canonically_ordered_comm_semiring_two_mul ⟷ Counterexamples.CanonicallyOrderedCommSemiringTwoMul

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Data.Zmod.Basic
+import Data.ZMod.Basic
 import RingTheory.Subsemiring.Basic
 import Algebra.Order.Monoid.Basic
 
@@ -241,7 +241,7 @@ theorem exists_add_of_le : ∀ a b : L, a ≤ b → ∃ c, b = a + c :=
   ·
     exact
       ⟨⟨b - a.1, fun H => (tsub_pos_of_lt h).ne' (Prod.mk.inj_iff.1 H).1⟩,
-        Subtype.ext <| Prod.ext (add_tsub_cancel_of_le h.le).symm (add_sub_cancel'_right _ _).symm⟩
+        Subtype.ext <| Prod.ext (add_tsub_cancel_of_le h.le).symm (add_sub_cancel _ _).symm⟩
 #align counterexample.ex_L.exists_add_of_le Counterexample.ExL.exists_add_of_le
 
 theorem le_self_add : ∀ a b : L, a ≤ a + b :=

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

@@ -113,7 +113,7 @@ theorem lt_def : a < b ↔ a.1 < b.1 :=
     · exact (not_or_distrib.mp h1).1.elim rfl
     · exact a1
   refine' ⟨Or.inr h, not_or_distrib.mpr ⟨fun k => _, not_lt.mpr h.le⟩⟩
-  rw [k] at h 
+  rw [k] at h
   exact Nat.lt_asymm h h
 #align counterexample.Nxzmod_2.lt_def Counterexample.Nxzmod2.lt_def
 
@@ -259,7 +259,7 @@ theorem eq_zero_or_eq_zero_of_hMul_eq_zero : ∀ a b : L, a * b = 0 → a = 0 
   rintro ⟨⟨a, a2⟩, ha⟩ ⟨⟨b, b2⟩, hb⟩ ab1
   injection ab1 with ab
   injection ab with abn ab2
-  rw [mul_eq_zero] at abn 
+  rw [mul_eq_zero] at abn
   rcases abn with (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩)
   · refine' Or.inl _
     rcases mem_zmod_2 a2 with (rfl | rfl)

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathbin.Data.Zmod.Basic
-import Mathbin.RingTheory.Subsemiring.Basic
-import Mathbin.Algebra.Order.Monoid.Basic
+import Data.Zmod.Basic
+import RingTheory.Subsemiring.Basic
+import Algebra.Order.Monoid.Basic
 
 #align_import canonically_ordered_comm_semiring_two_mul from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -138,13 +138,13 @@ theorem le_of_add_le_add_left : ∀ a b c : ℕ × ZMod 2, a + b ≤ a + c → b
 instance : ZeroLEOneClass (ℕ × ZMod 2) :=
   ⟨by decide⟩
 
-theorem mul_lt_mul_of_pos_left : ∀ a b c : ℕ × ZMod 2, a < b → 0 < c → c * a < c * b :=
+theorem hMul_lt_hMul_of_pos_left : ∀ a b c : ℕ × ZMod 2, a < b → 0 < c → c * a < c * b :=
   fun a b c ab c0 => lt_def.mpr ((mul_lt_mul_left (lt_def.mp c0)).mpr (lt_def.mp ab))
-#align counterexample.Nxzmod_2.mul_lt_mul_of_pos_left Counterexample.Nxzmod2.mul_lt_mul_of_pos_left
+#align counterexample.Nxzmod_2.mul_lt_mul_of_pos_left Counterexample.Nxzmod2.hMul_lt_hMul_of_pos_left
 
-theorem mul_lt_mul_of_pos_right : ∀ a b c : ℕ × ZMod 2, a < b → 0 < c → a * c < b * c :=
+theorem hMul_lt_hMul_of_pos_right : ∀ a b c : ℕ × ZMod 2, a < b → 0 < c → a * c < b * c :=
   fun a b c ab c0 => lt_def.mpr ((mul_lt_mul_right (lt_def.mp c0)).mpr (lt_def.mp ab))
-#align counterexample.Nxzmod_2.mul_lt_mul_of_pos_right Counterexample.Nxzmod2.mul_lt_mul_of_pos_right
+#align counterexample.Nxzmod_2.mul_lt_mul_of_pos_right Counterexample.Nxzmod2.hMul_lt_hMul_of_pos_right
 
 instance socsN2 : StrictOrderedCommSemiring (ℕ × ZMod 2) :=
   { Nxzmod2.csrN21, (inferInstance : PartialOrder (ℕ × ZMod 2)),
@@ -154,8 +154,8 @@ instance socsN2 : StrictOrderedCommSemiring (ℕ × ZMod 2) :=
     add_le_add_left := add_le_add_left
     le_of_add_le_add_left := le_of_add_le_add_left
     zero_le_one := zero_le_one
-    mul_lt_mul_of_pos_left := mul_lt_mul_of_pos_left
-    mul_lt_mul_of_pos_right := mul_lt_mul_of_pos_right }
+    mul_lt_mul_of_pos_left := hMul_lt_hMul_of_pos_left
+    mul_lt_mul_of_pos_right := hMul_lt_hMul_of_pos_right }
 #align counterexample.Nxzmod_2.socsN2 Counterexample.Nxzmod2.socsN2
 
 end Nxzmod2
@@ -180,7 +180,7 @@ theorem add_L {a b : ℕ × ZMod 2} (ha : a ≠ (0, 1)) (hb : b ≠ (0, 1)) : a
   · simp [(a + b).succ_ne_zero]
 #align counterexample.ex_L.add_L Counterexample.ExL.add_L
 
-theorem mul_L {a b : ℕ × ZMod 2} (ha : a ≠ (0, 1)) (hb : b ≠ (0, 1)) : a * b ≠ (0, 1) :=
+theorem hMul_L {a b : ℕ × ZMod 2} (ha : a ≠ (0, 1)) (hb : b ≠ (0, 1)) : a * b ≠ (0, 1) :=
   by
   rcases a with ⟨a, a2⟩
   rcases b with ⟨b, b2⟩
@@ -201,7 +201,7 @@ theorem mul_L {a b : ℕ × ZMod 2} (ha : a ≠ (0, 1)) (hb : b ≠ (0, 1)) : a
       simp
     exact ha rfl
   · simp [mul_ne_zero _ _, Nat.succ_ne_zero _]
-#align counterexample.ex_L.mul_L Counterexample.ExL.mul_L
+#align counterexample.ex_L.mul_L Counterexample.ExL.hMul_L
 
 /-- The subsemiring corresponding to the elements of `L`, used to transfer instances. -/
 def lSubsemiring : Subsemiring (ℕ × ZMod 2)
@@ -210,7 +210,7 @@ def lSubsemiring : Subsemiring (ℕ × ZMod 2)
   zero_mem' := by decide
   one_mem' := by decide
   add_mem' _ _ := add_L
-  mul_mem' _ _ := mul_L
+  hMul_mem' _ _ := hMul_L
 #align counterexample.ex_L.L_subsemiring Counterexample.ExL.lSubsemiring
 
 instance : OrderedCommSemiring L :=
@@ -254,7 +254,7 @@ theorem le_self_add : ∀ a b : L, a ≤ a + b :=
   · exact Or.inr ((lt_add_iff_pos_right _).mpr h)
 #align counterexample.ex_L.le_self_add Counterexample.ExL.le_self_add
 
-theorem eq_zero_or_eq_zero_of_mul_eq_zero : ∀ a b : L, a * b = 0 → a = 0 ∨ b = 0 :=
+theorem eq_zero_or_eq_zero_of_hMul_eq_zero : ∀ a b : L, a * b = 0 → a = 0 ∨ b = 0 :=
   by
   rintro ⟨⟨a, a2⟩, ha⟩ ⟨⟨b, b2⟩, hb⟩ ab1
   injection ab1 with ab
@@ -269,7 +269,7 @@ theorem eq_zero_or_eq_zero_of_mul_eq_zero : ∀ a b : L, a * b = 0 → a = 0 ∨
     rcases mem_zmod_2 b2 with (rfl | rfl)
     · rfl
     · exact (hb rfl).elim
-#align counterexample.ex_L.eq_zero_or_eq_zero_of_mul_eq_zero Counterexample.ExL.eq_zero_or_eq_zero_of_mul_eq_zero
+#align counterexample.ex_L.eq_zero_or_eq_zero_of_mul_eq_zero Counterexample.ExL.eq_zero_or_eq_zero_of_hMul_eq_zero
 
 instance can : CanonicallyOrderedCommSemiring L :=
   { (inferInstance : OrderBot L),
@@ -277,7 +277,7 @@ instance can : CanonicallyOrderedCommSemiring L :=
       OrderedCommSemiring L) with
     exists_add_of_le := exists_add_of_le
     le_self_add := le_self_add
-    eq_zero_or_eq_zero_of_mul_eq_zero := eq_zero_or_eq_zero_of_mul_eq_zero }
+    eq_zero_or_eq_zero_of_mul_eq_zero := eq_zero_or_eq_zero_of_hMul_eq_zero }
 #align counterexample.ex_L.can Counterexample.ExL.can
 
 /-- The elements `(1,0)` and `(1,1)` of `L` are different, but their doubles coincide.

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module canonically_ordered_comm_semiring_two_mul
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Zmod.Basic
 import Mathbin.RingTheory.Subsemiring.Basic
 import Mathbin.Algebra.Order.Monoid.Basic
 
+#align_import canonically_ordered_comm_semiring_two_mul from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 
 A `canonically_ordered_comm_semiring` with two different elements `a` and `b` such that

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 
 ! This file was ported from Lean 3 source module canonically_ordered_comm_semiring_two_mul
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -27,6 +27,9 @@ multiplication cannot be strengthened to **strict** monotonicity.
 
 Reference:
 https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/canonically_ordered.20pathology
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -199,7 +199,7 @@ theorem exists_add_of_le : ∀ a b : L, a ≤ b → ∃ c, b = a + c := by
   · exact ⟨0, (add_zero _).symm⟩
   · exact
       ⟨⟨b - a.1, fun H => (tsub_pos_of_lt h).ne' (Prod.mk.inj_iff.1 H).1⟩,
-        Subtype.ext <| Prod.ext (add_tsub_cancel_of_le h.le).symm (add_sub_cancel'_right _ _).symm⟩
+        Subtype.ext <| Prod.ext (add_tsub_cancel_of_le h.le).symm (add_sub_cancel _ _).symm⟩
 #align counterexample.ex_L.exists_add_of_le Counterexample.ExL.exists_add_of_le
 
 theorem le_self_add : ∀ a b : L, a ≤ a + b := by

Moving these to separate files should make typeclass synthesis less expensive. Additionally two of them are quite long and this shrinks them slightly.

This handles:

• Submonoid
• Subgroup
• Subsemiring
• Subring
• Subfield
• Submodule
• Subalgebra

This also moves Units.posSubgroup into its own file.

The copyright headers are from:

• https://github.com/leanprover-community/mathlib/pull/6489
• https://github.com/leanprover-community/mathlib/pull/8466

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
 import Mathlib.Data.ZMod.Basic
-import Mathlib.RingTheory.Subsemiring.Basic
+import Mathlib.RingTheory.Subsemiring.Order
 import Mathlib.Algebra.Order.Monoid.Basic
 
 #align_import canonically_ordered_comm_semiring_two_mul from "leanprover-community/mathlib"@"328375597f2c0dd00522d9c2e5a33b6a6128feeb"

borelize X fails when ‹TopologicalSpace X› depends on i : MeasurableSpace X, but this message isn't readable:

failed to create binder due to failure when reverting variable dependencies

This is probrem in this case: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/borelize.20gives.20.22failed.20to.20create.20binder.2E.2E.2E.22

This PR make error messages more readable:

‹TopologicalSpace X› := (expr depends on i)"
depends on
i : MeasurableSpace X
so `borelize` isn't avaliable

@@ -31,34 +31,6 @@ set_option linter.uppercaseLean3 false
 
 namespace Counterexample
 
-namespace FromBhavik
-
-/-- Bhavik Mehta's example.  There are only the initial definitions, but no proofs.  The Type
-`K` is a canonically ordered commutative semiring with the property that `2 * (1/2) ≤ 2 * 1`, even
-though it is not true that `1/2 ≤ 1`, since `1/2` and `1` are not comparable. -/
-def K : Type :=
-  Subsemiring.closure ({1.5} : Set ℚ)
-deriving CommSemiring
-#align counterexample.from_Bhavik.K Counterexample.FromBhavik.K
-
-instance : Coe K ℚ :=
-  ⟨fun x => x.1⟩
-
-instance inhabitedK : Inhabited K :=
-  ⟨0⟩
-#align counterexample.from_Bhavik.inhabited_K Counterexample.FromBhavik.inhabitedK
-
-instance : Preorder K where
-  le x y := x = y ∨ (x : ℚ) + 1 ≤ (y : ℚ)
-  le_refl x := Or.inl rfl
-  le_trans x y z xy yz := by
-    rcases xy with (rfl | xy); · apply yz
-    rcases yz with (rfl | yz); · right; apply xy
-    right
-    exact xy.trans (le_trans ((le_add_iff_nonneg_right _).mpr zero_le_one) yz)
-
-end FromBhavik
-
 theorem mem_zmod_2 (a : ZMod 2) : a = 0 ∨ a = 1 := by
   rcases a with ⟨_ | _, _ | _ | _ | _⟩
   · exact Or.inl rfl

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module canonically_ordered_comm_semiring_two_mul
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.ZMod.Basic
 import Mathlib.RingTheory.Subsemiring.Basic
 import Mathlib.Algebra.Order.Monoid.Basic
 
+#align_import canonically_ordered_comm_semiring_two_mul from "leanprover-community/mathlib"@"328375597f2c0dd00522d9c2e5a33b6a6128feeb"
+
 /-!
 
 A `CanonicallyOrderedCommSemiring` with two different elements `a` and `b` such that

Also fix bug in elementwise that wasn't caught while tests weren't running.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>