Update with new changes to Agda

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-03-03 16:44:10 -08:00
parent f00dabfc93
commit 2ddac38c3f
3 changed files with 18 additions and 7 deletions

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@ -1,7 +1,7 @@
module Isomorphism where
open import Agda.Primitive using (Level) renaming (_⊔_ to _⊔_)
open import Function.Definitions using (Inverseˡ; Inverseʳ; Injective)
open import Function.Definitions using (Injective)
open import Lattice
open import Equivalence
open import Relation.Binary.Core using (_Preserves_⟶_ )
@ -9,6 +9,16 @@ open import Data.Nat using ()
open import Data.Product using (_,_)
open import Relation.Nullary using (¬_)
IsInverseˡ : {a b} {A : Set a} {B : Set b}
(_≈₁_ : A A Set a) (_≈₂_ : B B Set b)
(f : A B) (g : B A) Set b
IsInverseˡ {A = A} {B = B} _≈₁_ _≈₂_ f g = (x : B) f (g x) ≈₂ x
IsInverseʳ : {a b} {A : Set a} {B : Set b}
(_≈₁_ : A A Set a) (_≈₂_ : B B Set b)
(f : A B) (g : B A) Set a
IsInverseʳ {A = A} {B = B} _≈₁_ _≈₂_ f g = (x : A) g (f x) ≈₁ x
module TransportFiniteHeight
{a b : Level} {A : Set a} {B : Set b}
{_≈₁_ : A A Set a} {_≈₂_ : B B Set b}
@ -20,7 +30,7 @@ module TransportFiniteHeight
(f-preserves-≈₁ : f Preserves _≈₁_ _≈₂_) (g-preserves-≈₂ : g Preserves _≈₂_ _≈₁_)
(f-⊔-distr : (a₁ a₂ : A) f (a₁ ⊔₁ a₂) ≈₂ ((f a₁) ⊔₂ (f a₂)))
(g-⊔-distr : (b₁ b₂ : B) g (b₁ ⊔₂ b₂) ≈₁ ((g b₁) ⊔₁ (g b₂)))
(inverseˡ : Inverseˡ _≈₁_ _≈₂_ f g) (inverseʳ : Inverseʳ _≈₁_ _≈₂_ f g) where
(inverseˡ : IsInverseˡ _≈₁_ _≈₂_ f g) (inverseʳ : IsInverseʳ _≈₁_ _≈₂_ f g) where
open IsFiniteHeightLattice fhlA using () renaming (_≺_ to _≺₁_; ≺-cong to ≺₁-cong; ≈-equiv to ≈₁-equiv)
open IsLattice lB using () renaming (_≺_ to _≺₂_; ≺-cong to ≺₂-cong; ≈-equiv to ≈₂-equiv)

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@ -27,6 +27,7 @@ open import Data.List.Properties using (∷-injectiveʳ)
open import Data.List.Relation.Unary.All using (All)
open import Data.List.Relation.Unary.Any using (Any; here; there)
open import Relation.Nullary using (¬_)
open import Isomorphism using (IsInverseˡ; IsInverseʳ)
open import Lattice.Map A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A lB
using
@ -105,8 +106,8 @@ module IterProdIsomorphism where
-- The left inverse is: from (to x) = x
from-to-inverseˡ : {ks : List A} (uks : Unique ks)
Inverseˡ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
(from {ks}) (to {ks} uks)
IsInverseˡ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
(from {ks}) (to {ks} uks)
from-to-inverseˡ {[]} _ _ = IsEquivalence.≈-refl (IP.≈-equiv 0)
from-to-inverseˡ {k ks'} (push k≢ks' uks') (v , rest)
with ((fm' , ufm') , refl) to uks' rest in p rewrite sym p =
@ -121,8 +122,8 @@ module IterProdIsomorphism where
--
-- The right inverse is: to (from x) = x
from-to-inverseʳ : {ks : List A} (uks : Unique ks)
Inverseʳ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
(from {ks}) (to {ks} uks)
IsInverseʳ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
(from {ks}) (to {ks} uks)
from-to-inverseʳ {[]} _ (([] , empty) , kvs≡ks) rewrite kvs≡ks =
( (λ k v ())
, (λ k v ())

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@ -168,7 +168,7 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
))
... | no a₁̷≈a | no b₁̷≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) =
((suc n₁ , suc n₂) , ( (step₁ (a₁≼a , a₁̷≈a) a≈a' c₁ , step₂ (b₁≼b , b₁̷≈b) b≈b' c₂)
, ≤-stepsˡ 1 (subst (n ≤_) (sym (+-suc n₁ n₂)) (+-monoʳ-≤ 1 n≤n₁+n₂))
, m≤n⇒m≤o+n 1 (subst (n ≤_) (sym (+-suc n₁ n₂)) (+-monoʳ-≤ 1 n≤n₁+n₂))
))
fixedHeight : IsLattice.FixedHeight isLattice (h₁ + h₂)