ring_theory.ring_hom_properties ⟷ Mathlib.RingTheory.RingHomProperties

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

@@ -5,7 +5,7 @@ Authors: Andrew Yang
 -/
 import Algebra.Category.Ring.Constructions
 import Algebra.Category.Ring.Colimits
-import CategoryTheory.Isomorphism
+import CategoryTheory.Iso
 import RingTheory.Localization.Away.Basic
 import RingTheory.IsTensorProduct
 

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

@@ -3,11 +3,11 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.Algebra.Category.Ring.Constructions
-import Mathbin.Algebra.Category.Ring.Colimits
-import Mathbin.CategoryTheory.Isomorphism
-import Mathbin.RingTheory.Localization.Away.Basic
-import Mathbin.RingTheory.IsTensorProduct
+import Algebra.Category.Ring.Constructions
+import Algebra.Category.Ring.Colimits
+import CategoryTheory.Isomorphism
+import RingTheory.Localization.Away.Basic
+import RingTheory.IsTensorProduct
 
 #align_import ring_theory.ring_hom_properties from "leanprover-community/mathlib"@"d07a9c875ed7139abfde6a333b2be205c5bd404e"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module ring_theory.ring_hom_properties
-! leanprover-community/mathlib commit d07a9c875ed7139abfde6a333b2be205c5bd404e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Category.Ring.Constructions
 import Mathbin.Algebra.Category.Ring.Colimits
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Isomorphism
 import Mathbin.RingTheory.Localization.Away.Basic
 import Mathbin.RingTheory.IsTensorProduct
 
+#align_import ring_theory.ring_hom_properties from "leanprover-community/mathlib"@"d07a9c875ed7139abfde6a333b2be205c5bd404e"
+
 /-!
 # Properties of ring homomorphisms
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9f55d0d4363ae59948c33864cbc52e0b12e0e8ce

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module ring_theory.ring_hom_properties
-! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
+! leanprover-community/mathlib commit d07a9c875ed7139abfde6a333b2be205c5bd404e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.RingTheory.IsTensorProduct
 /-!
 # Properties of ring homomorphisms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We provide the basic framework for talking about properties of ring homomorphisms.
 The following meta-properties of predicates on ring homomorphisms are defined
 

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

@@ -37,8 +37,6 @@ namespace RingHom
 
 variable (P : ∀ {R S : Type u} [CommRing R] [CommRing S] (f : R →+* S), Prop)
 
-include P
-
 section RespectsIso
 
 #print RingHom.RespectsIso /-
@@ -71,6 +69,7 @@ theorem RespectsIso.cancel_right_isIso (hP : RespectsIso @P) {R S T : CommRingCa
 #align ring_hom.respects_iso.cancel_right_is_iso RingHom.RespectsIso.cancel_right_isIso
 -/
 
+#print RingHom.RespectsIso.is_localization_away_iff /-
 theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S : Type _}
     (R' S' : Type _) [CommRing R] [CommRing S] [CommRing R'] [CommRing S'] [Algebra R R']
     [Algebra S S'] (f : R →+* S) (r : R) [IsLocalization.Away r R'] [IsLocalization.Away (f r) S'] :
@@ -93,6 +92,7 @@ theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S
     IsLocalization.ringEquivOfRingEquiv_apply, RingHom.coe_mk, RingEquiv.toFun_eq_coe,
     IsLocalization.ringEquivOfRingEquiv_eq, IsLocalization.map_eq]
 #align ring_hom.respects_iso.is_localization_away_iff RingHom.RespectsIso.is_localization_away_iff
+-/
 
 end RespectsIso
 
@@ -109,6 +109,7 @@ def StableUnderComposition : Prop :=
 
 variable {P}
 
+#print RingHom.StableUnderComposition.respectsIso /-
 theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition @P)
     (hP' : ∀ {R S : Type _} [CommRing R] [CommRing S] (e : R ≃+* S), P e.to_ring_hom) :
     RingHom.RespectsIso @P := by
@@ -116,6 +117,7 @@ theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition
   · introv H; skip; apply hP; exacts [H, hP' e]
   · introv H; skip; apply hP; exacts [hP' e, H]
 #align ring_hom.stable_under_composition.respects_iso RingHom.StableUnderComposition.respectsIso
+-/
 
 end StableUnderComposition
 
@@ -132,6 +134,7 @@ def StableUnderBaseChange : Prop :=
 #align ring_hom.stable_under_base_change RingHom.StableUnderBaseChange
 -/
 
+#print RingHom.StableUnderBaseChange.mk /-
 theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
     (h₂ :
       ∀ ⦃R S T⦄ [CommRing R] [CommRing S] [CommRing T],
@@ -163,8 +166,7 @@ theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
     dsimp only [e]
     rw [h.symm.1.equiv_tmul, Algebra.smul_def, AlgHom.toLinearMap_apply, map_one, mul_one]
 #align ring_hom.stable_under_base_change.mk RingHom.StableUnderBaseChange.mk
-
-omit P
+-/
 
 attribute [local instance] Algebra.TensorProduct.rightAlgebra
 

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

@@ -41,6 +41,7 @@ include P
 
 section RespectsIso
 
+#print RingHom.RespectsIso /-
 /-- A property `respects_iso` if it still holds when composed with an isomorphism -/
 def RespectsIso : Prop :=
   (∀ {R S T : Type u} [CommRing R] [CommRing S] [CommRing T],
@@ -48,22 +49,27 @@ def RespectsIso : Prop :=
     ∀ {R S T : Type u} [CommRing R] [CommRing S] [CommRing T],
       ∀ (f : S →+* T) (e : R ≃+* S) (hf : P f), P (f.comp e.toRingHom)
 #align ring_hom.respects_iso RingHom.RespectsIso
+-/
 
 variable {P}
 
+#print RingHom.RespectsIso.cancel_left_isIso /-
 theorem RespectsIso.cancel_left_isIso (hP : RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S)
     (g : S ⟶ T) [IsIso f] : P (f ≫ g) ↔ P g :=
   ⟨fun H => by
     convert hP.2 (f ≫ g) (as_iso f).symm.commRingCatIsoToRingEquiv H
     exact (is_iso.inv_hom_id_assoc _ _).symm, hP.2 g (asIso f).commRingCatIsoToRingEquiv⟩
 #align ring_hom.respects_iso.cancel_left_is_iso RingHom.RespectsIso.cancel_left_isIso
+-/
 
+#print RingHom.RespectsIso.cancel_right_isIso /-
 theorem RespectsIso.cancel_right_isIso (hP : RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S)
     (g : S ⟶ T) [IsIso g] : P (f ≫ g) ↔ P f :=
   ⟨fun H => by
     convert hP.1 (f ≫ g) (as_iso g).symm.commRingCatIsoToRingEquiv H
     change f = f ≫ g ≫ inv g; simp, hP.1 f (asIso g).commRingCatIsoToRingEquiv⟩
 #align ring_hom.respects_iso.cancel_right_is_iso RingHom.RespectsIso.cancel_right_isIso
+-/
 
 theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S : Type _}
     (R' S' : Type _) [CommRing R] [CommRing S] [CommRing R'] [CommRing S'] [Algebra R R']
@@ -92,12 +98,14 @@ end RespectsIso
 
 section StableUnderComposition
 
+#print RingHom.StableUnderComposition /-
 /-- A property is `stable_under_composition` if the composition of two such morphisms
 still falls in the class. -/
 def StableUnderComposition : Prop :=
   ∀ ⦃R S T⦄ [CommRing R] [CommRing S] [CommRing T],
     ∀ (f : R →+* S) (g : S →+* T) (hf : P f) (hg : P g), P (g.comp f)
 #align ring_hom.stable_under_composition RingHom.StableUnderComposition
+-/
 
 variable {P}
 
@@ -113,6 +121,7 @@ end StableUnderComposition
 
 section StableUnderBaseChange
 
+#print RingHom.StableUnderBaseChange /-
 /-- A morphism property `P` is `stable_under_base_change` if `P(S →+* A)` implies
 `P(B →+* A ⊗[S] B)`. -/
 def StableUnderBaseChange : Prop :=
@@ -121,6 +130,7 @@ def StableUnderBaseChange : Prop :=
       ∀ [IsScalarTower R S S'] [IsScalarTower R R' S'],
         ∀ [Algebra.IsPushout R S R' S'], P (algebraMap R S) → P (algebraMap R' S')
 #align ring_hom.stable_under_base_change RingHom.StableUnderBaseChange
+-/
 
 theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
     (h₂ :
@@ -158,6 +168,7 @@ omit P
 
 attribute [local instance] Algebra.TensorProduct.rightAlgebra
 
+#print RingHom.StableUnderBaseChange.pushout_inl /-
 theorem StableUnderBaseChange.pushout_inl (hP : RingHom.StableUnderBaseChange @P)
     (hP' : RingHom.RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S) (g : R ⟶ T) (H : P g) :
     P (pushout.inl : S ⟶ pushout f g) :=
@@ -173,6 +184,7 @@ theorem StableUnderBaseChange.pushout_inl (hP : RingHom.StableUnderBaseChange @P
   apply hP R T S (TensorProduct R S T)
   exact H
 #align ring_hom.stable_under_base_change.pushout_inl RingHom.StableUnderBaseChange.pushout_inl
+-/
 
 end StableUnderBaseChange
 

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

@@ -105,8 +105,8 @@ theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition
     (hP' : ∀ {R S : Type _} [CommRing R] [CommRing S] (e : R ≃+* S), P e.to_ring_hom) :
     RingHom.RespectsIso @P := by
   constructor
-  · introv H; skip; apply hP; exacts[H, hP' e]
-  · introv H; skip; apply hP; exacts[hP' e, H]
+  · introv H; skip; apply hP; exacts [H, hP' e]
+  · introv H; skip; apply hP; exacts [hP' e, H]
 #align ring_hom.stable_under_composition.respects_iso RingHom.StableUnderComposition.respectsIso
 
 end StableUnderComposition

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

@@ -84,7 +84,7 @@ theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S
   revert e₁ e₂
   dsimp [RingEquiv.toRingHom, IsLocalization.Away.map]
   simp only [CategoryTheory.comp_apply, RingEquiv.refl_apply, IsLocalization.algEquiv_apply,
-    IsLocalization.ringEquivOfRingEquiv_apply, RingHom.coe_mk, [anonymous],
+    IsLocalization.ringEquivOfRingEquiv_apply, RingHom.coe_mk, RingEquiv.toFun_eq_coe,
     IsLocalization.ringEquivOfRingEquiv_eq, IsLocalization.map_eq]
 #align ring_hom.respects_iso.is_localization_away_iff RingHom.RespectsIso.is_localization_away_iff
 

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

@@ -62,8 +62,7 @@ theorem RespectsIso.cancel_right_isIso (hP : RespectsIso @P) {R S T : CommRingCa
     (g : S ⟶ T) [IsIso g] : P (f ≫ g) ↔ P f :=
   ⟨fun H => by
     convert hP.1 (f ≫ g) (as_iso g).symm.commRingCatIsoToRingEquiv H
-    change f = f ≫ g ≫ inv g
-    simp, hP.1 f (asIso g).commRingCatIsoToRingEquiv⟩
+    change f = f ≫ g ≫ inv g; simp, hP.1 f (asIso g).commRingCatIsoToRingEquiv⟩
 #align ring_hom.respects_iso.cancel_right_is_iso RingHom.RespectsIso.cancel_right_isIso
 
 theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S : Type _}
@@ -106,14 +105,8 @@ theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition
     (hP' : ∀ {R S : Type _} [CommRing R] [CommRing S] (e : R ≃+* S), P e.to_ring_hom) :
     RingHom.RespectsIso @P := by
   constructor
-  · introv H
-    skip
-    apply hP
-    exacts[H, hP' e]
-  · introv H
-    skip
-    apply hP
-    exacts[hP' e, H]
+  · introv H; skip; apply hP; exacts[H, hP' e]
+  · introv H; skip; apply hP; exacts[hP' e, H]
 #align ring_hom.stable_under_composition.respects_iso RingHom.StableUnderComposition.respectsIso
 
 end StableUnderComposition

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,14 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module ring_theory.ring_hom_properties
-! leanprover-community/mathlib commit b5aecf07a179c60b6b37c1ac9da952f3b565c785
+! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Category.Ring.Constructions
 import Mathbin.Algebra.Category.Ring.Colimits
 import Mathbin.CategoryTheory.Isomorphism
-import Mathbin.RingTheory.Localization.Away
+import Mathbin.RingTheory.Localization.Away.Basic
 import Mathbin.RingTheory.IsTensorProduct
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -54,16 +54,16 @@ variable {P}
 theorem RespectsIso.cancel_left_isIso (hP : RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S)
     (g : S ⟶ T) [IsIso f] : P (f ≫ g) ↔ P g :=
   ⟨fun H => by
-    convert hP.2 (f ≫ g) (as_iso f).symm.commRingIsoToRingEquiv H
-    exact (is_iso.inv_hom_id_assoc _ _).symm, hP.2 g (asIso f).commRingIsoToRingEquiv⟩
+    convert hP.2 (f ≫ g) (as_iso f).symm.commRingCatIsoToRingEquiv H
+    exact (is_iso.inv_hom_id_assoc _ _).symm, hP.2 g (asIso f).commRingCatIsoToRingEquiv⟩
 #align ring_hom.respects_iso.cancel_left_is_iso RingHom.RespectsIso.cancel_left_isIso
 
 theorem RespectsIso.cancel_right_isIso (hP : RespectsIso @P) {R S T : CommRingCat} (f : R ⟶ S)
     (g : S ⟶ T) [IsIso g] : P (f ≫ g) ↔ P f :=
   ⟨fun H => by
-    convert hP.1 (f ≫ g) (as_iso g).symm.commRingIsoToRingEquiv H
+    convert hP.1 (f ≫ g) (as_iso g).symm.commRingCatIsoToRingEquiv H
     change f = f ≫ g ≫ inv g
-    simp, hP.1 f (asIso g).commRingIsoToRingEquiv⟩
+    simp, hP.1 f (asIso g).commRingCatIsoToRingEquiv⟩
 #align ring_hom.respects_iso.cancel_right_is_iso RingHom.RespectsIso.cancel_right_isIso
 
 theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S : Type _}

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

More tactics that are not used, found using the linter at #11308.

The PR consists of tactic removals, whitespace changes and replacing a porting note by an explanation.

@@ -109,11 +109,9 @@ theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition
     RingHom.RespectsIso @P := by
   constructor
   · introv H
-    skip
     apply hP
     exacts [H, hP' e]
   · introv H
-    skip
     apply hP
     exacts [hP' e, H]
 #align ring_hom.stable_under_composition.respects_iso RingHom.StableUnderComposition.respectsIso

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".

@@ -161,7 +161,7 @@ theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
     exact map_mul f' _ _
   · ext x
     change _ = e (x ⊗ₜ[R] 1)
-    --Porting note: Had `dsimp only [e]` here, which didn't work anymore
+    -- Porting note: Had `dsimp only [e]` here, which didn't work anymore
     rw [h.symm.1.equiv_tmul, Algebra.smul_def, AlgHom.toLinearMap_apply, map_one, mul_one]
 #align ring_hom.stable_under_base_change.mk RingHom.StableUnderBaseChange.mk
 

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -87,7 +87,7 @@ theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S
     convert this
   apply IsLocalization.ringHom_ext (Submonoid.powers r) _
   ext1 x
-  dsimp [IsLocalization.Away.map]
+  dsimp [e, e₁, e₂, IsLocalization.Away.map]
   simp only [IsLocalization.map_eq, id_apply, RingHomCompTriple.comp_apply]
 #align ring_hom.respects_iso.is_localization_away_iff RingHom.RespectsIso.is_localization_away_iff
 
@@ -149,7 +149,7 @@ theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
     congr 1
     apply TensorProduct.ext'
     intro x y
-    simp [IsBaseChange.equiv_tmul, Algebra.smul_def]
+    simp [e, f', IsBaseChange.equiv_tmul, Algebra.smul_def]
   -- Porting Note: This had a lot of implicit inferences which didn't resolve anymore.
   -- Added those in
   convert h₁.1 (_ : R' →+* TensorProduct R R' S) (_ : TensorProduct R R' S ≃+* S')

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

@@ -74,7 +74,7 @@ theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S
   refine' (hP.cancel_right_isIso (CommRingCat.ofHom _) e₂.toCommRingCatIso.hom).symm.trans _
   rw [← eq_iff_iff]
   congr 1
-  -- Porting Note : Here, the proof used to have a huge `simp` involving `[anonymous]`, which didn't
+  -- Porting note: Here, the proof used to have a huge `simp` involving `[anonymous]`, which didn't
   -- work out anymore. The issue seemed to be that it couldn't handle a term in which Ring
   -- homomorphisms were repeatedly casted to the bundled category and back. Here we resolve the
   -- problem by converting the goal to a more straightforward form.

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

@@ -62,8 +62,8 @@ theorem RespectsIso.cancel_right_isIso (hP : RespectsIso @P) {R S T : CommRingCa
     simp, hP.1 f (asIso g).commRingCatIsoToRingEquiv⟩
 #align ring_hom.respects_iso.cancel_right_is_iso RingHom.RespectsIso.cancel_right_isIso
 
-theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S : Type _}
-    (R' S' : Type _) [CommRing R] [CommRing S] [CommRing R'] [CommRing S'] [Algebra R R']
+theorem RespectsIso.is_localization_away_iff (hP : RingHom.RespectsIso @P) {R S : Type u}
+    (R' S' : Type u) [CommRing R] [CommRing S] [CommRing R'] [CommRing S'] [Algebra R R']
     [Algebra S S'] (f : R →+* S) (r : R) [IsLocalization.Away r R'] [IsLocalization.Away (f r) S'] :
     P (Localization.awayMap f r) ↔ P (IsLocalization.Away.map R' S' f r) := by
   let e₁ : R' ≃+* Localization.Away r :=
@@ -105,7 +105,7 @@ def StableUnderComposition : Prop :=
 variable {P}
 
 theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition @P)
-    (hP' : ∀ {R S : Type _} [CommRing R] [CommRing S] (e : R ≃+* S), P e.toRingHom) :
+    (hP' : ∀ {R S : Type u} [CommRing R] [CommRing S] (e : R ≃+* S), P e.toRingHom) :
     RingHom.RespectsIso @P := by
   constructor
   · introv H

This:

• Improves the module docstring, which was both out of date and not very informative
• Addresses a TODO to generalize includeLeft to commuting actions. As a result a few downstream results are changed to be about includeLeftRingHom or a ⊗ₜ 1, as carrying around the extra useless ring just makes the lemmas harder to use. Nothing seems to suffer from this change.
• Introduces TensorProduct.AlgebraTensorModule.rid
• Generalizes the following to work for towers of rings:
  • Algebra.TensorProduct.algHomOfLinearMapTensorProduct
  • Algebra.TensorProduct.map
  • Algebra.TensorProduct.congr
  • Algebra.TensorProduct.endTensorEndAlgHom
  • Algebra.TensorProduct.ext (and renames it to Algebra.TensorProduct.ext')
  • Algebra.TensorProduct.rid
• Introduces a new Algebra.TensorProduct.ext which follows "partially-applied ext lemmas", and uses it to golf a proof in RingTheory/Etale.lean

I need many of these results for building AlgEquivs relating to the base change of clifford algebras.

@@ -136,7 +136,7 @@ theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
       ∀ ⦃R S T⦄ [CommRing R] [CommRing S] [CommRing T],
         ∀ [Algebra R S] [Algebra R T],
           P (algebraMap R T) →
-            P (Algebra.TensorProduct.includeLeft.toRingHom : S →+* TensorProduct R S T)) :
+            P (Algebra.TensorProduct.includeLeftRingHom : S →+* TensorProduct R S T)) :
     StableUnderBaseChange @P := by
   introv R h H
   let e := h.symm.1.equiv

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module ring_theory.ring_hom_properties
-! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Category.Ring.Constructions
 import Mathlib.Algebra.Category.Ring.Colimits
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Iso
 import Mathlib.RingTheory.Localization.Away.Basic
 import Mathlib.RingTheory.IsTensorProduct
 
+#align_import ring_theory.ring_hom_properties from "leanprover-community/mathlib"@"a7c017d750512a352b623b1824d75da5998457d0"
+
 /-!
 # Properties of ring homomorphisms
 

@@ -20,10 +20,10 @@ import Mathlib.RingTheory.IsTensorProduct
 We provide the basic framework for talking about properties of ring homomorphisms.
 The following meta-properties of predicates on ring homomorphisms are defined
 
-* `ring_hom.respects_iso`: `P` respects isomorphisms if `P f → P (e ≫ f)` and
+* `RingHom.RespectsIso`: `P` respects isomorphisms if `P f → P (e ≫ f)` and
   `P f → P (f ≫ e)`, where `e` is an isomorphism.
-* `ring_hom.stable_under_composition`: `P` is stable under composition if `P f → P g → P (f ≫ g)`.
-* `ring_hom.stable_under_base_change`: `P` is stable under base change if `P (S ⟶ Y)`
+* `RingHom.StableUnderComposition`: `P` is stable under composition if `P f → P g → P (f ≫ g)`.
+* `RingHom.StableUnderBaseChange`: `P` is stable under base change if `P (S ⟶ Y)`
   implies `P (X ⟶ X ⊗[S] Y)`.
 
 -/
@@ -40,7 +40,7 @@ variable (P : ∀ {R S : Type u} [CommRing R] [CommRing S] (_ : R →+* S), Prop
 
 section RespectsIso
 
-/-- A property `respects_iso` if it still holds when composed with an isomorphism -/
+/-- A property `RespectsIso` if it still holds when composed with an isomorphism -/
 def RespectsIso : Prop :=
   (∀ {R S T : Type u} [CommRing R] [CommRing S] [CommRing T],
       ∀ (f : R →+* S) (e : S ≃+* T) (_ : P f), P (e.toRingHom.comp f)) ∧
@@ -98,7 +98,7 @@ end RespectsIso
 
 section StableUnderComposition
 
-/-- A property is `stable_under_composition` if the composition of two such morphisms
+/-- A property is `StableUnderComposition` if the composition of two such morphisms
 still falls in the class. -/
 def StableUnderComposition : Prop :=
   ∀ ⦃R S T⦄ [CommRing R] [CommRing S] [CommRing T],
@@ -114,18 +114,18 @@ theorem StableUnderComposition.respectsIso (hP : RingHom.StableUnderComposition
   · introv H
     skip
     apply hP
-    exacts[H, hP' e]
+    exacts [H, hP' e]
   · introv H
     skip
     apply hP
-    exacts[hP' e, H]
+    exacts [hP' e, H]
 #align ring_hom.stable_under_composition.respects_iso RingHom.StableUnderComposition.respectsIso
 
 end StableUnderComposition
 
 section StableUnderBaseChange
 
-/-- A morphism property `P` is `stable_under_base_change` if `P(S →+* A)` implies
+/-- A morphism property `P` is `StableUnderBaseChange` if `P(S →+* A)` implies
 `P(B →+* A ⊗[S] B)`. -/
 def StableUnderBaseChange : Prop :=
   ∀ (R S R' S') [CommRing R] [CommRing S] [CommRing R'] [CommRing S'],
@@ -142,7 +142,6 @@ theorem StableUnderBaseChange.mk (h₁ : RespectsIso @P)
             P (Algebra.TensorProduct.includeLeft.toRingHom : S →+* TensorProduct R S T)) :
     StableUnderBaseChange @P := by
   introv R h H
-  skip
   let e := h.symm.1.equiv
   let f' :=
     Algebra.TensorProduct.productMap (IsScalarTower.toAlgHom R R' S')

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