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Split out much more structure (#37)

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Patrick Stevens
2019-08-18 14:57:41 +01:00
committed by GitHub
parent 69389bb889
commit 1f26064502
52 changed files with 2137 additions and 2014 deletions
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7
Numbers/BinaryNaturals/Order.agda
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@@ -3,10 +3,11 @@
open import LogicalFormulae
open import Functions
open import Lists.Lists
open import Numbers.Naturals
open import Groups.GroupDefinition
open import Numbers.Naturals.Naturals
open import Groups.Definition
open import Numbers.BinaryNaturals.Definition
open import Orders
open import Semirings.Definition
module Numbers.BinaryNaturals.Order where
@@ -278,7 +279,7 @@ module Numbers.BinaryNaturals.Order where
chopDouble a b i | inr a=b | inr x = refl
succNotLess : {n : ℕ} → succ n <N n → False
succNotLess {succ n} (le x proof) = succNotLess {n} (le x (succInjective (transitivity (applyEquality succ (transitivity (additionNIsCommutative (succ x) (succ n)) (transitivity (applyEquality succ (transitivity (additionNIsCommutative n (succ x)) (applyEquality succ (additionNIsCommutative x n)))) (additionNIsCommutative (succ (succ n)) x)))) proof)))
succNotLess {succ n} (le x proof) = succNotLess {n} (le x (succInjective (transitivity (applyEquality succ (transitivity (Semiring.commutative ℕSemiring (succ x) (succ n)) (transitivity (applyEquality succ (transitivity (Semiring.commutative ℕSemiring n (succ x)) (applyEquality succ (Semiring.commutative ℕSemiring x n)))) (Semiring.commutative ℕSemiring (succ (succ n)) x)))) proof)))
<BIsInherited : (a b : BinNat) → a <BInherited b ≡ a <B b
<BIsInherited [] b with orderIsTotal 0 (binNatToN b)