mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-19 01:58:45 +00:00
30 lines
1.6 KiB
Agda
30 lines
1.6 KiB
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.Definition
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open import Setoids.Setoids
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open import Setoids.DirectSum
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open import Setoids.Subset
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open import Graphs.Definition
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open import Sets.FinSet.Definition
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open import Sets.FinSet.Lemmas
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open import Numbers.Naturals.Semiring
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open import Numbers.Naturals.Order
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open import Sets.EquivalenceRelations
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open import Graphs.PathGraph
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module Graphs.UnionGraph where
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unionGraph : {a b c d e f : _} {V' : Set a} {V : Setoid {a} {b} V'} (G : Graph c V) {W' : Set d} {W : Setoid {d} {e} W'} (H : Graph f W) → Graph (c ⊔ f) (directSumSetoid V W)
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Graph._<->_ (unionGraph {c = c} {f = f} G H) (inl v) (inl v2) = embedLevel {c} {f} (Graph._<->_ G v v2)
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Graph._<->_ (unionGraph G H) (inl v) (inr w) = False'
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Graph._<->_ (unionGraph G H) (inr w) (inl v) = False'
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Graph._<->_ (unionGraph {c = c} {f = f} G H) (inr w) (inr w2) = embedLevel {f} {c} (Graph._<->_ H w w2)
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Graph.noSelfRelation (unionGraph G H) (inl v) (v=v ,, _) = Graph.noSelfRelation G v v=v
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Graph.noSelfRelation (unionGraph G H) (inr w) (w=w ,, _) = Graph.noSelfRelation H w w=w
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Graph.symmetric (unionGraph G H) {inl x} {inl y} (x=y ,, _) = Graph.symmetric G x=y ,, record {}
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Graph.symmetric (unionGraph G H) {inr x} {inr y} (x=y ,, _) = Graph.symmetric H x=y ,, record {}
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Graph.wellDefined (unionGraph G H) {inl x} {inl y} {inl z} {inl w} (x=y ,, _) (y=z ,, _) (z=w ,, _) = Graph.wellDefined G x=y y=z z=w ,, record {}
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Graph.wellDefined (unionGraph G H) {inr x} {inr y} {inr z} {inr w} (x=y ,, _) (y=z ,, _) (z=w ,, _) = Graph.wellDefined H x=y y=z z=w ,, record {}
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