order.synonym
⟷
Mathlib.Order.Synonym
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
import Logic.Equiv.Defs
-import Logic.Nontrivial
+import Logic.Nontrivial.Defs
import Order.Basic
#align_import order.synonym from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
-import Mathbin.Logic.Equiv.Defs
-import Mathbin.Logic.Nontrivial
-import Mathbin.Order.Basic
+import Logic.Equiv.Defs
+import Logic.Nontrivial
+import Order.Basic
#align_import order.synonym from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -183,16 +183,16 @@ protected theorem exists {p : αᵒᵈ → Prop} : (∃ a, p a) ↔ ∃ a, p (to
#align order_dual.exists OrderDual.exists
-/
-alias to_dual_le_to_dual ↔ _ _root_.has_le.le.dual
+alias ⟨_, _root_.has_le.le.dual⟩ := to_dual_le_to_dual
#align has_le.le.dual LE.le.dual
-alias to_dual_lt_to_dual ↔ _ _root_.has_lt.lt.dual
+alias ⟨_, _root_.has_lt.lt.dual⟩ := to_dual_lt_to_dual
#align has_lt.lt.dual LT.lt.dual
-alias of_dual_le_of_dual ↔ _ _root_.has_le.le.of_dual
+alias ⟨_, _root_.has_le.le.of_dual⟩ := of_dual_le_of_dual
#align has_le.le.of_dual LE.le.ofDual
-alias of_dual_lt_of_dual ↔ _ _root_.has_lt.lt.of_dual
+alias ⟨_, _root_.has_lt.lt.of_dual⟩ := of_dual_lt_of_dual
#align has_lt.lt.of_dual LT.lt.ofDual
end OrderDual
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-
-! This file was ported from Lean 3 source module order.synonym
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Logic.Equiv.Defs
import Mathbin.Logic.Nontrivial
import Mathbin.Order.Basic
+#align_import order.synonym from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+
/-!
# Type synonyms
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -205,3 +205,6 @@ theorem ofLex_inj {a b : Lex α} : ofLex a = ofLex b ↔ a = b :=
/-- A recursor for `Lex`. Use as `induction x using Lex.rec`. -/
protected def Lex.rec {β : Lex α → Sort*} (h : ∀ a, β (toLex a)) : ∀ a, β a := fun a => h (ofLex a)
#align lex.rec Lex.rec
+
+@[simp] lemma Lex.forall {p : Lex α → Prop} : (∀ a, p a) ↔ ∀ a, p (toLex a) := Iff.rfl
+@[simp] lemma Lex.exists {p : Lex α → Prop} : (∃ a, p a) ↔ ∃ a, p (toLex a) := Iff.rfl
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
import Mathlib.Logic.Equiv.Defs
-import Mathlib.Logic.Nontrivial
+import Mathlib.Logic.Nontrivial.Defs
import Mathlib.Order.Basic
#align_import order.synonym from "leanprover-community/mathlib"@"c4658a649d216f57e99621708b09dcb3dcccbd23"
@@ -138,14 +138,14 @@ protected theorem «exists» {p : αᵒᵈ → Prop} : (∃ a, p a) ↔ ∃ a, p
Iff.rfl
#align order_dual.exists OrderDual.exists
-alias toDual_le_toDual ↔ _ _root_.LE.le.dual
+alias ⟨_, _root_.LE.le.dual⟩ := toDual_le_toDual
-alias toDual_lt_toDual ↔ _ _root_.LT.lt.dual
+alias ⟨_, _root_.LT.lt.dual⟩ := toDual_lt_toDual
-alias ofDual_le_ofDual ↔ _ _root_.LE.le.ofDual
+alias ⟨_, _root_.LE.le.ofDual⟩ := ofDual_le_ofDual
#align has_le.le.of_dual LE.le.ofDual
-alias ofDual_lt_ofDual ↔ _ _root_.LT.lt.ofDual
+alias ⟨_, _root_.LT.lt.ofDual⟩ := ofDual_lt_ofDual
#align has_lt.lt.of_dual LT.lt.ofDual
end OrderDual
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -36,7 +36,7 @@ This file is similar to `Algebra.Group.TypeTags`.
-/
-variable {α β γ : Type _}
+variable {α β γ : Type*}
/-! ### Order dual -/
@@ -124,7 +124,7 @@ theorem toDual_lt [LT α] {a : α} {b : αᵒᵈ} : toDual a < b ↔ ofDual b <
/-- Recursor for `αᵒᵈ`. -/
@[elab_as_elim]
-protected def rec {C : αᵒᵈ → Sort _} (h₂ : ∀ a : α, C (toDual a)) : ∀ a : αᵒᵈ, C a :=
+protected def rec {C : αᵒᵈ → Sort*} (h₂ : ∀ a : α, C (toDual a)) : ∀ a : αᵒᵈ, C a :=
h₂
#align order_dual.rec OrderDual.rec
@@ -154,7 +154,7 @@ end OrderDual
/-- A type synonym to equip a type with its lexicographic order. -/
-def Lex (α : Type _) :=
+def Lex (α : Type*) :=
α
#align lex Lex
@@ -203,5 +203,5 @@ theorem ofLex_inj {a b : Lex α} : ofLex a = ofLex b ↔ a = b :=
#align of_lex_inj ofLex_inj
/-- A recursor for `Lex`. Use as `induction x using Lex.rec`. -/
-protected def Lex.rec {β : Lex α → Sort _} (h : ∀ a, β (toLex a)) : ∀ a, β a := fun a => h (ofLex a)
+protected def Lex.rec {β : Lex α → Sort*} (h : ∀ a, β (toLex a)) : ∀ a, β a := fun a => h (ofLex a)
#align lex.rec Lex.rec
@@ -2,16 +2,13 @@
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-
-! This file was ported from Lean 3 source module order.synonym
-! leanprover-community/mathlib commit c4658a649d216f57e99621708b09dcb3dcccbd23
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Nontrivial
import Mathlib.Order.Basic
+#align_import order.synonym from "leanprover-community/mathlib"@"c4658a649d216f57e99621708b09dcb3dcccbd23"
+
/-!
# Type synonyms
fix-comments.py
on all files.@@ -167,7 +167,7 @@ def toLex : α ≃ Lex α :=
Equiv.refl _
#align to_lex toLex
-/-- `ofLex` is the identity function from the `lex` of a type. -/
+/-- `ofLex` is the identity function from the `Lex` of a type. -/
@[match_pattern]
def ofLex : Lex α ≃ α :=
Equiv.refl _
This PR is the result of a slight variant on the following "algorithm"
_
and make all uppercase letters into lowercase_
and make all uppercase letters into lowercase(original_lean3_name, OriginalLean4Name)
#align
statement just before the next empty line#align
statement to have been inserted too early)@@ -129,14 +129,17 @@ theorem toDual_lt [LT α] {a : α} {b : αᵒᵈ} : toDual a < b ↔ ofDual b <
@[elab_as_elim]
protected def rec {C : αᵒᵈ → Sort _} (h₂ : ∀ a : α, C (toDual a)) : ∀ a : αᵒᵈ, C a :=
h₂
+#align order_dual.rec OrderDual.rec
@[simp]
protected theorem «forall» {p : αᵒᵈ → Prop} : (∀ a, p a) ↔ ∀ a, p (toDual a) :=
Iff.rfl
+#align order_dual.forall OrderDual.forall
@[simp]
protected theorem «exists» {p : αᵒᵈ → Prop} : (∃ a, p a) ↔ ∃ a, p (toDual a) :=
Iff.rfl
+#align order_dual.exists OrderDual.exists
alias toDual_le_toDual ↔ _ _root_.LE.le.dual
@@ -156,16 +159,19 @@ end OrderDual
/-- A type synonym to equip a type with its lexicographic order. -/
def Lex (α : Type _) :=
α
+#align lex Lex
/-- `toLex` is the identity function to the `Lex` of a type. -/
@[match_pattern]
def toLex : α ≃ Lex α :=
Equiv.refl _
+#align to_lex toLex
/-- `ofLex` is the identity function from the `lex` of a type. -/
@[match_pattern]
def ofLex : Lex α ≃ α :=
Equiv.refl _
+#align of_lex ofLex
@[simp]
theorem toLex_symm_eq : (@toLex α).symm = ofLex :=
@@ -201,3 +207,4 @@ theorem ofLex_inj {a b : Lex α} : ofLex a = ofLex b ↔ a = b :=
/-- A recursor for `Lex`. Use as `induction x using Lex.rec`. -/
protected def Lex.rec {β : Lex α → Sort _} (h : ∀ a, β (toLex a)) : ∀ a, β a := fun a => h (ofLex a)
+#align lex.rec Lex.rec
@@ -52,10 +52,12 @@ instance [h : Nontrivial α] : Nontrivial αᵒᵈ :=
/-- `toDual` is the identity function to the `OrderDual` of a linear order. -/
def toDual : α ≃ αᵒᵈ :=
Equiv.refl _
+#align order_dual.to_dual OrderDual.toDual
/-- `ofDual` is the identity function from the `OrderDual` of a linear order. -/
def ofDual : αᵒᵈ ≃ α :=
Equiv.refl _
+#align order_dual.of_dual OrderDual.ofDual
@[simp]
theorem toDual_symm_eq : (@toDual α).symm = ofDual := rfl
@@ -155,12 +155,12 @@ end OrderDual
def Lex (α : Type _) :=
α
-/-- `to_lex` is the identity function to the `Lex` of a type. -/
+/-- `toLex` is the identity function to the `Lex` of a type. -/
@[match_pattern]
def toLex : α ≃ Lex α :=
Equiv.refl _
-/-- `of_lex` is the identity function from the `lex` of a type. -/
+/-- `ofLex` is the identity function from the `lex` of a type. -/
@[match_pattern]
def ofLex : Lex α ≃ α :=
Equiv.refl _
The script used to do this is included. The yaml file was obtained from https://raw.githubusercontent.com/wiki/leanprover-community/mathlib/mathlib4-port-status.md
@@ -2,6 +2,11 @@
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
+
+! This file was ported from Lean 3 source module order.synonym
+! leanprover-community/mathlib commit c4658a649d216f57e99621708b09dcb3dcccbd23
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Nontrivial
All dependencies are ported!