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https://github.com/Smaug123/agdaproofs
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19 lines
790 B
Agda
19 lines
790 B
Agda
{-# OPTIONS --warning=error --safe --without-K #-}
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open import LogicalFormulae
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import Functions
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open import Setoids.Setoids
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open import Setoids.Subset
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open import Graphs.Definition
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module Graphs.InducedSubgraph {a b c : _} {V' : Set a} {V : Setoid {a} {b} V'} (G : Graph c V) where
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open Graph G
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inducedSubgraph : {d : _} {pred : V' → Set d} (sub : subset V pred) → Graph c (subsetSetoid V sub)
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Graph._<->_ (inducedSubgraph sub) (x , _) (y , _) = x <-> y
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Graph.noSelfRelation (inducedSubgraph sub) (x , _) x=x = noSelfRelation x x=x
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Graph.symmetric (inducedSubgraph sub) {x , _} {y , _} x=y = symmetric x=y
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Graph.wellDefined (inducedSubgraph sub) {x , _} {y , _} {z , _} {w , _} x=y z=w x-z = wellDefined x=y z=w x-z
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