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Prove that AxB is a finite height semilattice

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin
2023-09-03 23:56:39 -07:00
parent fb86d3f84f
commit 5cab39ca82
2 changed files with 44 additions and 9 deletions
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Chain.agda
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@@ -16,7 +16,7 @@ module _ where
data Chain : A → A → ℕ → Set a where
done : ∀ {a a' : A} → a ≈ a' → Chain a a' 0
step : ∀ {a₁ a₂ a₂' a₃ : A} {n : ℕ} → a₁ R a₂ → a₂ ≈ a₂' → Chain a₂ a₃ n → Chain a₁ a₃ (suc n)
step : ∀ {a₁ a₂ a₂' a₃ : A} {n : ℕ} → a₁ R a₂ → a₂ ≈ a₂' → Chain a₂' a₃ n → Chain a₁ a₃ (suc n)
Chain-≈-cong₁ : ∀ {a₁ a₁' a₂} {n : ℕ} → a₁ ≈ a₁' → Chain a₁ a₂ n → Chain a₁' a₂ n
Chain-≈-cong₁ a₁≈a₁' (done a₁≈a₂) = done (≈-trans (≈-sym a₁≈a₁') a₁≈a₂)