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Lots of speedups (#116)

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This commit is contained in:
Patrick Stevens
2020-04-16 13:41:51 +01:00
committed by GitHub
parent 1bcb3f8537
commit 9b80058157
63 changed files with 1082 additions and 564 deletions
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16
Rings/Orders/Partial/Lemmas.agda
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@@ -3,7 +3,7 @@
open import LogicalFormulae
open import Groups.Lemmas
open import Groups.Definition
open import Setoids.Orders
open import Setoids.Orders.Partial.Definition
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
@@ -91,3 +91,17 @@ abstract
negativeInequality : {a : A} → a < 0G → 0G < inverse a
negativeInequality {a} a<0 = <WellDefined invRight identLeft (orderRespectsAddition a<0 (inverse a))
negativeInequality' : {a : A} → 0G < a → inverse a < 0G
negativeInequality' {a} 0<a = <WellDefined identLeft invRight (orderRespectsAddition 0<a (inverse a))
open import Rings.InitialRing R
fromNIncreasing : (0R < 1R) → (n : ℕ) → (fromN n) < (fromN (succ n))
fromNIncreasing 0<1 zero = <WellDefined reflexive (symmetric identRight) 0<1
fromNIncreasing 0<1 (succ n) = <WellDefined groupIsAbelian groupIsAbelian (orderRespectsAddition (fromNIncreasing 0<1 n) 1R)
fromNPreservesOrder : (0R < 1R) → {a b : ℕ} → (a <N b) → (fromN a) < (fromN b)
fromNPreservesOrder 0<1 {zero} {succ zero} a<b = fromNIncreasing 0<1 0
fromNPreservesOrder 0<1 {zero} {succ (succ b)} a<b = <Transitive (fromNPreservesOrder 0<1 (succIsPositive b)) (fromNIncreasing 0<1 (succ b))
fromNPreservesOrder 0<1 {succ a} {succ b} a<b = <WellDefined groupIsAbelian groupIsAbelian (orderRespectsAddition (fromNPreservesOrder 0<1 (canRemoveSuccFrom<N a<b)) 1R)