Rem unused opens in Safe (#93)

2025-10-05 11:58:41 +00:00 · 2020-01-05 15:06:35 +00:00
parent 019a9d9a07
commit cbe55c9b56
169 changed files with 0 additions and 960 deletions
--- a/Categories/Definition.agda
+++ b/Categories/Definition.agda
@@ -2,10 +2,6 @@

 open import LogicalFormulae
 open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Numbers.Naturals.Naturals
-open import Numbers.Naturals.Order
-open import Vectors
-open import Semirings.Definition

 module Categories.Definition where

--- a/Categories/Dual/Definition.agda
+++ b/Categories/Dual/Definition.agda
@@ -1,11 +1,6 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Numbers.Naturals.Naturals
-open import Numbers.Naturals.Order
-open import Vectors
-open import Semirings.Definition
 open import Categories.Definition

 module Categories.Dual.Definition where
--- a/Categories/Functor/Definition.agda
+++ b/Categories/Functor/Definition.agda
@@ -2,10 +2,6 @@

 open import LogicalFormulae
 open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Numbers.Naturals.Naturals
-open import Numbers.Naturals.Order
-open import Vectors
-open import Semirings.Definition
 open import Categories.Definition

 module Categories.Functor.Definition where
--- a/Categories/Functor/Lemmas.agda
+++ b/Categories/Functor/Lemmas.agda
@@ -1,11 +1,6 @@
 {-# OPTIONS --warning=error --without-K --safe #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Numbers.Naturals.Naturals
-open import Numbers.Naturals.Order
-open import Vectors
-open import Semirings.Definition
 open import Categories.Definition
 open import Categories.Functor.Definition

--- a/ClassicalLogic/ClassicalFive.agda
+++ b/ClassicalLogic/ClassicalFive.agda
@@ -2,7 +2,6 @@

 open import LogicalFormulae

-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module ClassicalLogic.ClassicalFive where

--- a/Decidable/Sets.agda
+++ b/Decidable/Sets.agda
@@ -1,7 +1,6 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module Decidable.Sets where

--- a/Fields/CauchyCompletion/Addition.agda
+++ b/Fields/CauchyCompletion/Addition.agda
@@ -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
--- a/Fields/CauchyCompletion/Approximation.agda
+++ b/Fields/CauchyCompletion/Approximation.agda
@@ -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
--- a/Fields/CauchyCompletion/Comparison.agda
+++ b/Fields/CauchyCompletion/Comparison.agda
@@ -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
--- a/Fields/CauchyCompletion/Definition.agda
+++ b/Fields/CauchyCompletion/Definition.agda
@@ -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
--- a/Fields/CauchyCompletion/Group.agda
+++ b/Fields/CauchyCompletion/Group.agda
@@ -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
--- a/Fields/CauchyCompletion/Multiplication.agda
+++ b/Fields/CauchyCompletion/Multiplication.agda
@@ -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
--- a/Fields/CauchyCompletion/Ring.agda
+++ b/Fields/CauchyCompletion/Ring.agda
@@ -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
--- a/Fields/CauchyCompletion/Setoid.agda
+++ b/Fields/CauchyCompletion/Setoid.agda
@@ -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
--- a/Fields/FieldOfFractions/Addition.agda
+++ b/Fields/FieldOfFractions/Addition.agda
@@ -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

--- a/Fields/FieldOfFractions/Field.agda
+++ b/Fields/FieldOfFractions/Field.agda
@@ -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
--- a/Fields/FieldOfFractions/Group.agda
+++ b/Fields/FieldOfFractions/Group.agda
@@ -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

--- a/Fields/FieldOfFractions/Lemmas.agda
+++ b/Fields/FieldOfFractions/Lemmas.agda
@@ -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)
--- a/Fields/FieldOfFractions/Multiplication.agda
+++ b/Fields/FieldOfFractions/Multiplication.agda
@@ -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

--- a/Fields/FieldOfFractions/Order.agda
+++ b/Fields/FieldOfFractions/Order.agda
@@ -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

--- a/Fields/FieldOfFractions/Ring.agda
+++ b/Fields/FieldOfFractions/Ring.agda
@@ -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

--- a/Fields/FieldOfFractions/Setoid.agda
+++ b/Fields/FieldOfFractions/Setoid.agda
@@ -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
--- a/Fields/Fields.agda
+++ b/Fields/Fields.agda
@@ -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; _⊔_)

--- a/Fields/Lemmas.agda
+++ b/Fields/Lemmas.agda
@@ -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
--- a/Fields/Orders/Lemmas.agda
+++ b/Fields/Orders/Lemmas.agda
@@ -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

--- a/Fields/Orders/Partial/Definition.agda
+++ b/Fields/Orders/Partial/Definition.agda
@@ -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
--- a/Fields/Orders/Total/Definition.agda
+++ b/Fields/Orders/Total/Definition.agda
@@ -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
--- a/Groups/Abelian/Definition.agda
+++ b/Groups/Abelian/Definition.agda
@@ -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

--- a/Groups/Abelian/DirectSum.agda
+++ b/Groups/Abelian/DirectSum.agda
@@ -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
--- a/Groups/Abelian/Lemmas.agda
+++ b/Groups/Abelian/Lemmas.agda
@@ -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
--- a/Groups/ActionIsSymmetry.agda
+++ b/Groups/ActionIsSymmetry.agda
@@ -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
--- a/Groups/Actions/Definition.agda
+++ b/Groups/Actions/Definition.agda
@@ -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

--- a/Groups/Actions/Orbit.agda
+++ b/Groups/Actions/Orbit.agda
@@ -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

--- a/Groups/Actions/Stabiliser.agda
+++ b/Groups/Actions/Stabiliser.agda
@@ -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
--- a/Groups/Cosets.agda
+++ b/Groups/Cosets.agda
@@ -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
--- a/Groups/Cyclic/Definition.agda
+++ b/Groups/Cyclic/Definition.agda
@@ -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

--- a/Groups/Cyclic/DefinitionLemmas.agda
+++ b/Groups/Cyclic/DefinitionLemmas.agda
@@ -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
--- a/Groups/Definition.agda
+++ b/Groups/Definition.agda
@@ -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

--- a/Groups/DirectSum/Definition.agda
+++ b/Groups/DirectSum/Definition.agda
@@ -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

--- a/Groups/FiniteGroups/Definition.agda
+++ b/Groups/FiniteGroups/Definition.agda
@@ -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

--- a/Groups/FinitePermutations.agda
+++ b/Groups/FinitePermutations.agda
@@ -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
--- a/Groups/FirstIsomorphismTheorem.agda
+++ b/Groups/FirstIsomorphismTheorem.agda
@@ -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

--- a/Groups/Groups.agda
+++ b/Groups/Groups.agda
@@ -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

--- a/Groups/Homomorphisms/Definition.agda
+++ b/Groups/Homomorphisms/Definition.agda
@@ -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

--- a/Groups/Homomorphisms/Examples.agda
+++ b/Groups/Homomorphisms/Examples.agda
@@ -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

--- a/Groups/Homomorphisms/Image.agda
+++ b/Groups/Homomorphisms/Image.agda
@@ -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; _⊔_)

--- a/Groups/Homomorphisms/Kernel.agda
+++ b/Groups/Homomorphisms/Kernel.agda
@@ -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

--- a/Groups/Homomorphisms/Lemmas.agda
+++ b/Groups/Homomorphisms/Lemmas.agda
@@ -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
--- a/Groups/Isomorphisms/Definition.agda
+++ b/Groups/Isomorphisms/Definition.agda
@@ -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

--- a/Groups/Isomorphisms/Lemmas.agda
+++ b/Groups/Isomorphisms/Lemmas.agda
@@ -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
--- a/Groups/Lemmas.agda
+++ b/Groups/Lemmas.agda
@@ -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

--- a/Groups/Polynomials/Addition.agda
+++ b/Groups/Polynomials/Addition.agda
@@ -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

--- a/Groups/Polynomials/Definition.agda
+++ b/Groups/Polynomials/Definition.agda
@@ -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

--- a/Groups/Polynomials/Examples.agda
+++ b/Groups/Polynomials/Examples.agda
@@ -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

--- a/Groups/Polynomials/Group.agda
+++ b/Groups/Polynomials/Group.agda
@@ -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

--- a/Groups/QuotientGroup/Definition.agda
+++ b/Groups/QuotientGroup/Definition.agda
@@ -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

--- a/Groups/QuotientGroup/Lemmas.agda
+++ b/Groups/QuotientGroup/Lemmas.agda
@@ -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
--- a/Groups/Subgroups/Definition.agda
+++ b/Groups/Subgroups/Definition.agda
@@ -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

--- a/Groups/Subgroups/Examples.agda
+++ b/Groups/Subgroups/Examples.agda
@@ -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
--- a/Groups/Subgroups/Normal/Definition.agda
+++ b/Groups/Subgroups/Normal/Definition.agda
@@ -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; _⊔_)

--- a/Groups/Subgroups/Normal/Examples.agda
+++ b/Groups/Subgroups/Normal/Examples.agda
@@ -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

--- a/Groups/Subgroups/Normal/Lemmas.agda
+++ b/Groups/Subgroups/Normal/Lemmas.agda
@@ -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; _⊔_)
--- a/Groups/SymmetricGroups/Definition.agda
+++ b/Groups/SymmetricGroups/Definition.agda
@@ -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
--- a/Groups/SymmetricGroups/Lemmas.agda
+++ b/Groups/SymmetricGroups/Lemmas.agda
@@ -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
--- a/KeyValue/KeyValue.agda
+++ b/KeyValue/KeyValue.agda
@@ -3,10 +3,8 @@
 open import LogicalFormulae
 open import Maybe
 open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Vectors

 open import Numbers.Naturals.Semiring
-open import Numbers.Naturals.Order

 module KeyValue.KeyValue {a b : _} (keys : Set a) (values : Set b) where

--- a/Lists/Concat.agda
+++ b/Lists/Concat.agda
@@ -1,7 +1,6 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Lists.Definition
 open import Lists.Length
 open import Numbers.Naturals.Semiring
--- a/Lists/Definition.agda
+++ b/Lists/Definition.agda
@@ -1,7 +1,5 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

-open import LogicalFormulae
-open import Functions

 module Lists.Definition {a : _} where

--- a/Lists/Fold/Fold.agda
+++ b/Lists/Fold/Fold.agda
@@ -1,7 +1,5 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

-open import LogicalFormulae
-open import Functions
 open import Lists.Definition

 module Lists.Fold.Fold {a b : _} {A : Set a} {B : Set b} where
--- a/Lists/Length.agda
+++ b/Lists/Length.agda
@@ -1,10 +1,7 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Numbers.Naturals.Semiring -- for length
-open import Numbers.Naturals.Order
-open import Semirings.Definition
 open import Lists.Definition
 open import Lists.Fold.Fold

--- a/Lists/Lists.agda
+++ b/Lists/Lists.agda
@@ -1,7 +1,6 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Numbers.Naturals.Semiring -- for length
 open import Numbers.Naturals.Order
 open import Semirings.Definition
--- a/Lists/Monad.agda
+++ b/Lists/Monad.agda
@@ -1,7 +1,6 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Lists.Definition
 open import Lists.Fold.Fold
 open import Lists.Concat
--- a/Lists/Reversal/Reversal.agda
+++ b/Lists/Reversal/Reversal.agda
@@ -1,11 +1,6 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Functions
-open import Numbers.Naturals.Semiring -- for length
-open import Numbers.Naturals.Order
-open import Semirings.Definition
-open import Maybe
 open import Lists.Definition
 open import Lists.Concat

--- a/Maybe.agda
+++ b/Maybe.agda
@@ -1,7 +1,6 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module Maybe where

--- a/Modules/Definition.agda
+++ b/Modules/Definition.agda
@@ -1,15 +1,8 @@
 {-# 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.Abelian.Definition
-open import Numbers.Naturals.Naturals
-open import Setoids.Orders
 open import Setoids.Setoids
-open import Functions
-open import Sets.EquivalenceRelations
 open import Rings.Definition

 open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
--- a/Modules/DirectSum.agda
+++ b/Modules/DirectSum.agda
@@ -1,19 +1,12 @@
 {-# 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.Abelian.Definition
-open import Numbers.Naturals.Naturals
-open import Setoids.Orders
 open import Setoids.Setoids
-open import Functions
-open import Sets.EquivalenceRelations
 open import Rings.Definition
 open import Modules.Definition

-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module Modules.DirectSum {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+R_ : A → A → A} {_*R_ : A → A → A} (R : Ring S _+R_ _*R_) {m n o p : _} {M : Set m} {T : Setoid {m} {n} M} {_+_ : M → M → M} {G' : Group T _+_} {G : AbelianGroup G'} {_·1_ : A → M → M} {N : Set o} {U : Setoid {o} {p} N} {_+'_ : N → N → N} {H' : Group U _+'_} {H : AbelianGroup H'} {_·2_ : A → N → N} (M1 : Module R G _·1_) (M2 : Module R H _·2_) where

--- a/Modules/Examples.agda
+++ b/Modules/Examples.agda
@@ -1,23 +1,15 @@
 {-# 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 Groups.Abelian.Definition
-open import Numbers.Naturals.Naturals
 open import Numbers.Integers.Integers
-open import Setoids.Orders
 open import Setoids.Setoids
-open import Functions
 open import Sets.EquivalenceRelations
-open import Rings.Definition
 open import Modules.Definition
 open import Groups.Cyclic.Definition
 open import Groups.Cyclic.DefinitionLemmas

-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module Modules.Examples where

--- a/Modules/Lemmas.agda
+++ b/Modules/Lemmas.agda
@@ -1,20 +1,13 @@
 {-# 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 Groups.Abelian.Definition
-open import Numbers.Naturals.Naturals
-open import Setoids.Orders
 open import Setoids.Setoids
-open import Functions
 open import Sets.EquivalenceRelations
 open import Rings.Definition
 open import Modules.Definition

-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module Modules.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+R_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+R_ _*_} {m n : _} {M : Set m} {T : Setoid {m} {n} M} {_+_ : M → M → M} {G' : Group T _+_} {G : AbelianGroup G'} {_·_ : A → M → M} (mod : Module R G _·_) where

--- a/Monoids/Definition.agda
+++ b/Monoids/Definition.agda
@@ -1,8 +1,6 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Functions
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

 module Monoids.Definition where

--- a/Numbers/BinaryNaturals/Addition.agda
+++ b/Numbers/BinaryNaturals/Addition.agda
@@ -1,12 +1,10 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Lists.Lists
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Naturals
 open import Numbers.Naturals.Order
-open import Groups.Definition
 open import Numbers.BinaryNaturals.Definition
 open import Semirings.Definition
 open import Orders.Total.Definition
--- a/Numbers/BinaryNaturals/Definition.agda
+++ b/Numbers/BinaryNaturals/Definition.agda
@@ -1,12 +1,9 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Lists.Lists
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Order
-open import Numbers.Naturals.Definition
-open import Groups.Definition
 open import Semirings.Definition
 open import Orders.Total.Definition

--- a/Numbers/BinaryNaturals/Multiplication.agda
+++ b/Numbers/BinaryNaturals/Multiplication.agda
@@ -1,11 +1,9 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Functions
 open import Lists.Lists
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Naturals
-open import Groups.Definition
 open import Numbers.BinaryNaturals.Definition
 open import Numbers.BinaryNaturals.Addition
 open import Semirings.Definition
--- a/Numbers/BinaryNaturals/Order.agda
+++ b/Numbers/BinaryNaturals/Order.agda
@@ -1,13 +1,10 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

-open import Orders.WellFounded.Induction
 open import LogicalFormulae
-open import Functions
 open import Lists.Lists
 open import Numbers.Naturals.Order
 open import Numbers.Naturals.Order.Lemmas
 open import Numbers.Naturals.Semiring
-open import Groups.Definition
 open import Numbers.BinaryNaturals.Definition
 open import Orders.Total.Definition
 open import Semirings.Definition
--- a/Numbers/BinaryNaturals/Subtraction.agda
+++ b/Numbers/BinaryNaturals/Subtraction.agda
@@ -9,7 +9,6 @@ open import Numbers.BinaryNaturals.Definition
 open import Numbers.BinaryNaturals.Addition
 open import Numbers.BinaryNaturals.SubtractionGo
 open import Numbers.BinaryNaturals.SubtractionGoPreservesCanonicalRight
-open import Numbers.BinaryNaturals.SubtractionGoPreservesCanonicalLeft
 open import Orders.Total.Definition
 open import Semirings.Definition
 open import Maybe
--- a/Numbers/BinaryNaturals/SubtractionGo.agda
+++ b/Numbers/BinaryNaturals/SubtractionGo.agda
@@ -2,9 +2,7 @@

 open import LogicalFormulae
 open import Lists.Lists
-open import Numbers.Naturals.Naturals
 open import Numbers.BinaryNaturals.Definition
-open import Semirings.Definition
 open import Maybe

 module Numbers.BinaryNaturals.SubtractionGo where
--- a/Numbers/BinaryNaturals/SubtractionGoPreservesCanonicalLeft.agda
+++ b/Numbers/BinaryNaturals/SubtractionGoPreservesCanonicalLeft.agda
@@ -1,179 +0,0 @@
-{-# OPTIONS --warning=error --safe --without-K #-}
-
-open import LogicalFormulae
-open import Lists.Lists
-open import Numbers.Naturals.Naturals
-open import Numbers.BinaryNaturals.Definition
-open import Maybe
-open import Numbers.BinaryNaturals.SubtractionGo
-
-module Numbers.BinaryNaturals.SubtractionGoPreservesCanonicalLeft where
-
-  goPreservesCanonicalLeftZero : (a b : BinNat) → mapMaybe canonical (go zero a b) ≡ mapMaybe canonical (go zero (canonical a) b)
-  goPreservesCanonicalLeftOne : (a b : BinNat) → mapMaybe canonical (go one a b) ≡ mapMaybe canonical (go one (canonical a) b)
-
-  goPreservesCanonicalLeftZero [] b = refl
-  goPreservesCanonicalLeftZero (zero :: a) [] with inspect (canonical a)
-  goPreservesCanonicalLeftZero (zero :: a) [] | [] with≡ pr rewrite pr = refl
-  goPreservesCanonicalLeftZero (zero :: a) [] | (x :: t) with≡ pr rewrite pr | transitivity (applyEquality canonical (equalityCommutative pr)) (transitivity (equalityCommutative (canonicalIdempotent a)) pr) = refl
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) with inspect (canonical a)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | [] with≡ pr with inspect (go zero a b)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | [] with≡ pr | no with≡ pr2 rewrite pr | pr2 = transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (λ i → mapMaybe canonical (go zero i b)) pr))
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | [] with≡ pr | yes x with≡ pr2 with inspect (canonical x)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | [] with≡ pr | yes x with≡ pr2 | [] with≡ pr3 rewrite pr | pr2 | pr3 = transitivity (equalityCommutative (transitivity (applyEquality (mapMaybe canonical) pr2) (applyEquality yes pr3))) (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (λ i → mapMaybe canonical (go zero i b)) pr))
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | [] with≡ pr | yes x with≡ pr2 | (y1 :: ys) with≡ pr3 = exFalso (nonEmptyNotEmpty (goZero b {y1 :: ys} t))
-    where
-      t : mapMaybe canonical (go zero [] b) ≡ yes (y1 :: ys)
-      t = transitivity (transitivity (applyEquality (λ i → mapMaybe canonical (go zero i b)) (equalityCommutative pr)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2))) (applyEquality yes pr3)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr with inspect (go zero a b)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr | no with≡ pr2 with inspect (go zero (x :: y) b)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr | no with≡ pr2 | no with≡ pr3 rewrite pr | pr2 | pr3 = refl
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr | no with≡ pr2 | yes r with≡ pr3 = exFalso (noNotYes (transitivity (equalityCommutative (transitivity (applyEquality (λ i → mapMaybe canonical (go zero i b)) (equalityCommutative pr)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2)))) (applyEquality (mapMaybe canonical) pr3)))
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr | yes x1 with≡ pr2 with inspect (go zero (x :: y) b)
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr | yes x1 with≡ pr2 | no with≡ pr3 rewrite equalityCommutative pr = exFalso (noNotYes {b = canonical x1} (transitivity (applyEquality (mapMaybe canonical) (equalityCommutative pr3)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2))))
-  goPreservesCanonicalLeftZero (zero :: a) (zero :: b) | (x :: y) with≡ pr | yes x1 with≡ pr2 | yes x2 with≡ pr3 with yesInjective {x = canonical x1} {y = canonical x2} (transitivity (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) (transitivity (applyEquality (λ i → go zero i b) pr) pr3)))
-  ... | k rewrite pr | pr2 | pr3 | equalityCommutative pr = applyEquality yes t
-    where
-      t : canonical (zero :: x1) ≡ canonical (zero :: x2)
-      t with inspect (canonical x1)
-      t | [] with≡ pr rewrite pr | equalityCommutative k = refl
-      t | (x :: bl) with≡ pr rewrite pr | equalityCommutative k = refl
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) with inspect (canonical a)
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | [] with≡ x with inspect (go one a b)
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | [] with≡ pr | no with≡ pr1 rewrite pr | pr1 = refl
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | [] with≡ pr | yes x₂ with≡ pr1 with goPreservesCanonicalLeftOne a b
-  ... | bl rewrite pr1 | pr = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) (goOneEmpty' b))) (equalityCommutative bl)))
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (x₁ :: y) with≡ x with inspect (go one a b)
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (r :: rs) with≡ pr1 | no with≡ pr2 with inspect (go one (r :: rs) b)
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (r :: rs) with≡ pr1 | no with≡ pr2 | no with≡ pr3 rewrite pr1 | pr2 | pr3 = refl
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (r :: rs) with≡ pr1 | no with≡ pr2 | yes x with≡ pr3 rewrite pr1 | pr2 | pr3 | equalityCommutative pr1 = exFalso (noNotYes (transitivity (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (goPreservesCanonicalLeftOne a b)) (applyEquality (mapMaybe canonical) pr3)))
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (r :: rs) with≡ pr1 | yes m with≡ pr2 with inspect (go one (r :: rs) b)
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (r :: rs) with≡ pr1 | yes m with≡ pr2 | no with≡ x rewrite pr1 | pr2 | x | equalityCommutative pr1 = exFalso (noNotYes (transitivity (equalityCommutative (transitivity (goPreservesCanonicalLeftOne a b) (applyEquality (mapMaybe canonical) x))) (applyEquality (mapMaybe canonical) pr2)))
-  goPreservesCanonicalLeftZero (zero :: a) (one :: b) | (r :: rs) with≡ pr1 | yes m with≡ pr2 | yes x₁ with≡ x rewrite pr1 | pr2 | x | equalityCommutative pr1 = applyEquality (λ i → yes (one :: i)) (yesInjective (transitivity (transitivity (applyEquality (mapMaybe canonical) (equalityCommutative pr2)) (goPreservesCanonicalLeftOne a b)) (applyEquality (mapMaybe canonical) x)))
-  goPreservesCanonicalLeftZero (one :: a) [] rewrite equalityCommutative (canonicalIdempotent a) = refl
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) with inspect (canonical a)
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | [] with≡ pr with inspect (go zero a b)
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | [] with≡ pr | no with≡ pr2 with inspect (go zero [] b)
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | [] with≡ pr | no with≡ pr2 | no with≡ pr3 rewrite pr | pr2 | pr3 = refl
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | [] with≡ pr | no with≡ pr2 | yes x with≡ pr3 rewrite pr | pr2 | pr3 = exFalso (noNotYes (transitivity (equalityCommutative (transitivity (transitivity (applyEquality (λ i → mapMaybe canonical (go zero i b)) (equalityCommutative pr)) (equalityCommutative (goPreservesCanonicalLeftZero a b))) (applyEquality (mapMaybe canonical) pr2))) (applyEquality (mapMaybe canonical) pr3)))
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | [] with≡ pr | yes x with≡ pr2 with inspect (go zero [] b)
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 = exFalso (noNotYes (transitivity (applyEquality (mapMaybe canonical) (equalityCommutative pr3)) (transitivity (applyEquality (λ i → mapMaybe canonical (go zero i b)) (equalityCommutative pr)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2)))))
-  ... | yes y with≡ pr3 rewrite pr | pr2 | pr3 = applyEquality (λ i → yes (one :: i)) (yesInjective (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (λ i → mapMaybe canonical (go zero i b)) pr)) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | (x :: y) with≡ pr with inspect (go zero a b)
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | (x :: y) with≡ pr | no with≡ pr2 with inspect (go zero (x :: y) b)
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 = refl
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftZero (one :: a) (zero :: b) | (x :: y) with≡ pr | yes x₁ with≡ pr2 with inspect (go zero (x :: y) b)
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (equalityCommutative (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (mapMaybe canonical) pr3))) (applyEquality (mapMaybe canonical) pr2)))
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = applyEquality (λ i → yes (one :: i)) (yesInjective (transitivity (equalityCommutative (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2))) (applyEquality (mapMaybe canonical) pr3)))
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) with inspect (canonical a)
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | [] with≡ x with inspect (go zero a b)
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | [] with≡ pr | no with≡ pr2 with inspect (go zero [] b)
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = refl
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (applyEquality (mapMaybe canonical) (equalityCommutative pr2)) (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | [] with≡ pr | yes y with≡ pr2 with inspect (go zero [] b)
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (applyEquality (mapMaybe canonical) (equalityCommutative pr3)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2))))
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = applyEquality yes v
-    where
-      t : canonical y ≡ canonical z
-      t = yesInjective (transitivity (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr3))
-      v : canonical (zero :: y) ≡ canonical (zero :: z)
-      v with inspect (canonical y)
-      v | [] with≡ pr4 rewrite pr4 | (transitivity (equalityCommutative t) pr4) = refl
-      v | (x :: r) with≡ pr4 rewrite pr4 | transitivity (equalityCommutative t) pr4 = refl
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | (r :: rs) with≡ x with inspect (go zero a b)
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | (r :: rs) with≡ pr | no with≡ pr2 with inspect (go zero (r :: rs) b)
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | (r :: rs) with≡ pr | no with≡ pr2 | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = refl
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | (r :: rs) with≡ pr | no with≡ pr2 | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (goPreservesCanonicalLeftZero a b) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftZero (one :: a) (one :: b) | (r :: rs) with≡ pr | yes y with≡ pr2 with inspect (go zero (r :: rs) b)
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr3)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2))))
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = applyEquality yes v
-    where
-      t : canonical y ≡ canonical z
-      t = yesInjective (transitivity (equalityCommutative (transitivity (equalityCommutative (goPreservesCanonicalLeftZero a b)) (applyEquality (mapMaybe canonical) pr2))) (applyEquality (mapMaybe canonical) pr3))
-      v : canonical (zero :: y) ≡ canonical (zero :: z)
-      v with inspect (canonical y)
-      ... | [] with≡ pr4 rewrite pr4 | transitivity (equalityCommutative t) pr4 = refl
-      ... | (r :: rs) with≡ pr4 rewrite pr4 | transitivity (equalityCommutative t) pr4 = refl
-
-  badLemma : (a b : BinNat) {t : BinNat} → go one a b ≡ yes t → canonical a ≡ [] → False
-  badLemma a b pr1 pr2 with applyEquality (mapMaybe canonical) pr1
-  badLemma a b pr1 pr2 | t with goPreservesCanonicalLeftOne a b
-  ... | th rewrite pr2 | t | goOneEmpty' b = noNotYes (equalityCommutative th)
-
-  goPreservesCanonicalLeftOne [] [] = refl
-  goPreservesCanonicalLeftOne [] (x :: b) = refl
-  goPreservesCanonicalLeftOne (zero :: a) [] with inspect (canonical a)
-  goPreservesCanonicalLeftOne (zero :: a) [] | [] with≡ pr with inspect (go one a [])
-  goPreservesCanonicalLeftOne (zero :: a) [] | [] with≡ pr | no with≡ x rewrite pr | x = refl
-  goPreservesCanonicalLeftOne (zero :: a) [] | [] with≡ pr | yes y with≡ x rewrite pr | x = exFalso (noNotYes (transitivity (equalityCommutative (transitivity (goPreservesCanonicalLeftOne a []) (transitivity (applyEquality (λ i → mapMaybe canonical (go one i [])) pr) refl))) (applyEquality (mapMaybe canonical) x)))
-  goPreservesCanonicalLeftOne (zero :: a) [] | (x :: xs) with≡ pr with inspect (go one a [])
-  goPreservesCanonicalLeftOne (zero :: a) [] | (x :: xs) with≡ pr | no with≡ pr2 with inspect (go one (canonical a) [])
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = refl
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (goPreservesCanonicalLeftOne a []) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftOne (zero :: a) [] | (x :: xs) with≡ pr | yes y with≡ pr2 with inspect (go one (x :: xs) [])
-  ... | no with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr3)) (transitivity (equalityCommutative (goPreservesCanonicalLeftOne a [])) (applyEquality (mapMaybe canonical) pr2))))
-  ... | yes z with≡ pr3 rewrite pr | pr2 | pr3 | equalityCommutative pr = applyEquality (λ i → yes (one :: i)) (yesInjective (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (goPreservesCanonicalLeftOne a []) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftOne (one :: a) [] with inspect (canonical a)
-  ... | [] with≡ pr rewrite pr = refl
-  ... | (x :: xs) with≡ pr rewrite pr | equalityCommutative pr = applyEquality yes (transitivity (canonicalAscends' {zero} a λ pr2 → nonEmptyNotEmpty (transitivity (equalityCommutative pr) pr2)) (lemma a))
-    where
-      lemma : (a : BinNat) → canonical (zero :: a) ≡ canonical (zero :: canonical a)
-      lemma [] = refl
-      lemma (zero :: a) with inspect (canonical a)
-      lemma (zero :: a) | [] with≡ pr rewrite pr = refl
-      lemma (zero :: a) | (x :: bl) with≡ pr rewrite pr | equalityCommutative pr | equalityCommutative (canonicalIdempotent a) | pr = refl
-      lemma (one :: a) rewrite equalityCommutative (canonicalIdempotent a) = refl
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) with inspect (go one as bs)
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) | no with≡ pr1 with inspect (canonical as)
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) | no with≡ pr1 | [] with≡ pr2 rewrite pr1 | pr2 = refl
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) | no with≡ pr1 | (a1 :: a) with≡ pr2 with inspect (go one (a1 :: a) bs)
-  ... | no with≡ pr3 rewrite pr1 | pr2 | pr3 = refl
-  ... | yes z with≡ pr3 rewrite pr1 | pr2 | pr3 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr1)) (transitivity (transitivity (goPreservesCanonicalLeftOne as bs) (applyEquality (λ i → mapMaybe canonical (go one i bs)) pr2)) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) | yes x with≡ pr1 with inspect (canonical as)
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) | yes x with≡ pr1 | [] with≡ pr2 rewrite pr1 | pr2 = exFalso (badLemma as bs pr1 pr2)
-  goPreservesCanonicalLeftOne (zero :: as) (zero :: bs) | yes x with≡ pr1 | (r :: rs) with≡ pr2 with inspect (go one (r :: rs) bs)
-  ... | no with≡ pr3 rewrite pr1 | pr2 | pr3 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr3)) (transitivity (equalityCommutative (transitivity (goPreservesCanonicalLeftOne as bs) (applyEquality (λ i → mapMaybe canonical (go one i bs)) pr2))) (applyEquality (mapMaybe canonical) pr1))))
-  ... | yes z with≡ pr3 rewrite pr1 | pr2 | pr3 = applyEquality (λ i → yes (one :: i)) (yesInjective (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr1)) (transitivity (transitivity (goPreservesCanonicalLeftOne as bs) (applyEquality (λ i → mapMaybe canonical (go one i bs)) pr2)) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) with inspect (go one as bs)
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | no with≡ pr with inspect (canonical as)
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | no with≡ pr | [] with≡ pr2 rewrite pr | pr2 = refl
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | no with≡ pr | (r :: rs) with≡ pr2 with inspect (go one (r :: rs) bs)
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | no with≡ pr | (r :: rs) with≡ pr2 | no with≡ pr3 rewrite pr | pr2 | pr3 = refl
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | no with≡ pr | (r :: rs) with≡ pr2 | yes z with≡ pr3 rewrite pr | pr2 | pr3 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr)) (transitivity (transitivity (goPreservesCanonicalLeftOne as bs) (applyEquality (λ i → mapMaybe canonical (go one i bs)) pr2)) (applyEquality (mapMaybe canonical) pr3))))
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | yes x₁ with≡ pr with inspect (canonical as)
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | yes x₁ with≡ pr | [] with≡ pr2 rewrite pr | pr2 = exFalso (badLemma as bs pr pr2)
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | yes x₁ with≡ pr | (r :: rs) with≡ pr2 with inspect (go one (r :: rs) bs)
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | yes x₁ with≡ pr | (r :: rs) with≡ pr2 | no with≡ pr3 rewrite pr | pr2 | pr3 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr3)) (transitivity (transitivity (applyEquality (λ i → mapMaybe canonical (go one i bs)) (equalityCommutative pr2)) (equalityCommutative (goPreservesCanonicalLeftOne as bs))) (applyEquality (mapMaybe canonical) pr))))
-  goPreservesCanonicalLeftOne (zero :: as) (one :: bs) | yes x with≡ pr | (r :: rs) with≡ pr2 | yes y with≡ pr3 rewrite pr | pr2 | pr3 = applyEquality yes v
-    where
-      t : canonical x ≡ canonical y
-      t = yesInjective (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr)) (transitivity (transitivity (goPreservesCanonicalLeftOne as bs) (applyEquality (λ i → mapMaybe canonical (go one i bs)) pr2)) (applyEquality (mapMaybe canonical) pr3)))
-      v : canonical (zero :: x) ≡ canonical (zero :: y)
-      v with inspect (canonical x)
-      ... | [] with≡ pr3 rewrite pr3 | transitivity (equalityCommutative t) pr3 = refl
-      ... | (r :: rs) with≡ pr3 rewrite pr3 | transitivity (equalityCommutative t) pr3 = refl
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) with inspect (go zero as bs)
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) | no with≡ pr with inspect (go zero (canonical as) bs)
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) | no with≡ pr | no with≡ pr2 rewrite pr | pr2 = refl
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) | no with≡ pr | yes x with≡ pr2 rewrite pr | pr2 = exFalso (noNotYes (transitivity (applyEquality (mapMaybe canonical) (equalityCommutative pr)) (transitivity (goPreservesCanonicalLeftZero as bs) (applyEquality (mapMaybe canonical) pr2))))
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) | yes x with≡ pr with inspect (go zero (canonical as) bs)
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) | yes x with≡ pr | yes y with≡ pr2 rewrite pr | pr2 = applyEquality yes v
-    where
-      t : canonical x ≡ canonical y
-      t = yesInjective (transitivity (equalityCommutative (transitivity (equalityCommutative (goPreservesCanonicalLeftZero as bs)) (applyEquality (mapMaybe canonical) pr))) (applyEquality (mapMaybe canonical) pr2))
-      v : canonical (zero :: x) ≡ canonical (zero :: y)
-      v with inspect (canonical x)
-      ... | [] with≡ pr3 rewrite pr3 | transitivity (equalityCommutative t) pr3 = refl
-      ... | (r :: rs) with≡ pr3 rewrite pr3 | transitivity (equalityCommutative t) pr3 = refl
-  goPreservesCanonicalLeftOne (one :: as) (zero :: bs) | yes x with≡ pr | no with≡ pr2 rewrite pr | pr2 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (equalityCommutative (goPreservesCanonicalLeftZero as bs)) (applyEquality (mapMaybe canonical) pr))))
-  goPreservesCanonicalLeftOne (one :: as) (one :: bs) with inspect (go one as bs)
-  goPreservesCanonicalLeftOne (one :: as) (one :: bs) | y with≡ pr with inspect (go one (canonical as) bs)
-  goPreservesCanonicalLeftOne (one :: as) (one :: bs) | no with≡ pr | no with≡ pr2 rewrite pr | pr2 = refl
-  goPreservesCanonicalLeftOne (one :: as) (one :: bs) | no with≡ pr | yes x₁ with≡ pr2 rewrite pr | pr2 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr)) (transitivity (goPreservesCanonicalLeftOne as bs) (applyEquality (mapMaybe canonical) pr2))))
-  goPreservesCanonicalLeftOne (one :: as) (one :: bs) | yes x₁ with≡ pr | no with≡ pr2 rewrite pr | pr2 = exFalso (noNotYes (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr2)) (transitivity (equalityCommutative (goPreservesCanonicalLeftOne as bs)) (applyEquality (mapMaybe canonical) pr))))
-  goPreservesCanonicalLeftOne (one :: as) (one :: bs) | yes x₁ with≡ pr | yes x₂ with≡ pr2 rewrite pr | pr2 = applyEquality (λ i → yes (one :: i)) (yesInjective (transitivity (transitivity (equalityCommutative (applyEquality (mapMaybe canonical) pr)) (goPreservesCanonicalLeftOne as bs)) (applyEquality (mapMaybe canonical) pr2)))
-
-  goPreservesCanonicalLeft : (state : Bit) → (a b : BinNat) → mapMaybe canonical (go state a b) ≡ mapMaybe canonical (go state (canonical a) b)
-  goPreservesCanonicalLeft zero = goPreservesCanonicalLeftZero
-  goPreservesCanonicalLeft one = goPreservesCanonicalLeftOne
--- a/Numbers/BinaryNaturals/SubtractionGoPreservesCanonicalRight.agda
+++ b/Numbers/BinaryNaturals/SubtractionGoPreservesCanonicalRight.agda
@@ -2,7 +2,6 @@

 open import LogicalFormulae
 open import Lists.Lists
-open import Numbers.Naturals.Naturals
 open import Numbers.BinaryNaturals.Definition
 open import Maybe
 open import Numbers.BinaryNaturals.SubtractionGo
--- a/Numbers/Integers/Addition.agda
+++ b/Numbers/Integers/Addition.agda
@@ -4,7 +4,6 @@ open import LogicalFormulae
 open import Numbers.Naturals.Semiring
 open import Numbers.Integers.Definition
 open import Semirings.Definition
-open import Groups.Groups
 open import Groups.Abelian.Definition
 open import Groups.Definition
 open import Setoids.Setoids
--- a/Numbers/Integers/Multiplication.agda
+++ b/Numbers/Integers/Multiplication.agda
@@ -2,13 +2,7 @@

 open import LogicalFormulae
 open import Numbers.Naturals.Semiring
-open import Numbers.Naturals.Multiplication
 open import Numbers.Integers.Definition
-open import Numbers.Integers.Addition
-open import Semirings.Definition
-open import Groups.Definition
-open import Rings.Definition
-open import Setoids.Setoids

 module Numbers.Integers.Multiplication where

--- a/Numbers/Integers/Order.agda
+++ b/Numbers/Integers/Order.agda
@@ -3,15 +3,10 @@
 open import LogicalFormulae
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Order
-open import Numbers.Integers.Definition
 open import Numbers.Integers.RingStructure.Ring
-open import Numbers.Integers.Addition
-open import Numbers.Integers.Multiplication
 open import Semirings.Definition
-open import Rings.Definition
 open import Rings.Orders.Partial.Definition
 open import Rings.Orders.Total.Definition
-open import Setoids.Setoids
 open import Setoids.Orders
 open import Orders.Total.Definition
 open import Orders.Partial.Definition
--- a/Numbers/Integers/RingStructure/EuclideanDomain.agda
+++ b/Numbers/Integers/RingStructure/EuclideanDomain.agda
@@ -9,9 +9,6 @@ open import Numbers.Integers.Order
 open import Numbers.Integers.RingStructure.Ring
 open import Numbers.Integers.RingStructure.IntegralDomain
 open import Semirings.Definition
-open import Groups.Definition
-open import Rings.Definition
-open import Setoids.Setoids
 open import Rings.EuclideanDomains.Definition
 open import Orders.Total.Definition
 open import Numbers.Naturals.EuclideanAlgorithm
--- a/Numbers/Integers/RingStructure/IntegralDomain.agda
+++ b/Numbers/Integers/RingStructure/IntegralDomain.agda
@@ -2,12 +2,7 @@

 open import LogicalFormulae
 open import Numbers.Naturals.Semiring
-open import Numbers.Naturals.Multiplication
 open import Numbers.Integers.RingStructure.Ring
-open import Semirings.Definition
-open import Groups.Definition
-open import Rings.Definition
-open import Setoids.Setoids
 open import Rings.IntegralDomains.Definition

 module Numbers.Integers.RingStructure.IntegralDomain where
--- a/Numbers/Integers/RingStructure/Ring.agda
+++ b/Numbers/Integers/RingStructure/Ring.agda
@@ -4,7 +4,6 @@ open import LogicalFormulae
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Multiplication
 open import Semirings.Definition
-open import Groups.Definition
 open import Rings.Definition
 open import Setoids.Setoids

--- a/Numbers/Modulo/Addition.agda
+++ b/Numbers/Modulo/Addition.agda
@@ -3,16 +3,8 @@
 -- a natural together with a proof that it is small.

 open import LogicalFormulae
-open import Groups.Definition
-open import Groups.Groups
-open import Groups.Abelian.Definition
-open import Groups.FiniteGroups.Definition
 open import Numbers.Naturals.Semiring
-open import Numbers.Naturals.Naturals
 open import Numbers.Naturals.Order
-open import Setoids.Setoids
-open import Sets.FinSet.Definition
-open import Functions
 open import Semirings.Definition
 open import Orders.Total.Definition
 open import Numbers.Modulo.Definition
--- a/Numbers/Modulo/Definition.agda
+++ b/Numbers/Modulo/Definition.agda
@@ -1,19 +1,8 @@
 {-# OPTIONS --safe --warning=error --without-K #-}

 open import LogicalFormulae
-open import Groups.Definition
-open import Groups.Groups
-open import Groups.Abelian.Definition
-open import Groups.FiniteGroups.Definition
 open import Numbers.Naturals.Semiring
-open import Numbers.Naturals.Naturals
 open import Numbers.Naturals.Order
-open import Setoids.Setoids
-open import Sets.FinSet.Definition
-open import Functions
-open import Semirings.Definition
-open import Numbers.Naturals.EuclideanAlgorithm
-open import Orders.Total.Definition

 module Numbers.Modulo.Definition where

--- a/Numbers/Modulo/Group.agda
+++ b/Numbers/Modulo/Group.agda
@@ -2,23 +2,19 @@

 open import LogicalFormulae
 open import Groups.Definition
-open import Groups.Groups
 open import Groups.Abelian.Definition
 open import Groups.FiniteGroups.Definition
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Order
 open import Numbers.Naturals.Order.Lemmas
-open import Numbers.Naturals.Naturals
 open import Setoids.Setoids
 open import Sets.FinSet.Definition
 open import Sets.FinSet.Lemmas
-open import Sets.Cardinality.Finite.Definition
 open import Functions
 open import Semirings.Definition
 open import Numbers.Modulo.Definition
 open import Numbers.Modulo.Addition
 open import Orders.Total.Definition
-open import Numbers.Naturals.EuclideanAlgorithm
 open import Numbers.Modulo.ModuloFunction

 module Numbers.Modulo.Group where
--- a/Numbers/Naturals/EuclideanAlgorithm.agda
+++ b/Numbers/Naturals/EuclideanAlgorithm.agda
@@ -7,10 +7,7 @@ open import Numbers.Naturals.Order
 open import Numbers.Naturals.Order.Lemmas
 open import Numbers.Naturals.Order.WellFounded
 open import Orders.WellFounded.Induction
-open import KeyValue.KeyValue
 open import Orders.Total.Definition
-open import Vectors
-open import Maybe
 open import Semirings.Definition

 module Numbers.Naturals.EuclideanAlgorithm where
--- a/Numbers/Naturals/Naturals.agda
+++ b/Numbers/Naturals/Naturals.agda
@@ -1,17 +1,11 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Functions
-open import Numbers.Naturals.Definition
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Addition
 open import Numbers.Naturals.Order
 open import Numbers.Naturals.Multiplication
-open import Numbers.Naturals.Exponentiation
-open import Numbers.Naturals.Subtraction
 open import Semirings.Definition
-open import Monoids.Definition
 open import Orders.Total.Definition

 module Numbers.Naturals.Naturals where
--- a/Numbers/Naturals/Order.agda
+++ b/Numbers/Naturals/Order.agda
@@ -2,7 +2,6 @@

 open import LogicalFormulae
 open import Semirings.Definition
-open import Numbers.Naturals.Definition
 open import Numbers.Naturals.Semiring
 open import Orders.Total.Definition
 open import Orders.Partial.Definition
--- a/Numbers/Naturals/Order/WellFounded.agda
+++ b/Numbers/Naturals/Order/WellFounded.agda
@@ -1,13 +1,10 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
 open import Orders.WellFounded.Definition
-open import Functions
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Order
 open import Semirings.Definition
-open import Orders.Total.Definition

 module Numbers.Naturals.Order.WellFounded where
 open Semiring ℕSemiring
--- a/Numbers/Naturals/Semiring.agda
+++ b/Numbers/Naturals/Semiring.agda
@@ -1,8 +1,6 @@
 {-# OPTIONS --warning=error --safe --without-K #-}

 open import LogicalFormulae
-open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
-open import Functions
 open import Numbers.Naturals.Definition
 open import Numbers.Naturals.Addition
 open import Numbers.Naturals.Multiplication
--- a/Show More
+++ b/Show More