@@ -177,9 +177,9 @@ module _ {_≈_ : Rel A ℓ₁} {_≺_ : Rel A ℓ₂} where
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∀ {n} → Antisymmetric (_≋_ {n} {n}) _≤_
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≤-antisym = Core.antisym
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- ≤-respects ₂ : IsPartialEquivalence _≈_ → _≺_ Respects₂ _≈_ →
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- ∀ {n} → _Respects₂_ (_≤_ {n} {n}) _≋_
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- ≤-respects ₂ = Core.respects₂
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+ ≤-resp ₂ : IsPartialEquivalence _≈_ → _≺_ Respects₂ _≈_ →
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+ ∀ {n} → _Respects₂_ (_≤_ {n} {n}) _≋_
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+ ≤-resp ₂ = Core.respects₂
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≤-trans : IsPartialEquivalence _≈_ → _≺_ Respects₂ _≈_ → Transitive _≺_ →
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∀ {m n o} → Trans (_≤_ {m} {n}) (_≤_ {n} {o}) _≤_
@@ -209,9 +209,9 @@ module _ {_≈_ : Rel A ℓ₁} {_≺_ : Rel A ℓ₂} where
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... | inj₁ xs<ys = inj₁ (next x≈y xs<ys)
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... | inj₂ xs>ys = inj₂ (next (≈-sym x≈y) xs>ys)
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- ≤-decidable : Decidable _≈_ → Decidable _≺_ →
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- ∀ {m n} → Decidable (_≤_ {m} {n})
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- ≤-decidable = Core.decidable (yes tt)
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+ ≤-dec : Decidable _≈_ → Decidable _≺_ →
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+ ∀ {m n} → Decidable (_≤_ {m} {n})
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+ ≤-dec = Core.decidable (yes tt)
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≤-irrelevant : Irrelevant _≈_ → Irrelevant _≺_ → Irreflexive _≈_ _≺_ →
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∀ {m n} → Irrelevant (_≤_ {m} {n})
@@ -240,7 +240,7 @@ module _ {_≈_ : Rel A ℓ₁} {_≺_ : Rel A ℓ₂} where
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≤-isDecPartialOrder ≺-isDecStrictPartialOrder = record
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{ isPartialOrder = ≤-isPartialOrder isStrictPartialOrder
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; _≟_ = Pointwise.decidable _≟_
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- ; _≤?_ = ≤-decidable _≟_ _<?_
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+ ; _≤?_ = ≤-dec _≟_ _<?_
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} where open IsDecStrictPartialOrder ≺-isDecStrictPartialOrder
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≤-isTotalOrder : IsStrictTotalOrder _≈_ _≺_ →
@@ -255,7 +255,7 @@ module _ {_≈_ : Rel A ℓ₁} {_≺_ : Rel A ℓ₂} where
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≤-isDecTotalOrder ≺-isStrictTotalOrder = record
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{ isTotalOrder = ≤-isTotalOrder ≺-isStrictTotalOrder
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; _≟_ = Pointwise.decidable _≟_
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- ; _≤?_ = ≤-decidable _≟_ _<?_
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+ ; _≤?_ = ≤-dec _≟_ _<?_
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} where open IsStrictTotalOrder ≺-isStrictTotalOrder
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