patrick/agdaproofs
1
0
Fork 0
mirror of https://github.com/Smaug123/agdaproofs synced 2025-10-21 02:58:40 +00:00
Code Issues Packages Projects Releases Wiki Activity

Lots of speedups (#116)

Browse Source
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
Download Patch File Download Diff File Expand all files Collapse all files

16
Fields/CauchyCompletion/Group.agda
View File

@@ -10,7 +10,8 @@ open import Groups.Homomorphisms.Definition
open import Fields.Fields
open import Sets.EquivalenceRelations
open import Sequences
open import Setoids.Orders
open import Setoids.Orders.Partial.Definition
open import Setoids.Orders.Total.Definition
open import Functions
open import LogicalFormulae
open import Numbers.Naturals.Semiring
@@ -28,13 +29,14 @@ open Group (Ring.additiveGroup R)
open Ring R
open import Rings.Orders.Total.Lemmas order
open import Rings.Orders.Total.AbsoluteValue order
open import Fields.CauchyCompletion.Definition order F
open import Fields.CauchyCompletion.Addition order F
open import Fields.CauchyCompletion.Setoid order F
abstract
+CCommutative : {a b : CauchyCompletion} → Setoid._∼_ cauchyCompletionSetoid (a +C b) (b +C a)
+CCommutative {a} {b} ε 0<e = 0 , ans
+CCommutative : (a b : CauchyCompletion) → Setoid._∼_ cauchyCompletionSetoid (a +C b) (b +C a)
+CCommutative a b ε 0<e = 0 , ans
where
foo : {x y : A} → (x + y) + inverse (y + x) ∼ 0G
foo = Equivalence.transitive eq (+WellDefined (Equivalence.reflexive eq) (inverseWellDefined additiveGroup groupIsAbelian)) invRight
@@ -58,13 +60,13 @@ private
additionPreservedLeft {a} {b} {c} a=b = additionWellDefinedLeft (injection a) (injection b) c (injectionPreservesSetoid a b a=b)
additionPreservedRight : {a b : A} {c : CauchyCompletion} → (a ∼ b) → Setoid._∼_ cauchyCompletionSetoid (c +C injection a) (c +C injection b)
additionPreservedRight {a} {b} {c} a=b = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {c +C injection a} {injection a +C c} {c +C injection b} (+CCommutative {c} {injection a}) (Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {injection a +C c} {injection b +C c} {c +C injection b} (additionPreservedLeft {a} {b} {c} a=b) (+CCommutative {injection b} {c}))
additionPreservedRight {a} {b} {c} a=b = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {c +C injection a} {injection a +C c} {c +C injection b} (+CCommutative c (injection a)) (Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {injection a +C c} {injection b +C c} {c +C injection b} (additionPreservedLeft {a} {b} {c} a=b) (+CCommutative (injection b) c))
additionPreserved : {a b c d : A} → (a ∼ b) → (c ∼ d) → Setoid._∼_ cauchyCompletionSetoid (injection a +C injection c) (injection b +C injection d)
additionPreserved {a} {b} {c} {d} a=b c=d = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {injection a +C injection c} {injection a +C injection d} {injection b +C injection d} (additionPreservedRight {c} {d} {injection a} c=d) (additionPreservedLeft {a} {b} {injection d} a=b)
additionWellDefinedRight : (a b c : CauchyCompletion) → Setoid._∼_ cauchyCompletionSetoid b c → Setoid._∼_ cauchyCompletionSetoid (a +C b) (a +C c)
additionWellDefinedRight a b c b=c = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {a +C b} {b +C a} {a +C c} (+CCommutative {a} {b}) (Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {b +C a} {c +C a} {a +C c} (additionWellDefinedLeft b c a b=c) (+CCommutative {c} {a}))
additionWellDefinedRight a b c b=c = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {a +C b} {b +C a} {a +C c} (+CCommutative a b) (Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {b +C a} {c +C a} {a +C c} (additionWellDefinedLeft b c a b=c) (+CCommutative c a))
additionWellDefined : {a b c d : CauchyCompletion} → Setoid._∼_ cauchyCompletionSetoid a b → Setoid._∼_ cauchyCompletionSetoid c d → Setoid._∼_ cauchyCompletionSetoid (a +C c) (b +C d)
additionWellDefined {a} {b} {c} {d} a=b c=d = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {a +C c} {a +C d} {b +C d} (additionWellDefinedRight a c d c=d) (additionWellDefinedLeft a b d a=b)
@@ -88,7 +90,7 @@ private
ans {m} 0<m rewrite indexAndApply (CauchyCompletion.elts (a +C injection 0G)) (map inverse (CauchyCompletion.elts a)) _+_ {m} | indexAndApply (CauchyCompletion.elts a) (constSequence 0G) _+_ {m} | equalityCommutative (mapAndIndex (CauchyCompletion.elts a) inverse m) | indexAndConst 0G m = <WellDefined (Equivalence.symmetric eq (Equivalence.transitive eq (absWellDefined _ _ (Equivalence.transitive eq (+WellDefined (identRight) (Equivalence.reflexive eq)) (invRight))) (identityOfIndiscernablesRight _∼_ (Equivalence.reflexive eq) absZero))) (Equivalence.reflexive eq) 0<e
CidentLeft : {a : CauchyCompletion} → Setoid._∼_ cauchyCompletionSetoid (injection 0G +C a) a
CidentLeft {a} = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {injection 0G +C a} {a +C injection 0G} {a} (+CCommutative {injection 0G} {a}) (CidentRight {a})
CidentLeft {a} = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {injection 0G +C a} {a +C injection 0G} {a} (+CCommutative (injection 0G) a) (CidentRight {a})
CinvRight : {a : CauchyCompletion} → Setoid._∼_ cauchyCompletionSetoid (a +C (-C a)) (injection 0G)
CinvRight {a} ε 0<e = 0 , ans
@@ -103,7 +105,7 @@ Group.inverse CGroup = -C_
Group.+Associative CGroup {a} {b} {c} = Cassoc {a} {b} {c}
Group.identRight CGroup {a} = CidentRight {a}
Group.identLeft CGroup {a} = CidentLeft {a}
Group.invLeft CGroup {a} = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {(-C a) +C a} {a +C (-C a)} {injection 0G} (+CCommutative { -C a} {a}) (CinvRight {a})
Group.invLeft CGroup {a} = Equivalence.transitive (Setoid.eq cauchyCompletionSetoid) {(-C a) +C a} {a +C (-C a)} {injection 0G} (+CCommutative (-C a) a) (CinvRight {a})
Group.invRight CGroup {a} = CinvRight {a}
CInjectionGroupHom : GroupHom (Ring.additiveGroup R) CGroup injection