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Rem unused opens in Safe (#93)

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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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4
Groups/Abelian/Definition.agda
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@@ -1,12 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
module Groups.Abelian.Definition where

5
Groups/Abelian/DirectSum.agda
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@@ -1,12 +1,7 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Abelian.Definition
module Groups.Abelian.DirectSum {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_+1_ : A → A → A} {_+2_ : B → B → B} {G1' : Group S _+1_} {G2' : Group T _+2_} (G1 : AbelianGroup G1') (G2 : AbelianGroup G2') where

5
Groups/Abelian/Lemmas.agda
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@@ -2,16 +2,11 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Setoids.DirectSum
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Abelian.Definition
open import Groups.Homomorphisms.Definition
open import Groups.DirectSum.Definition
open import Groups.Subgroups.Definition
open import Groups.Isomorphisms.Definition
module Groups.Abelian.Lemmas where

5
Groups/ActionIsSymmetry.agda
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@@ -2,13 +2,8 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Homomorphisms.Definition
open import Groups.Groups
open import Groups.SymmetricGroups.Definition
open import Groups.Actions.Definition
open import Sets.EquivalenceRelations

6
Groups/Actions/Definition.agda
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@@ -1,14 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Groups
open import Sets.EquivalenceRelations
module Groups.Actions.Definition where

5
Groups/Actions/Orbit.agda
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@@ -1,13 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Groups
open import Groups.Actions.Definition
open import Sets.EquivalenceRelations

7
Groups/Actions/Stabiliser.agda
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@@ -1,15 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Groups
open import Groups.Subgroups.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Actions.Definition
open import Sets.EquivalenceRelations
open import Groups.Actions.Definition

3
Groups/Cosets.agda
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@@ -1,11 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Sets.EquivalenceRelations
open import Setoids.Setoids
open import Setoids.Subset
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Groups.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Subgroups.Definition

6
Groups/Cyclic/Definition.agda
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@@ -3,15 +3,9 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Semiring
open import Numbers.Integers.Integers
open import Numbers.Integers.Addition
open import Groups.Homomorphisms.Definition
open import Groups.Groups
open import Groups.Subgroups.Definition
open import Groups.Abelian.Definition
open import Groups.Definition
open import Groups.Lemmas

6
Groups/Cyclic/DefinitionLemmas.agda
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@@ -3,16 +3,10 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Semiring
open import Numbers.Integers.Integers
open import Numbers.Integers.Addition
open import Groups.Homomorphisms.Definition
open import Groups.Groups
open import Groups.Lemmas
open import Groups.Subgroups.Definition
open import Groups.Abelian.Definition
open import Groups.Definition
open import Groups.Cyclic.Definition
open import Semirings.Definition

3
Groups/Definition.agda
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@@ -1,10 +1,7 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
module Groups.Definition where

4
Groups/DirectSum/Definition.agda
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@@ -2,11 +2,7 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
module Groups.DirectSum.Definition {m n o p : _} {A : Set m} {S : Setoid {m} {o} A} {_·A_ : A → A → A} {B : Set n} {T : Setoid {n} {p} B} {_·B_ : B → B → B} (G : Group S _·A_) (H : Group T _·B_) where

3
Groups/FiniteGroups/Definition.agda
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@@ -1,13 +1,10 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Semiring
open import Sets.Cardinality.Finite.Definition
open import Groups.Definition
open import Sets.EquivalenceRelations
module Groups.FiniteGroups.Definition where

2
Groups/FinitePermutations.agda
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@@ -4,8 +4,6 @@ open import LogicalFormulae
open import Numbers.Naturals.Semiring -- for length
open import Lists.Lists
open import Functions
open import Groups.SymmetricGroups.Definition
open import Setoids.Setoids
--open import Groups.Actions
module Groups.FinitePermutations where

8
Groups/FirstIsomorphismTheorem.agda
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@@ -1,23 +1,15 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Groups
open import Groups.Definition
open import Numbers.Integers.Integers
open import Setoids.Setoids
open import LogicalFormulae
open import Functions
open import Sets.EquivalenceRelations
open import Numbers.Naturals.Naturals
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Isomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Subgroups.Normal.Definition
open import Groups.Subgroups.Normal.Lemmas
open import Groups.Lemmas
open import Groups.Abelian.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.FirstIsomorphismTheorem {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_+G_ : A → A → A} {_+H_ : B → B → B} {G : Group S _+G_} {H : Group T _+H_} {f : A → B} (fHom : GroupHom G H f) where

6
Groups/Groups.agda
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@@ -2,14 +2,8 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Homomorphisms.Definition
open import Groups.Lemmas
open import Groups.Homomorphisms.Lemmas
module Groups.Groups where

4
Groups/Homomorphisms/Definition.agda
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@@ -1,12 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
module Groups.Homomorphisms.Definition where

4
Groups/Homomorphisms/Examples.agda
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@@ -1,14 +1,10 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Homomorphisms.Definition
open import Groups.Lemmas
module Groups.Homomorphisms.Examples where

7
Groups/Homomorphisms/Image.agda
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@@ -1,21 +1,14 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Groups
open import Groups.Definition
open import Numbers.Integers.Integers
open import Setoids.Setoids
open import Setoids.Subset
open import LogicalFormulae
open import Functions
open import Sets.EquivalenceRelations
open import Numbers.Naturals.Naturals
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Isomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Lemmas
open import Groups.Abelian.Definition
open import Groups.QuotientGroup.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

11
Groups/Homomorphisms/Kernel.agda
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@@ -1,25 +1,14 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Groups
open import Groups.Definition
open import Numbers.Integers.Integers
open import Setoids.Setoids
open import LogicalFormulae
open import Functions
open import Sets.EquivalenceRelations
open import Numbers.Naturals.Naturals
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Isomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Subgroups.Normal.Definition
open import Groups.Subgroups.Normal.Lemmas
open import Groups.Lemmas
open import Groups.Abelian.Definition
open import Groups.QuotientGroup.Definition
open import Groups.Cosets
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.Homomorphisms.Kernel {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_+G_ : A → A → A} {_+H_ : B → B → B} {G : Group S _+G_} {H : Group T _+H_} {f : A → B} (fHom : GroupHom G H f) where

3
Groups/Homomorphisms/Lemmas.agda
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@@ -1,10 +1,7 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Homomorphisms.Definition

4
Groups/Isomorphisms/Definition.agda
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@@ -1,13 +1,9 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Homomorphisms.Definition
open import Sets.EquivalenceRelations
module Groups.Isomorphisms.Definition where

2
Groups/Isomorphisms/Lemmas.agda
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@@ -3,8 +3,6 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Isomorphisms.Definition

4
Groups/Lemmas.agda
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@@ -1,10 +1,6 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Sets.EquivalenceRelations

7
Groups/Polynomials/Addition.agda
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@@ -1,20 +1,13 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Abelian.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Numbers.Naturals.Definition
open import Setoids.Orders
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
open import Vectors
open import Lists.Lists
open import Maybe
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.Polynomials.Addition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where

5
Groups/Polynomials/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.Homomorphisms.Definition
open import Groups.Definition
open import Numbers.Naturals.Definition
open import Setoids.Orders
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
open import Vectors
open import Lists.Lists
open import Maybe

10
Groups/Polynomials/Examples.agda
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@@ -1,21 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Numbers.Naturals.Definition
open import Numbers.Integers.Integers
open import Numbers.Integers.Definition
open import Setoids.Orders
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
open import Vectors
open import Lists.Lists
open import Maybe
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.Polynomials.Examples where

9
Groups/Polynomials/Group.agda
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@@ -1,20 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Abelian.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Numbers.Naturals.Definition
open import Setoids.Orders
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
open import Vectors
open import Lists.Lists
open import Maybe
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.Polynomials.Group {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where

5
Groups/QuotientGroup/Definition.agda
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@@ -1,17 +1,12 @@
{-# OPTIONS --warning=error --safe --without-K #-}
open import Functions
open import LogicalFormulae
open import Groups.Definition
open import Groups.Groups
open import Groups.FiniteGroups.Definition
open import Groups.Homomorphisms.Definition
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Groups.Lemmas
open import Groups.Homomorphisms.Lemmas
open import Groups.Subgroups.Definition
open import Groups.Subgroups.Normal.Definition
module Groups.QuotientGroup.Definition {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_·A_ : A → A → A} {_·B_ : B → B → B} (G : Group S _·A_) {H : Group T _·B_} {f : A → B} (fHom : GroupHom G H f) where

4
Groups/QuotientGroup/Lemmas.agda
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@@ -1,12 +1,8 @@
{-# OPTIONS --warning=error --safe --without-K #-}
open import Functions
open import LogicalFormulae
open import Groups.Definition
open import Groups.Groups
open import Groups.FiniteGroups.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Abelian.Definition
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Groups.Lemmas

3
Groups/Subgroups/Definition.agda
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@@ -2,11 +2,8 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Homomorphisms.Definition
module Groups.Subgroups.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where

3
Groups/Subgroups/Examples.agda
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@@ -3,9 +3,6 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
module Groups.Subgroups.Examples {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where

11
Groups/Subgroups/Normal/Definition.agda
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@@ -1,19 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Groups
open import Groups.Definition
open import Numbers.Integers.Integers
open import Setoids.Setoids
open import LogicalFormulae
open import Functions
open import Sets.EquivalenceRelations
open import Numbers.Naturals.Naturals
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Isomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Lemmas
open import Groups.Abelian.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

13
Groups/Subgroups/Normal/Examples.agda
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@@ -1,23 +1,10 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Groups
open import Groups.Definition
open import Numbers.Integers.Integers
open import Setoids.Setoids
open import LogicalFormulae
open import Functions
open import Sets.EquivalenceRelations
open import Numbers.Naturals.Naturals
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Isomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Lemmas
open import Groups.Abelian.Definition
open import Groups.QuotientGroup.Definition
open import Groups.Subgroups.Normal.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.Subgroups.Normal.Examples {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where

7
Groups/Subgroups/Normal/Lemmas.agda
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@@ -1,20 +1,13 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Groups
open import Groups.Definition
open import Numbers.Integers.Integers
open import Setoids.Setoids
open import LogicalFormulae
open import Functions
open import Sets.EquivalenceRelations
open import Numbers.Naturals.Naturals
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Isomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Lemmas
open import Groups.Abelian.Definition
open import Groups.QuotientGroup.Definition
open import Groups.Subgroups.Normal.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

3
Groups/SymmetricGroups/Definition.agda
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@@ -2,10 +2,7 @@
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Groups
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Setoids.Functions.Extension

6
Groups/SymmetricGroups/Lemmas.agda
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@@ -1,14 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Groups.Lemmas
open import Groups.Groups
open import Groups.Subgroups.Definition
open import Groups.Homomorphisms.Definition
open import Groups.QuotientGroup.Definition
open import Groups.Homomorphisms.Lemmas