pseudoelement ⟷ Counterexamples.Pseudoelement

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
 import CategoryTheory.Abelian.Pseudoelements
-import Algebra.Category.Module.Biproducts
+import Algebra.Category.ModuleCat.Biproducts
 
 #align_import pseudoelement from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

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

@@ -77,25 +77,25 @@ theorem x_not_pseudo_eq : ¬PseudoEqual _ x y :=
   by
   intro h
   replace h := Module.eq_range_of_pseudoequal h
-  dsimp [x, y] at h 
+  dsimp [x, y] at h
   let φ := biprod.lift (of_hom (id : ℚ →ₗ[ℤ] ℚ)) (of_hom (2 * id))
   have mem_range := mem_range_self φ (1 : ℚ)
-  rw [h] at mem_range 
+  rw [h] at mem_range
   obtain ⟨a, ha⟩ := mem_range
   rw [← ModuleCat.id_apply (φ (1 : ℚ)), ← biprod.total, ← LinearMap.comp_apply, ← comp_def,
-    preadditive.comp_add] at ha 
+    preadditive.comp_add] at ha
   let π₁ := (biprod.fst : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₁ := congr_arg π₁ ha
-  simp only [← LinearMap.comp_apply, ← comp_def] at ha₁ 
+  simp only [← LinearMap.comp_apply, ← comp_def] at ha₁
   simp only [biprod.lift_fst, of_hom_apply, id_coe, id.def, preadditive.add_comp, category.assoc,
-    biprod.inl_fst, category.comp_id, biprod.inr_fst, limits.comp_zero, add_zero] at ha₁ 
+    biprod.inl_fst, category.comp_id, biprod.inr_fst, limits.comp_zero, add_zero] at ha₁
   let π₂ := (biprod.snd : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₂ := congr_arg π₂ ha
-  simp only [← LinearMap.comp_apply, ← comp_def] at ha₂ 
+  simp only [← LinearMap.comp_apply, ← comp_def] at ha₂
   have : (2 : ℚ →ₗ[ℤ] ℚ) 1 = 1 + 1 := rfl
   simp only [ha₁, this, biprod.lift_snd, of_hom_apply, id_coe, id.def, preadditive.add_comp,
     category.assoc, biprod.inl_snd, limits.comp_zero, biprod.inr_snd, category.comp_id, zero_add,
-    mul_apply, self_eq_add_left] at ha₂ 
+    mul_apply, self_eq_add_left] at ha₂
   exact one_ne_zero' ℚ ha₂
 #align counterexample.x_not_pseudo_eq Counterexample.x_not_pseudo_eq
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.CategoryTheory.Abelian.Pseudoelements
-import Mathbin.Algebra.Category.Module.Biproducts
+import CategoryTheory.Abelian.Pseudoelements
+import Algebra.Category.Module.Biproducts
 
 #align_import pseudoelement from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module pseudoelement
-! 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.CategoryTheory.Abelian.Pseudoelements
 import Mathbin.Algebra.Category.Module.Biproducts
 
+#align_import pseudoelement from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # Pseudoelements and pullbacks
 

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: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module pseudoelement
-! 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.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Algebra.Category.Module.Biproducts
 
 /-!
 # Pseudoelements and pullbacks
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 Borceux claims in Proposition 1.9.5 that the pseudoelement constructed in
 `category_theory.abelian.pseudoelement.pseudo_pullback` is unique. We show here that this claim is
 false. This means in particular that we cannot have an extensionality principle for pullbacks in

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

It started with the one in Convex/Combination and spiralled into revisiting all notes with needs in them. The ToLin changes overlap with #11171.

@@ -122,8 +122,8 @@ theorem snd_mk'_x_eq_snd_mk'_y :
 #align counterexample.snd_mk_x_eq_snd_mk_y Counterexample.snd_mk'_x_eq_snd_mk'_y
 
 -- Porting note: needs explicit type ascription `: Quotient <| Pseudoelement.setoid _`
---               for some reason the setoid instance isn't picked up automatically
---               despite the local instance ~20 lines up
+-- for some reason the setoid instance isn't picked up automatically,
+-- despite the local instance ~20 lines up
 /-- `⟦x⟧ ≠ ⟦y⟧`. -/
 theorem mk'_x_ne_mk'_y : (⟦x⟧ : Quotient <| Pseudoelement.setoid _) ≠ ⟦y⟧ :=
   fun h => x_not_pseudo_eq <| Quotient.eq'.1 h

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

@@ -89,14 +89,14 @@ theorem x_not_pseudo_eq : ¬PseudoEqual _ x y := by
   have ha₁ := congr_arg π₁ ha
     -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
-  simp only [BinaryBiproduct.bicone_fst, biprod.lift_fst, CategoryTheory.id_apply,
+  simp only [π₁, φ, BinaryBiproduct.bicone_fst, biprod.lift_fst, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_fst, BinaryBicone.inr_fst, smul_zero, add_zero] at ha₁
   let π₂ := (biprod.snd : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₂ := congr_arg π₂ ha
     -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
-  simp only [BinaryBiproduct.bicone_snd, biprod.lift_snd, CategoryTheory.id_apply,
+  simp only [π₁, π₂, φ, BinaryBiproduct.bicone_snd, biprod.lift_snd, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_snd, BinaryBicone.inr_snd, zero_add, two_smul] at ha₂
   erw [add_apply, CategoryTheory.id_apply] at ha₂

This reverts commit f3695eb2.

@@ -87,13 +87,15 @@ theorem x_not_pseudo_eq : ¬PseudoEqual _ x y := by
     Preadditive.comp_add] at ha
   let π₁ := (biprod.fst : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₁ := congr_arg π₁ ha
-  rw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
   simp only [BinaryBiproduct.bicone_fst, biprod.lift_fst, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_fst, BinaryBicone.inr_fst, smul_zero, add_zero] at ha₁
   let π₂ := (biprod.snd : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₂ := congr_arg π₂ ha
-  rw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
   simp only [BinaryBiproduct.bicone_snd, biprod.lift_snd, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_snd, BinaryBicone.inr_snd, zero_add, two_smul] at ha₂

This reverts commit 26eb2b0a.

@@ -87,15 +87,13 @@ theorem x_not_pseudo_eq : ¬PseudoEqual _ x y := by
     Preadditive.comp_add] at ha
   let π₁ := (biprod.fst : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₁ := congr_arg π₁ ha
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
+  rw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
   simp only [BinaryBiproduct.bicone_fst, biprod.lift_fst, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_fst, BinaryBicone.inr_fst, smul_zero, add_zero] at ha₁
   let π₂ := (biprod.snd : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₂ := congr_arg π₂ ha
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
+  rw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
   simp only [BinaryBiproduct.bicone_snd, biprod.lift_snd, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_snd, BinaryBicone.inr_snd, zero_add, two_smul] at ha₂

This includes all the changes from #7606.

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

@@ -87,13 +87,15 @@ theorem x_not_pseudo_eq : ¬PseudoEqual _ x y := by
     Preadditive.comp_add] at ha
   let π₁ := (biprod.fst : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₁ := congr_arg π₁ ha
-  rw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₁
   simp only [BinaryBiproduct.bicone_fst, biprod.lift_fst, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_fst, BinaryBicone.inr_fst, smul_zero, add_zero] at ha₁
   let π₂ := (biprod.snd : of ℤ ℚ ⊞ of ℤ ℚ ⟶ _)
   have ha₂ := congr_arg π₂ ha
-  rw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [← CategoryTheory.comp_apply, ← CategoryTheory.comp_apply] at ha₂
   simp only [BinaryBiproduct.bicone_snd, biprod.lift_snd, CategoryTheory.id_apply,
     biprod.lift_fst_assoc, Category.id_comp, biprod.lift_snd_assoc, Linear.smul_comp,
     Preadditive.add_comp, BinaryBicone.inl_snd, BinaryBicone.inr_snd, zero_add, two_smul] at ha₂

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module pseudoelement
-! 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.CategoryTheory.Abelian.Pseudoelements
 import Mathlib.Algebra.Category.ModuleCat.Biproducts
 
+#align_import pseudoelement from "leanprover-community/mathlib"@"328375597f2c0dd00522d9c2e5a33b6a6128feeb"
+
 /-!
 # Pseudoelements and pullbacks
 Borceux claims in Proposition 1.9.5 that the pseudoelement constructed in

Add lemma tendsto_pow_atTop_nhds_0_iff_lt_1 showing the reverse implication of tendsto_pow_atTop_nhds_0_of_lt_1: if the geometric progression of an element in an Archimedean field tends to 0, the element is strictly less than 1.