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https://github.com/Smaug123/agdaproofs
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17 lines
570 B
Agda
17 lines
570 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import LogicalFormulae
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open import Functions
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module Orders.Partial.Definition {a : _} (carrier : Set a) where
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record PartialOrder {b : _} : Set (a ⊔ lsuc b) where
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field
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_<_ : Rel {a} {b} carrier
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irreflexive : {x : carrier} → (x < x) → False
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<Transitive : {a b c : carrier} → (a < b) → (b < c) → (a < c)
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<WellDefined : {r s t u : carrier} → (r ≡ t) → (s ≡ u) → r < s → t < u
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<WellDefined refl refl r<s = r<s
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