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Move Bool to live on its own (#118)

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Patrick Stevens
2020-04-18 17:14:39 +01:00
committed by GitHub
parent 264a5e2bd9
commit 84a146f72c
30 changed files with 270 additions and 123 deletions
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8
Numbers/Naturals/Naturals.agda
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@@ -98,14 +98,6 @@ lessImpliesNotEqual {a} {.a} prAB refl = TotalOrder.irreflexive ℕTotalOrder pr
-NIsDecreasing {a} {b} prAB with (-N (inl prAB))
-NIsDecreasing {a} {b} (le x proof) | record { result = result ; pr = pr } = record { x = a ; proof = pr }
equalityN : (a b : ℕ) → Sg Bool (λ truth → if truth then a ≡ b else True)
equalityN zero zero = ( BoolTrue , refl )
equalityN zero (succ b) = ( BoolFalse , record {} )
equalityN (succ a) zero = ( BoolFalse , record {} )
equalityN (succ a) (succ b) with equalityN a b
equalityN (succ a) (succ b) | BoolTrue , val = (BoolTrue , applyEquality succ val)
equalityN (succ a) (succ b) | BoolFalse , val = (BoolFalse , record {})
sumZeroImpliesSummandsZero : {a b : ℕ} → (a +N b ≡ zero) → ((a ≡ zero) && (b ≡ zero))
sumZeroImpliesSummandsZero {zero} {zero} pr = record { fst = refl ; snd = refl }
sumZeroImpliesSummandsZero {zero} {(succ b)} pr = record { fst = refl ; snd = pr }