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Reshuffle orders (#91)

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This commit is contained in:
Patrick Stevens
2019-12-29 12:11:21 +00:00
committed by GitHub
parent 876396eaaa
commit b6ef9b46f2
57 changed files with 476 additions and 462 deletions
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7
Setoids/Orders.agda
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@@ -1,7 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Orders
open import Orders.Total.Definition
open import Orders.Partial.Definition
open import Setoids.Setoids
open import Functions
@@ -33,10 +34,10 @@ record SetoidTotalOrder {a b c : _} {A : Set a} {S : Setoid {a} {b} A} {_<_ : Re
max a b | inl (inr b<a) = a
max a b | inr a=b = b
partialOrderToSetoidPartialOrder : {a b : _} {A : Set a} (P : PartialOrder {a} {b} A) → SetoidPartialOrder (reflSetoid A) (PartialOrder._<_ P)
partialOrderToSetoidPartialOrder : {a b : _} {A : Set a} (P : PartialOrder {a} A {b}) → SetoidPartialOrder (reflSetoid A) (PartialOrder._<_ P)
SetoidPartialOrder.<WellDefined (partialOrderToSetoidPartialOrder P) a=b c=d a<c rewrite a=b | c=d = a<c
SetoidPartialOrder.irreflexive (partialOrderToSetoidPartialOrder P) = PartialOrder.irreflexive P
SetoidPartialOrder.<Transitive (partialOrderToSetoidPartialOrder P) = PartialOrder.<Transitive P
totalOrderToSetoidTotalOrder : {a b : _} {A : Set a} (T : TotalOrder {a} {b} A) → SetoidTotalOrder (partialOrderToSetoidPartialOrder (TotalOrder.order T))
totalOrderToSetoidTotalOrder : {a b : _} {A : Set a} (T : TotalOrder {a} A {b}) → SetoidTotalOrder (partialOrderToSetoidPartialOrder (TotalOrder.order T))
SetoidTotalOrder.totality (totalOrderToSetoidTotalOrder T) = TotalOrder.totality T