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Move some more things over to Without K (#40)

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This commit is contained in:
Patrick Stevens
2019-08-22 20:32:34 +01:00
committed by GitHub
parent 9c14e7c439
commit 61f3dc7306
8 changed files with 48 additions and 42 deletions
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6
Numbers/BinaryNaturals/Multiplication.agda
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@@ -1,4 +1,4 @@
{-# OPTIONS --warning=error --safe #-}
{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Functions
@@ -144,7 +144,9 @@ module Numbers.BinaryNaturals.Multiplication where
NToBinNatDistributesPlus : (a b : ℕ) → NToBinNat (a +N b) ≡ NToBinNat a +B NToBinNat b
NToBinNatDistributesPlus zero b = refl
NToBinNatDistributesPlus (succ a) b rewrite equalityCommutative (NToBinNatSucc (a +N b)) | NToBinNatDistributesPlus a b = incrPullsOut (NToBinNat a) (NToBinNat b)
NToBinNatDistributesPlus (succ a) b with inspect (NToBinNat a)
... | bl with≡ prA with inspect (NToBinNat (a +N b))
... | q with≡ prAB = transitivity (applyEquality incr (NToBinNatDistributesPlus a b)) (incrPullsOut (NToBinNat a) (NToBinNat b))
timesCommutative : (a b : BinNat) → canonical (a *B b) ≡ canonical (b *B a)
timesCommLemma : (a b : BinNat) → canonical (zero :: (b *B a)) ≡ canonical (b *B (zero :: a))