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remove unnecessary case split on m and n in the definition of _≟_
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Cubical/Data/Nat/Order.agda

Lines changed: 1 addition & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -341,10 +341,7 @@ private
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∸→>ᵇ (suc m) (suc n) t = ∸→>ᵇ m n t
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_≟_ : m n Trichotomy m n
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zero ≟ zero = eq refl
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zero ≟ suc n = lt (n , +-comm n 1)
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suc m ≟ zero = gt (m , +-comm m 1)
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suc m ≟ suc n with m ∸ n UsingEq | n ∸ m UsingEq
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m ≟ n with m ∸ n UsingEq | n ∸ m UsingEq
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... | zero , p | zero , q = eq (∸≡0→≡ p q)
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... | zero , p | suc _ , q = lt (<ᵇ→< $ ∸→>ᵇ n m $ subst (caseNat ⊥.⊥ Unit) (sym q) tt)
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... | suc _ , p | zero , q = gt (<ᵇ→< $ ∸→>ᵇ m n $ subst (caseNat ⊥.⊥ Unit) (sym p) tt)

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