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https://github.com/Smaug123/agdaproofs
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Rem unused opens in Safe (#93)
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@@ -1,19 +1,12 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Lemmas
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open import Groups.Homomorphisms.Definition
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open import Groups.Definition
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open import Groups.Subgroups.Definition
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open import Numbers.Naturals.Naturals
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Rings.Definition
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open import Rings.Homomorphisms.Definition
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open import Groups.Homomorphisms.Lemmas
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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@@ -1,14 +1,10 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Homomorphisms.Definition
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open import Groups.Definition
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open import Groups.Lemmas
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open import Numbers.Naturals.Naturals
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Rings.Definition
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open import Rings.Homomorphisms.Definition
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@@ -18,7 +14,6 @@ open import Rings.Cosets
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open import Rings.Isomorphisms.Definition
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open import Groups.Isomorphisms.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.FirstIsomorphismTheorem {a b c d : _} {A : Set a} {B : Set c} {S : Setoid {a} {b} A} {T : Setoid {c} {d} B} {_+A_ _*A_ : A → A → A} {_+B_ _*B_ : B → B → B} {R1 : Ring S _+A_ _*A_} {R2 : Ring T _+B_ _*B_} {f : A → B} (hom : RingHom R1 R2 f) where
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@@ -1,25 +1,19 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Homomorphisms.Definition
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open import Groups.Definition
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open import Numbers.Naturals.Naturals
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Rings.Definition
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open import Rings.Homomorphisms.Definition
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open import Groups.Homomorphisms.Lemmas
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open import Groups.Subgroups.Definition
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open import Rings.Homomorphisms.Kernel
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open import Rings.Cosets
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open import Groups.Lemmas
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open import Setoids.Functions.Lemmas
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open import Rings.Ideals.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
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@@ -1,13 +1,8 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Lemmas
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open import Groups.Definition
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open import Setoids.Setoids
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open import Rings.Definition
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open import Rings.Lemmas
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open import Sets.EquivalenceRelations
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open import Rings.Ideals.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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@@ -1,18 +1,14 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Cosets
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open import Groups.Homomorphisms.Definition
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open import Rings.Homomorphisms.Definition
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open import Groups.Lemmas
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open import Groups.Definition
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open import Setoids.Setoids
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open import Setoids.Subset
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open import Setoids.Functions.Definition
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open import Setoids.Functions.Lemmas
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open import Rings.Definition
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open import Rings.Lemmas
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open import Sets.EquivalenceRelations
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open import Rings.Ideals.Definition
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open import Fields.Fields
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@@ -28,7 +24,6 @@ open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.Maximal.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} {c : _} {pred : A → Set c} (i : Ideal R pred) where
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open import Rings.Divisible.Definition R
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open Ring R
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open Group additiveGroup
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@@ -1,16 +1,8 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Lemmas
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open import Groups.Definition
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open import Numbers.Naturals.Naturals
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open import Setoids.Setoids
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open import Functions
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open import Rings.Definition
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open import Rings.Lemmas
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open import Sets.EquivalenceRelations
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open import Fields.Fields
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open import Rings.Ideals.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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@@ -1,19 +1,15 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Lemmas
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open import Groups.Definition
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open import Setoids.Setoids
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open import Rings.Definition
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open import Sets.EquivalenceRelations
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open import Rings.Ideals.Definition
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open import Rings.IntegralDomains.Definition
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open import Rings.IntegralDomains.Lemmas
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open import Rings.Ideals.Prime.Definition
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open import Rings.Cosets
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.Prime.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} {c : _} {pred : A → Set c} (i : Ideal R pred) where
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@@ -1,10 +1,6 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Rings.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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@@ -1,13 +1,9 @@
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{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Rings.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.Principal.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
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