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Reshuffle in preparation to break the dependency on N's implementation (#75)

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Patrick Stevens
2019-11-17 10:01:39 +00:00
committed by GitHub
parent ff6ef4f1a1
commit c55dd5f63e
53 changed files with 2493 additions and 2388 deletions
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7
Numbers/Integers/Order.agda
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@@ -1,7 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Numbers.Naturals.Naturals
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Integers.Definition
open import Numbers.Integers.Addition
open import Numbers.Integers.Multiplication
@@ -68,13 +69,13 @@ _<Z_.proof (lessNegsuccNonneg {zero} {b}) = refl
_<Z_.proof (lessNegsuccNonneg {succ a} {b}) = _<Z_.proof (lessNegsuccNonneg {a} {b})
lessThanTotalZ : {a b : ℤ} → ((a <Z b) || (b <Z a)) || (a ≡ b)
lessThanTotalZ {nonneg a} {nonneg b} with orderIsTotal a b
lessThanTotalZ {nonneg a} {nonneg b} with TotalOrder.totality ℕTotalOrder a b
lessThanTotalZ {nonneg a} {nonneg b} | inl (inl a<b) = inl (inl (lessInherits a<b))
lessThanTotalZ {nonneg a} {nonneg b} | inl (inr b<a) = inl (inr (lessInherits b<a))
lessThanTotalZ {nonneg a} {nonneg b} | inr a=b = inr (applyEquality nonneg a=b)
lessThanTotalZ {nonneg a} {negSucc b} = inl (inr (lessNegsuccNonneg {b} {a}))
lessThanTotalZ {negSucc a} {nonneg x} = inl (inl (lessNegsuccNonneg {a} {x}))
lessThanTotalZ {negSucc a} {negSucc b} with orderIsTotal a b
lessThanTotalZ {negSucc a} {negSucc b} with TotalOrder.totality ℕTotalOrder a b
... | inl (inl a<b) = inl (inr (lessInheritsNegsucc a<b))
... | inl (inr b<a) = inl (inl (lessInheritsNegsucc b<a))
lessThanTotalZ {negSucc a} {negSucc .a} | inr refl = inr refl