model_theory.quotients
⟷
Mathlib.ModelTheory.Quotients
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import Mathbin.Data.Fintype.Quotient
-import Mathbin.ModelTheory.Semantics
+import Data.Fintype.Quotient
+import ModelTheory.Semantics
#align_import model_theory.quotients from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module model_theory.quotients
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Fintype.Quotient
import Mathbin.ModelTheory.Semantics
+#align_import model_theory.quotients from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
/-!
# Quotients of First-Order Structures
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -61,8 +61,7 @@ instance quotientStructure : L.Structure (Quotient s)
variable (s)
-include s
-
+#print FirstOrder.Language.funMap_quotient_mk' /-
theorem funMap_quotient_mk' {n : ℕ} (f : L.Functions n) (x : Fin n → M) :
(funMap f fun i => ⟦x i⟧) = ⟦@funMap _ _ ps.toStructure _ f x⟧ :=
by
@@ -71,7 +70,9 @@ theorem funMap_quotient_mk' {n : ℕ} (f : L.Functions n) (x : Fin n → M) :
_
rw [Quotient.finChoice_eq, Quotient.map_mk]
#align first_order.language.fun_map_quotient_mk FirstOrder.Language.funMap_quotient_mk'
+-/
+#print FirstOrder.Language.relMap_quotient_mk' /-
theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
(RelMap r fun i => ⟦x i⟧) ↔ @RelMap _ _ ps.toStructure _ r x :=
by
@@ -80,7 +81,9 @@ theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
_
rw [Quotient.finChoice_eq, Quotient.lift_mk]
#align first_order.language.rel_map_quotient_mk FirstOrder.Language.relMap_quotient_mk'
+-/
+#print FirstOrder.Language.Term.realize_quotient_mk' /-
theorem Term.realize_quotient_mk' {β : Type _} (t : L.term β) (x : β → M) :
(t.realize fun i => ⟦x i⟧) = ⟦@Term.realize _ _ ps.toStructure _ x t⟧ :=
by
@@ -88,6 +91,7 @@ theorem Term.realize_quotient_mk' {β : Type _} (t : L.term β) (x : β → M) :
· rfl
· simp only [ih, fun_map_quotient_mk, term.realize]
#align first_order.language.term.realize_quotient_mk FirstOrder.Language.Term.realize_quotient_mk'
+-/
end Language
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -33,7 +33,7 @@ namespace Language
variable (L : Language) {M : Type _}
-open FirstOrder
+open scoped FirstOrder
open Structure
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -63,12 +63,6 @@ variable (s)
include s
-/- warning: first_order.language.fun_map_quotient_mk -> FirstOrder.Language.funMap_quotient_mk' is a dubious translation:
-lean 3 declaration is
- forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [s : Setoid.{succ u3} M] [ps : FirstOrder.Language.Prestructure.{u1, u2, u3} L M s] {n : Nat} (f : FirstOrder.Language.Functions.{u1, u2} L n) (x : (Fin n) -> M), Eq.{succ u3} (Quotient.{succ u3} M s) (FirstOrder.Language.Structure.funMap.{u1, u2, u3} L (Quotient.{succ u3} M s) (FirstOrder.Language.quotientStructure.{u1, u2, u3} L M s ps) n f (fun (i : Fin n) => Quotient.mk'.{succ u3} M s (x i))) (Quotient.mk'.{succ u3} M s (FirstOrder.Language.Structure.funMap.{u1, u2, u3} L M (FirstOrder.Language.Prestructure.toStructure.{u1, u2, u3} L M s ps) n f x))
-but is expected to have type
- forall {L : FirstOrder.Language.{u3, u2}} {M : Type.{u1}} (s : Setoid.{succ u1} M) [ps : FirstOrder.Language.Prestructure.{u3, u2, u1} L M s] {n : Nat} (f : FirstOrder.Language.Functions.{u3, u2} L n) (x : (Fin n) -> M), Eq.{succ u1} (Quotient.{succ u1} M s) (FirstOrder.Language.Structure.funMap.{u3, u2, u1} L (Quotient.{succ u1} M s) (FirstOrder.Language.quotientStructure.{u3, u2, u1} L M s ps) n f (fun (i : Fin n) => Quotient.mk.{succ u1} M s (x i))) (Quotient.mk.{succ u1} M s (FirstOrder.Language.Structure.funMap.{u3, u2, u1} L M (FirstOrder.Language.Prestructure.toStructure.{u3, u2, u1} L M s ps) n f x))
-Case conversion may be inaccurate. Consider using '#align first_order.language.fun_map_quotient_mk FirstOrder.Language.funMap_quotient_mk'ₓ'. -/
theorem funMap_quotient_mk' {n : ℕ} (f : L.Functions n) (x : Fin n → M) :
(funMap f fun i => ⟦x i⟧) = ⟦@funMap _ _ ps.toStructure _ f x⟧ :=
by
@@ -78,12 +72,6 @@ theorem funMap_quotient_mk' {n : ℕ} (f : L.Functions n) (x : Fin n → M) :
rw [Quotient.finChoice_eq, Quotient.map_mk]
#align first_order.language.fun_map_quotient_mk FirstOrder.Language.funMap_quotient_mk'
-/- warning: first_order.language.rel_map_quotient_mk -> FirstOrder.Language.relMap_quotient_mk' is a dubious translation:
-lean 3 declaration is
- forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [s : Setoid.{succ u3} M] [ps : FirstOrder.Language.Prestructure.{u1, u2, u3} L M s] {n : Nat} (r : FirstOrder.Language.Relations.{u1, u2} L n) (x : (Fin n) -> M), Iff (FirstOrder.Language.Structure.RelMap.{u1, u2, u3} L (Quotient.{succ u3} M s) (FirstOrder.Language.quotientStructure.{u1, u2, u3} L M s ps) n r (fun (i : Fin n) => Quotient.mk'.{succ u3} M s (x i))) (FirstOrder.Language.Structure.RelMap.{u1, u2, u3} L M (FirstOrder.Language.Prestructure.toStructure.{u1, u2, u3} L M s ps) n r x)
-but is expected to have type
- forall {L : FirstOrder.Language.{u3, u2}} {M : Type.{u1}} (s : Setoid.{succ u1} M) [ps : FirstOrder.Language.Prestructure.{u3, u2, u1} L M s] {n : Nat} (r : FirstOrder.Language.Relations.{u3, u2} L n) (x : (Fin n) -> M), Iff (FirstOrder.Language.Structure.RelMap.{u3, u2, u1} L (Quotient.{succ u1} M s) (FirstOrder.Language.quotientStructure.{u3, u2, u1} L M s ps) n r (fun (i : Fin n) => Quotient.mk.{succ u1} M s (x i))) (FirstOrder.Language.Structure.RelMap.{u3, u2, u1} L M (FirstOrder.Language.Prestructure.toStructure.{u3, u2, u1} L M s ps) n r x)
-Case conversion may be inaccurate. Consider using '#align first_order.language.rel_map_quotient_mk FirstOrder.Language.relMap_quotient_mk'ₓ'. -/
theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
(RelMap r fun i => ⟦x i⟧) ↔ @RelMap _ _ ps.toStructure _ r x :=
by
@@ -93,12 +81,6 @@ theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
rw [Quotient.finChoice_eq, Quotient.lift_mk]
#align first_order.language.rel_map_quotient_mk FirstOrder.Language.relMap_quotient_mk'
-/- warning: first_order.language.term.realize_quotient_mk -> FirstOrder.Language.Term.realize_quotient_mk' is a dubious translation:
-lean 3 declaration is
- forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [s : Setoid.{succ u3} M] [ps : FirstOrder.Language.Prestructure.{u1, u2, u3} L M s] {β : Type.{u4}} (t : FirstOrder.Language.Term.{u1, u2, u4} L β) (x : β -> M), Eq.{succ u3} (Quotient.{succ u3} M s) (FirstOrder.Language.Term.realize.{u1, u2, u3, u4} L (Quotient.{succ u3} M s) (FirstOrder.Language.quotientStructure.{u1, u2, u3} L M s ps) β (fun (i : β) => Quotient.mk'.{succ u3} M s (x i)) t) (Quotient.mk'.{succ u3} M s (FirstOrder.Language.Term.realize.{u1, u2, u3, u4} L M (FirstOrder.Language.Prestructure.toStructure.{u1, u2, u3} L M s ps) β x t))
-but is expected to have type
- forall {L : FirstOrder.Language.{u3, u2}} {M : Type.{u1}} (s : Setoid.{succ u1} M) [ps : FirstOrder.Language.Prestructure.{u3, u2, u1} L M s] {β : Type.{u4}} (t : FirstOrder.Language.Term.{u3, u2, u4} L β) (x : β -> M), Eq.{succ u1} (Quotient.{succ u1} M s) (FirstOrder.Language.Term.realize.{u3, u2, u1, u4} L (Quotient.{succ u1} M s) (FirstOrder.Language.quotientStructure.{u3, u2, u1} L M s ps) β (fun (i : β) => Quotient.mk.{succ u1} M s (x i)) t) (Quotient.mk.{succ u1} M s (FirstOrder.Language.Term.realize.{u3, u2, u1, u4} L M (FirstOrder.Language.Prestructure.toStructure.{u3, u2, u1} L M s ps) β x t))
-Case conversion may be inaccurate. Consider using '#align first_order.language.term.realize_quotient_mk FirstOrder.Language.Term.realize_quotient_mk'ₓ'. -/
theorem Term.realize_quotient_mk' {β : Type _} (t : L.term β) (x : β → M) :
(t.realize fun i => ⟦x i⟧) = ⟦@Term.realize _ _ ps.toStructure _ x t⟧ :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
! This file was ported from Lean 3 source module model_theory.quotients
-! leanprover-community/mathlib commit d78597269638367c3863d40d45108f52207e03cf
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.ModelTheory.Semantics
/-!
# Quotients of First-Order Structures
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
This file defines prestructures and quotients of first-order structures.
## Main Definitions
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -34,6 +34,7 @@ open FirstOrder
open Structure
+#print FirstOrder.Language.Prestructure /-
/-- A prestructure is a first-order structure with a `setoid` equivalence relation on it,
such that quotienting by that equivalence relation is still a structure. -/
class Prestructure (s : Setoid M) where
@@ -41,9 +42,11 @@ class Prestructure (s : Setoid M) where
fun_equiv : ∀ {n} {f : L.Functions n} (x y : Fin n → M), x ≈ y → funMap f x ≈ funMap f y
rel_equiv : ∀ {n} {r : L.Relations n} (x y : Fin n → M) (h : x ≈ y), RelMap r x = RelMap r y
#align first_order.language.prestructure FirstOrder.Language.Prestructure
+-/
variable {L} {s : Setoid M} [ps : L.Prestructure s]
+#print FirstOrder.Language.quotientStructure /-
instance quotientStructure : L.Structure (Quotient s)
where
funMap n f x :=
@@ -51,11 +54,18 @@ instance quotientStructure : L.Structure (Quotient s)
rel_map n r x :=
Quotient.lift (@RelMap L M ps.toStructure n r) Prestructure.rel_equiv (Quotient.finChoice x)
#align first_order.language.quotient_structure FirstOrder.Language.quotientStructure
+-/
variable (s)
include s
+/- warning: first_order.language.fun_map_quotient_mk -> FirstOrder.Language.funMap_quotient_mk' is a dubious translation:
+lean 3 declaration is
+ forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [s : Setoid.{succ u3} M] [ps : FirstOrder.Language.Prestructure.{u1, u2, u3} L M s] {n : Nat} (f : FirstOrder.Language.Functions.{u1, u2} L n) (x : (Fin n) -> M), Eq.{succ u3} (Quotient.{succ u3} M s) (FirstOrder.Language.Structure.funMap.{u1, u2, u3} L (Quotient.{succ u3} M s) (FirstOrder.Language.quotientStructure.{u1, u2, u3} L M s ps) n f (fun (i : Fin n) => Quotient.mk'.{succ u3} M s (x i))) (Quotient.mk'.{succ u3} M s (FirstOrder.Language.Structure.funMap.{u1, u2, u3} L M (FirstOrder.Language.Prestructure.toStructure.{u1, u2, u3} L M s ps) n f x))
+but is expected to have type
+ forall {L : FirstOrder.Language.{u3, u2}} {M : Type.{u1}} (s : Setoid.{succ u1} M) [ps : FirstOrder.Language.Prestructure.{u3, u2, u1} L M s] {n : Nat} (f : FirstOrder.Language.Functions.{u3, u2} L n) (x : (Fin n) -> M), Eq.{succ u1} (Quotient.{succ u1} M s) (FirstOrder.Language.Structure.funMap.{u3, u2, u1} L (Quotient.{succ u1} M s) (FirstOrder.Language.quotientStructure.{u3, u2, u1} L M s ps) n f (fun (i : Fin n) => Quotient.mk.{succ u1} M s (x i))) (Quotient.mk.{succ u1} M s (FirstOrder.Language.Structure.funMap.{u3, u2, u1} L M (FirstOrder.Language.Prestructure.toStructure.{u3, u2, u1} L M s ps) n f x))
+Case conversion may be inaccurate. Consider using '#align first_order.language.fun_map_quotient_mk FirstOrder.Language.funMap_quotient_mk'ₓ'. -/
theorem funMap_quotient_mk' {n : ℕ} (f : L.Functions n) (x : Fin n → M) :
(funMap f fun i => ⟦x i⟧) = ⟦@funMap _ _ ps.toStructure _ f x⟧ :=
by
@@ -65,6 +75,12 @@ theorem funMap_quotient_mk' {n : ℕ} (f : L.Functions n) (x : Fin n → M) :
rw [Quotient.finChoice_eq, Quotient.map_mk]
#align first_order.language.fun_map_quotient_mk FirstOrder.Language.funMap_quotient_mk'
+/- warning: first_order.language.rel_map_quotient_mk -> FirstOrder.Language.relMap_quotient_mk' is a dubious translation:
+lean 3 declaration is
+ forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [s : Setoid.{succ u3} M] [ps : FirstOrder.Language.Prestructure.{u1, u2, u3} L M s] {n : Nat} (r : FirstOrder.Language.Relations.{u1, u2} L n) (x : (Fin n) -> M), Iff (FirstOrder.Language.Structure.RelMap.{u1, u2, u3} L (Quotient.{succ u3} M s) (FirstOrder.Language.quotientStructure.{u1, u2, u3} L M s ps) n r (fun (i : Fin n) => Quotient.mk'.{succ u3} M s (x i))) (FirstOrder.Language.Structure.RelMap.{u1, u2, u3} L M (FirstOrder.Language.Prestructure.toStructure.{u1, u2, u3} L M s ps) n r x)
+but is expected to have type
+ forall {L : FirstOrder.Language.{u3, u2}} {M : Type.{u1}} (s : Setoid.{succ u1} M) [ps : FirstOrder.Language.Prestructure.{u3, u2, u1} L M s] {n : Nat} (r : FirstOrder.Language.Relations.{u3, u2} L n) (x : (Fin n) -> M), Iff (FirstOrder.Language.Structure.RelMap.{u3, u2, u1} L (Quotient.{succ u1} M s) (FirstOrder.Language.quotientStructure.{u3, u2, u1} L M s ps) n r (fun (i : Fin n) => Quotient.mk.{succ u1} M s (x i))) (FirstOrder.Language.Structure.RelMap.{u3, u2, u1} L M (FirstOrder.Language.Prestructure.toStructure.{u3, u2, u1} L M s ps) n r x)
+Case conversion may be inaccurate. Consider using '#align first_order.language.rel_map_quotient_mk FirstOrder.Language.relMap_quotient_mk'ₓ'. -/
theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
(RelMap r fun i => ⟦x i⟧) ↔ @RelMap _ _ ps.toStructure _ r x :=
by
@@ -74,6 +90,12 @@ theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
rw [Quotient.finChoice_eq, Quotient.lift_mk]
#align first_order.language.rel_map_quotient_mk FirstOrder.Language.relMap_quotient_mk'
+/- warning: first_order.language.term.realize_quotient_mk -> FirstOrder.Language.Term.realize_quotient_mk' is a dubious translation:
+lean 3 declaration is
+ forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [s : Setoid.{succ u3} M] [ps : FirstOrder.Language.Prestructure.{u1, u2, u3} L M s] {β : Type.{u4}} (t : FirstOrder.Language.Term.{u1, u2, u4} L β) (x : β -> M), Eq.{succ u3} (Quotient.{succ u3} M s) (FirstOrder.Language.Term.realize.{u1, u2, u3, u4} L (Quotient.{succ u3} M s) (FirstOrder.Language.quotientStructure.{u1, u2, u3} L M s ps) β (fun (i : β) => Quotient.mk'.{succ u3} M s (x i)) t) (Quotient.mk'.{succ u3} M s (FirstOrder.Language.Term.realize.{u1, u2, u3, u4} L M (FirstOrder.Language.Prestructure.toStructure.{u1, u2, u3} L M s ps) β x t))
+but is expected to have type
+ forall {L : FirstOrder.Language.{u3, u2}} {M : Type.{u1}} (s : Setoid.{succ u1} M) [ps : FirstOrder.Language.Prestructure.{u3, u2, u1} L M s] {β : Type.{u4}} (t : FirstOrder.Language.Term.{u3, u2, u4} L β) (x : β -> M), Eq.{succ u1} (Quotient.{succ u1} M s) (FirstOrder.Language.Term.realize.{u3, u2, u1, u4} L (Quotient.{succ u1} M s) (FirstOrder.Language.quotientStructure.{u3, u2, u1} L M s ps) β (fun (i : β) => Quotient.mk.{succ u1} M s (x i)) t) (Quotient.mk.{succ u1} M s (FirstOrder.Language.Term.realize.{u3, u2, u1, u4} L M (FirstOrder.Language.Prestructure.toStructure.{u3, u2, u1} L M s ps) β x t))
+Case conversion may be inaccurate. Consider using '#align first_order.language.term.realize_quotient_mk FirstOrder.Language.Term.realize_quotient_mk'ₓ'. -/
theorem Term.realize_quotient_mk' {β : Type _} (t : L.term β) (x : β → M) :
(t.realize fun i => ⟦x i⟧) = ⟦@Term.realize _ _ ps.toStructure _ x t⟧ :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -25,7 +25,7 @@ namespace FirstOrder
namespace Language
-variable (L : Language) {M : Type _}
+variable (L : Language) {M : Type*}
open FirstOrder
@@ -70,7 +70,7 @@ theorem relMap_quotient_mk' {n : ℕ} (r : L.Relations n) (x : Fin n → M) :
rw [Quotient.finChoice_eq, Quotient.lift_mk]
#align first_order.language.rel_map_quotient_mk FirstOrder.Language.relMap_quotient_mk'
-theorem Term.realize_quotient_mk' {β : Type _} (t : L.Term β) (x : β → M) :
+theorem Term.realize_quotient_mk' {β : Type*} (t : L.Term β) (x : β → M) :
(t.realize fun i => (⟦x i⟧ : Quotient s)) = ⟦@Term.realize _ _ ps.toStructure _ x t⟧ := by
induction' t with _ _ _ _ ih
· rfl
@@ -2,15 +2,12 @@
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module model_theory.quotients
-! leanprover-community/mathlib commit d78597269638367c3863d40d45108f52207e03cf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Fintype.Quotient
import Mathlib.ModelTheory.Semantics
+#align_import model_theory.quotients from "leanprover-community/mathlib"@"d78597269638367c3863d40d45108f52207e03cf"
+
/-!
# Quotients of First-Order Structures
This file defines prestructures and quotients of first-order structures.
The unported dependencies are