rcases hex (|g|) (abs_pos.2 hg₀) with ⟨n, hn⟩
+    exact ⟨n, _, (@abs_mem_iff (AddSubgroup G) G _ _).2 hgH, hn⟩
+  classical rcases Nat.findX this with ⟨n, ⟨x, hxH, hnx, hxn⟩, hmin⟩
+  by_contra hxmin
+  simp only [IsLeast, not_and, mem_setOf_eq, mem_lowerBounds, not_exists, not_forall,
+    not_le] at hxmin
+  rcases hxmin x ⟨hxH, (nsmul_nonneg h₀.le _).trans_lt hnx⟩ with ⟨y, ⟨hyH, hy₀⟩, hxy⟩
+  rcases hex y hy₀ with ⟨m, hm⟩
+  cases' lt_or_le m n with hmn hnm
+  · exact hmin m hmn ⟨y, hyH, hm⟩
+  · refine disjoint_left.1 hd (sub_mem hxH hyH) ⟨sub_pos.2 hxy, sub_lt_iff_lt_add'.2 ?_⟩
+    calc x ≤ (n + 1) • a := hxn
+    _ ≤ (m + 1) • a := nsmul_le_nsmul h₀.le (add_le_add_right hnm _)
+    _ = m • a + a := succ_nsmul' _ _
+    _ < y + a := add_lt_add_right hm.1 _
+
+/-- If an additive subgroup of a linear ordered additive commutative group is disjoint with the
+interval `Set.Ioo 0 a` for some positive `a`, then this is a cyclic subgroup. -/
+theorem AddSubgroup.cyclic_of_isolated_zero {H : AddSubgroup G} {a : G} (h₀ : 0 < a)
+    (hd : Disjoint (H : Set G) (Ioo 0 a)) : ∃ b, H = closure {b} := by
+  rcases eq_or_ne H ⊥ with rfl | hbot
+  · exact ⟨0, closure_singleton_zero.symm⟩
+  · exact (exists_isLeast_pos hbot h₀ hd).imp fun _ => cyclic_of_min
+
 /-- Every subgroup of `ℤ` is cyclic. -/
-theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closure {a} := by
-  cases' AddSubgroup.bot_or_exists_ne_zero H with h h
-  · use 0
-    rw [h]
-    exact AddSubgroup.closure_singleton_zero.symm
-  let s := { g : ℤ | g ∈ H ∧ 0 < g }
-  have h_bdd : ∀ g ∈ s, (0 : ℤ) ≤ g := fun _ h => le_of_lt h.2
-  obtain ⟨g₀, g₀_in, g₀_ne⟩ := h
-  obtain ⟨g₁, g₁_in, g₁_pos⟩ : ∃ g₁ : ℤ, g₁ ∈ H ∧ 0 < g₁ :=
-    by
-    cases' lt_or_gt_of_ne g₀_ne with Hg₀ Hg₀
-    · exact ⟨-g₀, H.neg_mem g₀_in, neg_pos.mpr Hg₀⟩
-    · exact ⟨g₀, g₀_in, Hg₀⟩
-  classical
-  obtain ⟨a, ha, ha'⟩ := Int.exists_least_of_bdd ⟨(0 : ℤ), h_bdd⟩ ⟨g₁, g₁_in, g₁_pos⟩
-  exact ⟨a, AddSubgroup.cyclic_of_min ⟨ha, ha'⟩⟩
+theorem Int.subgroup_cyclic (H : AddSubgroup ℤ) : ∃ a, H = AddSubgroup.closure {a} :=
+  have : Ioo (0 : ℤ) 1 = ∅ := eq_empty_of_forall_not_mem fun m hm =>
+    hm.1.not_le (lt_add_one_iff.1 hm.2) 
+  AddSubgroup.cyclic_of_isolated_zero one_pos <| by simp [this]
 #align int.subgroup_cyclic Int.subgroup_cyclic

f93c1193

feat: port GroupTheory.Archimedean (#1856)

porting note: I just used classical to get a Decidable instance for membership. I think there is nothing wrong with this, but thought I would mention it just in case.

13a04975

`group_theory.archimedean` ⟷ `Mathlib.GroupTheory.Archimedean`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`

Lemmas added

Lemmas removed

Other changes

Dependencies 4 + 211

group_theory.archimedean ⟷ Mathlib.GroupTheory.Archimedean

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Algebra.GroupPower.Order

Algebra.GroupPower.CovariantClass

Data.Nat.Pow

Lemmas added

Lemmas removed

Other changes

Dependencies 4 + 211

`group_theory.archimedean` ⟷ `Mathlib.GroupTheory.Archimedean`

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`