48 lines
1.4 KiB
Plaintext
48 lines
1.4 KiB
Plaintext
open import Graph.Base
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module Graph.Reasoning where
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module ≡-Reasoning where
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infix 1 begin_
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infixr 2 _≡⟨⟩_ _≡⟨_⟩_
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infix 3 _∎
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begin_ : ∀ { A : Set } { G H : Graph A } → G ≡ H → G ≡ H
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begin G≡H = G≡H
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_≡⟨⟩_ : ∀ { A : Set } (G : Graph A) { H : Graph A } → G ≡ H → G ≡ H
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G ≡⟨⟩ G≡H = G≡H
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_≡⟨_⟩_ : ∀ { A : Set } (G : Graph A) { H I : Graph A } → G ≡ H → H ≡ I → G ≡ I
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G ≡⟨ G≡H ⟩ H≡I = trans G≡H H≡I
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_∎ : ∀ { A : Set } (G : Graph A) → G ≡ G
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G ∎ = refl
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module ≤-Reasoning where
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infix 1 begin_
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infixr 2 _≡⟨⟩_ _≡⟨_⟩_ _≤⟨⟩_ _≤⟨_⟩_
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infix 3 _∎
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begin_ : ∀ { A : Set } { G H : Graph A } → G ≤ H → G ≤ H
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begin G≤H = G≤H
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_≡⟨⟩_ : ∀ { A : Set } (G : Graph A) { H : Graph A } → G ≤ H → G ≤ H
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G ≡⟨⟩ G≤H = G≤H
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_≡⟨_⟩_ : ∀ { A : Set } (G : Graph A) { H I : Graph A } → G ≡ H → H ≤ I → G ≤ I
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G ≡⟨ G≡H ⟩ H≤I = ≤-trans (≡-to-≤ G≡H) H≤I
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_≤⟨⟩_ : ∀ { A : Set } (G : Graph A) { H : Graph A } → G ≤ H → G ≤ H
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G ≤⟨⟩ G≤H = G≤H
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_≤⟨_⟩_ : ∀ { A : Set } (G : Graph A) { H I : Graph A } → G ≤ H → H ≤ I → G ≤ I
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G ≤⟨ G≤H ⟩ H≤I = ≤-trans G≤H H≤I
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_∎ : ∀ { A : Set } (G : Graph A) → G ≤ G
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G ∎ = ≤-refl
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