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Rem unused opens in Safe (#93)

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This commit is contained in:
Patrick Stevens
2020-01-05 15:06:35 +00:00
committed by GitHub
parent 019a9d9a07
commit cbe55c9b56
169 changed files with 0 additions and 960 deletions
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3
Fields/CauchyCompletion/Addition.agda
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@@ -1,14 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Groups
open import Fields.Fields
open import Sets.EquivalenceRelations
open import Sequences

3
Fields/CauchyCompletion/Approximation.agda
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@@ -1,13 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Groups.Lemmas
open import Fields.Fields
open import Sets.EquivalenceRelations
@@ -37,7 +35,6 @@ open import Rings.Orders.Total.Lemmas order
open import Rings.Orders.Partial.Lemmas pRing
open import Fields.CauchyCompletion.Definition order F
open import Fields.CauchyCompletion.Addition order F charNot2
open import Fields.CauchyCompletion.Setoid order F charNot2
open import Fields.CauchyCompletion.Comparison order F charNot2
abstract

3
Fields/CauchyCompletion/Comparison.agda
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@@ -3,14 +3,11 @@
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Groups.Lemmas
open import Fields.Fields
open import Fields.Orders.Total.Definition
open import Sets.EquivalenceRelations
open import Sequences
open import Setoids.Orders

2
Fields/CauchyCompletion/Definition.agda
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@@ -3,11 +3,9 @@
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Fields.Fields
open import Sets.EquivalenceRelations
open import Sequences

3
Fields/CauchyCompletion/Group.agda
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@@ -1,15 +1,12 @@
{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Homomorphisms.Definition
open import Groups.Groups
open import Fields.Fields
open import Sets.EquivalenceRelations
open import Sequences

5
Fields/CauchyCompletion/Multiplication.agda
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@@ -1,13 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Groups.Lemmas
open import Fields.Fields
open import Sets.EquivalenceRelations
@@ -18,7 +16,6 @@ open import LogicalFormulae
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Naturals.Order.Lemmas
open import Semirings.Definition
module Fields.CauchyCompletion.Multiplication {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {m} {o} A} {pOrder : SetoidPartialOrder S _<_} {R : Ring S _+_ _*_} {pRing : PartiallyOrderedRing R pOrder} (order : TotallyOrderedRing pRing) (F : Field R) (charNot2 : Setoid._∼_ S ((Ring.1R R) + (Ring.1R R)) (Ring.0R R) → False) where
@@ -37,8 +34,6 @@ open import Rings.Orders.Partial.Lemmas pRing
open import Rings.Orders.Total.Lemmas order
open import Fields.CauchyCompletion.Definition order F
open import Fields.CauchyCompletion.Setoid order F charNot2
open import Fields.CauchyCompletion.Comparison order F charNot2
open import Fields.CauchyCompletion.Addition order F charNot2
open import Fields.CauchyCompletion.Approximation order F charNot2
0!=1 : {e : A} → (0G < e) → 0R ∼ 1R → False

5
Fields/CauchyCompletion/Ring.agda
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@@ -1,13 +1,10 @@
{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Groups.Lemmas
open import Fields.Fields
open import Sets.EquivalenceRelations
@@ -17,7 +14,6 @@ open import Functions
open import LogicalFormulae
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Naturals.Order.Lemmas
module Fields.CauchyCompletion.Ring {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {m} {o} A} {pOrder : SetoidPartialOrder S _<_} {R : Ring S _+_ _*_} {pRing : PartiallyOrderedRing R pOrder} (order : TotallyOrderedRing pRing) (F : Field R) (charNot2 : Setoid._∼_ S ((Ring.1R R) + (Ring.1R R)) (Ring.0R R) → False) where
@@ -29,7 +25,6 @@ open PartiallyOrderedRing pRing
open Field F
open Group (Ring.additiveGroup R)
open import Rings.Orders.Partial.Lemmas pRing
open import Rings.Orders.Total.Lemmas order
open import Fields.CauchyCompletion.Definition order F
open import Fields.CauchyCompletion.Multiplication order F charNot2

1
Fields/CauchyCompletion/Setoid.agda
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@@ -7,7 +7,6 @@ open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Groups.Lemmas
open import Fields.Fields
open import Sets.EquivalenceRelations

6
Fields/FieldOfFractions/Addition.agda
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@@ -1,18 +1,12 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Addition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (I : IntegralDomain R) where

9
Fields/FieldOfFractions/Field.agda
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@@ -1,24 +1,15 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Field {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (I : IntegralDomain R) where
open import Fields.FieldOfFractions.Setoid I
open import Fields.FieldOfFractions.Addition I
open import Fields.FieldOfFractions.Multiplication I
open import Fields.FieldOfFractions.Ring I
fieldOfFractions : Field fieldOfFractionsRing

6
Fields/FieldOfFractions/Group.agda
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@@ -1,18 +1,12 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Group {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (I : IntegralDomain R) where

9
Fields/FieldOfFractions/Lemmas.agda
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@@ -1,28 +1,19 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Homomorphisms.Definition
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (I : IntegralDomain R) where
open import Fields.FieldOfFractions.Setoid I
open import Fields.FieldOfFractions.Addition I
open import Fields.FieldOfFractions.Multiplication I
open import Fields.FieldOfFractions.Ring I
open import Fields.FieldOfFractions.Field I
embedIntoFieldOfFractions : A → fieldOfFractionsSet
embedIntoFieldOfFractions a = a ,, (Ring.1R R , IntegralDomain.nontrivial I)

7
Fields/FieldOfFractions/Multiplication.agda
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@@ -1,18 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Multiplication {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (I : IntegralDomain R) where

5
Fields/FieldOfFractions/Order.agda
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@@ -1,22 +1,17 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Rings.Orders.Total.Lemmas
open import Rings.Lemmas
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Setoids.Orders
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Order {a b c : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} {_<_ : Rel {_} {c} A} {pOrder : SetoidPartialOrder S _<_} {pRing : PartiallyOrderedRing R pOrder} (I : IntegralDomain R) (order : TotallyOrderedRing pRing) where

6
Fields/FieldOfFractions/Ring.agda
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@@ -1,18 +1,12 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.FieldOfFractions.Ring {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (I : IntegralDomain R) where

6
Fields/FieldOfFractions/Setoid.agda
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@@ -1,13 +1,7 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Fields.Fields
open import Functions
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Rings.IntegralDomains.Definition

5
Fields/Fields.agda
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@@ -1,14 +1,9 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Rings.Definition
open import Rings.Lemmas
open import Setoids.Setoids
open import Rings.IntegralDomains.Definition
open import Functions
open import Sets.EquivalenceRelations
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

7
Fields/Lemmas.agda
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@@ -1,18 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Groups
open import Fields.Fields
open import Sets.EquivalenceRelations
open import Setoids.Orders
open import Functions
open import LogicalFormulae
open import Numbers.Naturals.Naturals
open import Rings.IntegralDomains.Definition
module Fields.Lemmas {m n : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) where

2
Fields/Orders/Lemmas.agda
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@@ -1,7 +1,6 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Lemmas
open import Groups.Definition
open import Rings.Definition
@@ -16,7 +15,6 @@ open import Sets.EquivalenceRelations
open import Fields.Fields
open import Fields.Orders.Total.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.Orders.Lemmas {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {_} {o} A} {R : Ring S _+_ _*_} {pOrder : SetoidPartialOrder S _<_} {F : Field R} {pRing : PartiallyOrderedRing R pOrder} (oF : TotallyOrderedField F pRing) where

6
Fields/Orders/Partial/Definition.agda
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@@ -1,15 +1,10 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Rings.Definition
open import Rings.Orders.Partial.Definition
open import Rings.Lemmas
open import Setoids.Setoids
open import Setoids.Orders
open import Functions
open import Sets.EquivalenceRelations
open import Fields.Fields
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
@@ -17,7 +12,6 @@ open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.Orders.Partial.Definition {m n : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) where
open Ring R
open import Fields.Lemmas F
record PartiallyOrderedField {p} {_<_ : Rel {_} {p} A} (pOrder : SetoidPartialOrder S _<_) : Set (lsuc (m ⊔ n ⊔ p)) where
field

6
Fields/Orders/Total/Definition.agda
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@@ -1,16 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Rings.Definition
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Rings.Lemmas
open import Setoids.Setoids
open import Setoids.Orders
open import Functions
open import Sets.EquivalenceRelations
open import Fields.Fields
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
@@ -18,7 +13,6 @@ open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.Orders.Total.Definition {m n : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) where
open Ring R
open import Fields.Lemmas F
record TotallyOrderedField {p} {_<_ : Rel {_} {p} A} {pOrder : SetoidPartialOrder S _<_} (pRing : PartiallyOrderedRing R pOrder) : Set (lsuc (m ⊔ n ⊔ p)) where
field