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Add proof of decidable equivalence for products

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-02-11 15:35:50 -08:00
parent 7e5cc1b316
commit 0ba4b46e16
1 changed files with 10 additions and 0 deletions
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Lattice/Prod.agda
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@ -94,6 +94,16 @@ isLattice = record
)
}
module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_) where
≈-dec : IsDecidable _≈_
≈-dec (a₁ , b₁) (a₂ , b₂)
with ≈₁-dec a₁ a₂ | ≈₂-dec b₁ b₂
... | yes a₁≈a₂ | yes b₁≈b₂ = yes (a₁≈a₂ , b₁≈b₂)
... | no a₁̷≈a₂ | _ = no (λ (a₁≈a₂ , _) → a₁̷≈a₂ a₁≈a₂)
... | _ | no b₁̷≈b₂ = no (λ (_ , b₁≈b₂) → b₁̷≈b₂ b₁≈b₂)
module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
(h₁ h₂ : ℕ)
(fhA : FixedHeight₁ h₁) (fhB : FixedHeight₂ h₂) where