@@ -14,6 +14,7 @@ open import Function.Base using (flip)
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open import Level using (Level; suc; _⊔_)
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open import Relation.Nullary.Negation.Core using (¬_)
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open import Relation.Binary.Core using (Rel)
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+ open import Relation.Binary.Bundles.Raw
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open import Relation.Binary.Structures -- most of it
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------------------------------------------------------------------------
@@ -29,9 +30,11 @@ record PartialSetoid a ℓ : Set (suc (a ⊔ ℓ)) where
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open IsPartialEquivalence isPartialEquivalence public
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- infix 4 _≉_
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- _≉_ : Rel Carrier _
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- x ≉ y = ¬ (x ≈ y)
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+ rawSetoid : RawSetoid _ _
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+ rawSetoid = record { _≈_ = _≈_ }
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+
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+ open RawSetoid rawSetoid public
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+ hiding (Carrier; _≈_ )
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record Setoid c ℓ : Set (suc (c ⊔ ℓ)) where
@@ -94,19 +97,13 @@ record Preorder c ℓ₁ ℓ₂ : Set (suc (c ⊔ ℓ₁ ⊔ ℓ₂)) where
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open Setoid setoid public
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- infix 4 _⋦_
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- _⋦_ : Rel Carrier _
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- x ⋦ y = ¬ (x ≲ y)
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-
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- infix 4 _≳_
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- _≳_ = flip _≲_
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-
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- infix 4 _⋧_
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- _⋧_ = flip _⋦_
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+ rawRelation : RawRelation _ _ _
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+ rawRelation = record { _≈_ = _≈_ ; _∼_ = _≲_ }
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+ open RawRelation rawRelation public
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+ renaming (_≁_ to _⋦_; _∼ᵒ_ to _≳_; _≁ᵒ_ to _⋧_)
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+ hiding (Carrier; _≈_)
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-- Deprecated.
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- infix 4 _∼_
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- _∼_ = _≲_
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{-# WARNING_ON_USAGE _∼_
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"Warning: _∼_ was deprecated in v2.0.
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Please use _≲_ instead. "
@@ -183,14 +180,17 @@ record Poset c ℓ₁ ℓ₂ : Set (suc (c ⊔ ℓ₁ ⊔ ℓ₂)) where
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}
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open Preorder preorder public
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- hiding (Carrier; _≈_; _≲_; isPreorder)
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+ hiding (Carrier; _≈_; _≲_; isPreorder; _⋦_; _≳_; _⋧_ )
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renaming
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- ( _⋦_ to _≰_; _≳_ to _≥_; _⋧_ to _≱_
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- ; ≲-respˡ-≈ to ≤-respˡ-≈
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+ ( ≲-respˡ-≈ to ≤-respˡ-≈
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; ≲-respʳ-≈ to ≤-respʳ-≈
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; ≲-resp-≈ to ≤-resp-≈
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)
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+ open RawRelation rawRelation public
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+ renaming (_≁_ to _≰_; _∼ᵒ_ to _≥_; _≁ᵒ_ to _≱_)
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+ hiding (Carrier; _≈_ ; _∼_; _≉_; rawSetoid)
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+
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record DecPoset c ℓ₁ ℓ₂ : Set (suc (c ⊔ ℓ₁ ⊔ ℓ₂)) where
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infix 4 _≈_ _≤_
@@ -239,15 +239,12 @@ record StrictPartialOrder c ℓ₁ ℓ₂ : Set (suc (c ⊔ ℓ₁ ⊔ ℓ₂))
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open Setoid setoid public
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- infix 4 _≮_
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- _≮_ : Rel Carrier _
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- x ≮ y = ¬ (x < y)
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+ rawRelation : RawRelation _ _ _
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+ rawRelation = record { _≈_ = _≈_ ; _∼_ = _<_ }
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- infix 4 _>_
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- _>_ = flip _<_
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-
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- infix 4 _≯_
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- _≯_ = flip _≮_
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+ open RawRelation rawRelation public
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+ renaming (_≁_ to _≮_; _∼ᵒ_ to _>_; _≁ᵒ_ to _≯_)
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+ hiding (Carrier; _≈_ ; _∼_)
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record DecStrictPartialOrder c ℓ₁ ℓ₂ : Set (suc (c ⊔ ℓ₁ ⊔ ℓ₂)) where
@@ -418,3 +415,12 @@ record ApartnessRelation c ℓ₁ ℓ₂ : Set (suc (c ⊔ ℓ₁ ⊔ ℓ₂)) w
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isApartnessRelation : IsApartnessRelation _≈_ _#_
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open IsApartnessRelation isApartnessRelation public
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+ hiding (_¬#_)
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+
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+ rawRelation : RawRelation _ _ _
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+ rawRelation = record { _≈_ = _≈_ ; _∼_ = _#_ }
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+
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+ open RawRelation rawRelation public
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+ renaming (_≁_ to _¬#_; _∼ᵒ_ to _#ᵒ_; _≁ᵒ_ to _¬#ᵒ_)
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+ hiding (Carrier; _≈_ ; _∼_)
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+
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